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+The Project Gutenberg EBook of Kinematics of Mechanisms from the Time of
+Watt, by Eugene S. Ferguson
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Kinematics of Mechanisms from the Time of Watt
+
+Author: Eugene S. Ferguson
+
+Release Date: October 31, 2008 [EBook #27106]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK KINEMATICS OF MECHANISMS ***
+
+
+
+
+Produced by Chris Curnow, Viv, Joseph Cooper and the Online
+Distributed Proofreading Team at http://www.pgdp.net
+
+
+
+
+
+[Transcriber's notes:
+
+1) Peaucillier is a printers error and has been changed to Peaucellier.
+
+2) The 4 characters at the end of the word 'Pafnutï[)i]' denote a letter
+'i' with a breve accent.]
+
+
+CONTRIBUTIONS FROM
+
+THE MUSEUM OF HISTORY AND TECHNOLOGY
+
+PAPER 27
+
+
+
+KINEMATICS OF MECHANISMS FROM THE TIME OF WATT
+
+_Eugene S. Ferguson_
+
+
+JAMES WATT, KINEMATIC SYNTHESIST      187
+
+TO DRAW A STRAIGHT LINE               199
+
+SCHOLARS AND MACHINES                 209
+
+MECHANICIANS AND MECHANISMS           216
+
+MECHANISMS IN AMERICA, 1875-1955      223
+
+ADDITIONAL REFERENCES                 229
+
+
+
+
+KINEMATICS OF MECHANISMS FROM THE TIME OF WATT
+
+
+_In an inventive tour de force that seldom, if ever, has been equalled
+for its brilliance and far-reaching consequences, James Watt radically
+altered the steam engine not only by adding a separate condenser but by
+creating a whole new family of linkages. His approach was largely
+empirical, as we use the word today._
+
+_This study suggests that, despite the glamor of today's sophisticated
+methods of calculation, a highly developed intuitive sense, reinforced
+by a knowledge of the past, is still indispensable to the design of
+successful mechanisms._
+
+THE AUTHOR: _Eugene S. Ferguson, formerly curator of mechanical and
+civil engineering in the United States National Museum, Smithsonian
+Institution, is now professor of mechanical engineering at Iowa State
+University of Science and Technology._
+
+In engineering schools today, a student is introduced to the kinematics
+of mechanisms by means of a course of kinematic analysis, which is
+concerned with principles underlying the motions occurring in
+mechanisms. These principles are demonstrated by a study of mechanisms
+already in existence, such as the linkage of a retractable landing gear,
+computing mechanisms, mechanisms used in an automobile, and the like. A
+systematic, if not rigorous, approach to the design of gears and cams
+also is usually presented in such a course. Until recently, however, no
+serious attempt was made to apply the principles developed in kinematic
+analysis to the more complex problem of kinematic synthesis of linkages.
+By kinematic synthesis is meant the designing of a linkage to produce a
+given series of motions for a particular purpose.
+
+That a rational--numerical or geometrical--approach to kinematic
+synthesis is possible is a relatively recent idea, not yet fully
+accepted; but it is this idea that is responsible for the intense
+scholarly interest in the kinematics of mechanisms that has occurred in
+this country within the last 10 years.
+
+This scholarly activity has resulted in the rediscovery of many earlier
+works on the subject, and nearly all the scholars now working in this
+field have acknowledged in one way or another their debt to those who
+arrived on the scene at an earlier time than they. There have been
+occasional reviews of the sequence and nature of developments, but the
+emphasis naturally has been upon the recent past. It seems to me that
+there is something to be gained in looking beyond our own generation, or
+even beyond the time of Franz Reuleaux (1829-1905), who is generally
+credited with originating many of our modern concepts of mechanism
+analysis and design, and to inquire into the ideas that made possible
+Reuleaux's contributions.
+
+     _Take to Kinematics. It will repay you. It is more fecund than
+     geometry; it adds a fourth dimension to space._
+
+     --Chebyshev to Sylvester, 1873
+
+While no pretense of completeness is made, I have tried in this paper to
+trace the high points in the development of kinematic analysis and
+synthesis, both in academic circles and in the workshop, noting where
+possible the influence of one upon the other. If I have devoted more
+space to particular people and episodes than is warranted by their
+contributions to the modern treatment of the subject, it is because I
+have found that the history of kinematics of mechanisms, like the
+history of any other branch of engineering, is more interesting and more
+plausible if it is recognized that its evolutionary development is the
+result of human activity. This history was wrought by people like us, no
+less intelligent and no less subject than we are to environment, to a
+subjective way of looking at things, and to a heritage of ideas and
+beliefs.
+
+I have selected the period from the time of Watt because modern
+mechanisms originated with him, and I have emphasized the first century
+of the period because by 1885 many of the ideas of modern kinematics of
+mechanisms were well developed. Linkages are discussed, to the virtual
+exclusion of gears and cams, because much of the scholarly work in
+kinematic synthesis is presently directed toward the design of linkages
+and because linkages provide a convenient thread for a narrative that
+would have become unnecessarily complex if detailed treatment of gears
+and cams had been included. I have brought the narrative down to the
+present by tracing kinematics as taught in American engineering
+schools, closing with brief mention of the scholarly activity in
+kinematics in this country since 1950. An annotated list of additional
+references is appended as an encouragement to further work in the
+history of the subject.
+
+
+James Watt, Kinematic Synthesist
+
+James Watt (1736-1819), improver of the steam engine, was a highly
+gifted designer of mechanisms, although his background included no
+formal study of mechanisms. Indeed, the study of mechanisms, without
+immediate regard to the machines in which they were used, was not
+introduced until after Watt's important work had been completed, while
+the actual design of mechanisms had been going on for several centuries
+before the time of Watt.
+
+Mechanisms that employed screws, cams, and gears were certainly in use
+by the beginning of the Christian era. While I am not aware of
+unequivocal evidence of the existence of four-bar linkages before the
+16th century, their widespread application by that time indicates that
+they probably originated much earlier. A tantalizing 13th-century sketch
+of an up-and-down sawmill (fig. 1) suggests, but does not prove, that
+the four-bar linkage was then in use. Leonardo da Vinci (1452-1519)
+delineated, if he did not build, a crank and slider mechanism, also for
+a sawmill (fig. 2). In the 16th century may be found the conversion of
+rotary to reciprocating motion (strictly speaking, an oscillation
+through a small arc of a large circle) and vice versa by use of linkages
+of rigid members (figs. 3 and 4), although the conversion of rotary to
+reciprocating motion was at that time more frequently accomplished by
+cams and intermittent gearing. Nevertheless, the idea of linkages was a
+firmly established part of the repertory of the machine builder before
+1600. In fact one might have wondered in 1588, when Agostino Ramelli
+published his book on machines,[1] whether linkages had not indeed
+reached their ultimate stage of development. To illustrate my point, I
+have selected the plate of Ramelli that most appeals to me (fig. 5),
+although the book exhibits more than 200 other machines of comparable
+complexity and ingenuity.
+
+[Footnote 1: Agostino Ramelli, _Le Diverse et Artificiose Machine_,
+Paris, 1588.]
+
+[Illustration: Figure 1.--Up-and-down sawmill of the 13th century. The
+guide mechanism at lower left, attached to the saw blade, appears to be
+a 4-bar linkage. After Robert Willis, trans. and ed., _Facsimile of the
+Sketch-Book of Wilars de Honecort_ (London, 1859, pl. 43).]
+
+[Illustration: Figure 2.--Slider-crank mechanism of Leonardo da Vinci
+(1452-1519), redrawn from his manuscript notebooks. A frame saw is
+depicted at the lower end of the guides. From Theodor Beck, _Beiträge
+zur Geschichte des Maschinenbaues_ (Berlin, 1899, p. 323).]
+
+[Illustration: Figure 3.--Blowing engine by Vanuccio Biringuccio, about
+1540, showing conversion of motion of the waterwheel shaft from rotation
+to oscillation. From Theodor Beck, _Beiträge zur Geschichte des
+Maschinenbaues_ (Berlin, 1899, p. 120).]
+
+[Illustration: Figure 4.--Grain mill, 1588, showing conversion of motion
+of the operating bars from oscillation to rotation. Note the
+fly-weights, predecessors of the flywheel. From Agostino Ramelli, _Le
+Diverse et Artificiose Machine_ (Paris, 1588, pl. opposite p. 199).]
+
+[Illustration: Figure 5.--Machine for raising water. Such a machine was
+built in Spain during the 16th century and was operated for some 80
+years. From Agostino Ramelli, _Le Diverse et Artificiose Machine_
+(Paris, 1588, p. 199).]
+
+There was a vast difference, both in conception and execution, between
+the linkages of Ramelli and those of James Watt some 200 years later.
+Watt was responsible for initiating profound changes in mechanical
+technology, but it should be recognized that the mechanic arts had,
+through centuries of slow development, reached the stage where his
+genius could flourish. The knowledge and ability to provide the
+materials and tools necessary for Watt's researches were at hand, and
+through the optimism and patient encouragement of his partner, Matthew
+Boulton, they were placed at his disposal.
+
+Watt's genius was nowhere more evident than in his synthesis of
+linkages. An essential ingredient in the success of Watt's linkages,
+however, was his partner's appreciation of the entirely new order of
+refinement that they called for. Matthew Boulton, who had been a
+successful manufacturer of buttons and metal novelties long before his
+partnership with Watt was formed, had recognized at once the need for
+care in the building of Watt's steam engine. On February 7, 1769, he had
+written Watt:[2] "I presumed that your engine would require money,
+very accurate workmanship and extensive correspondence to make it turn
+out to the best advantage and that the best means of keeping up the
+reputation and doing the invention justice would be to keep the
+executive part of it out of the hands of the multitude of empirical
+engineers, who from ignorance, want of experience and want of necessary
+convenience, would be very liable to produce bad and inaccurate
+workmanship; all of which deficiencies would affect the reputation of
+the invention." Boulton expected to build the engines in his shop "with
+as great a difference of accuracy as there is between the blacksmith and
+the mathematical instrument maker." The Soho Works of Boulton and Watt,
+in Birmingham, England, solved for Watt the problem of producing "in
+great" (that is, in sizes large enough to be useful in steam engines)
+the mechanisms that he devised.[3]
+
+[Footnote 2: Henry W. Dickinson, _James Watt, Craftsman & Engineer_,
+Cambridge, Cambridge University Press, 1936, pp. 52-53.]
+
+[Footnote 3: James P. Muirhead, _The Origin and Progress of the
+Mechanical Inventions of James Watt_, London, 1854, vol. 1, pp. 56, 64.
+This work, in three volumes, contains letters, other documents, and
+plates of patent specification drawings.]
+
+The contributions of Boulton and Watt to practical mechanics "in great"
+cannot be overestimated. There were in the 18th century instrument
+makers and makers of timekeepers who had produced astonishingly
+accurate work, but such work comprised relatively small items, all being
+within the scope of a bench lathe, hand tools, and superb handwork. The
+rapid advancement of machine tools, which greatly expanded the scope of
+the machine-building art, began during the Boulton and Watt partnership
+(1775-1800).
+
+In April 1775 the skirmish at Concord between American colonists and
+British redcoats marked the beginning of a war that was to determine for
+the future the course of political events in the Western Hemisphere.
+
+Another event of April 1775 occurring in Birmingham now appears to have
+been one that marked the beginning of a new era of technological
+advance. It was near the end of this month that Boulton, at the Soho
+Works, wrote to his partner and commented upon receiving the cast iron
+steam engine cylinder that had been finished in John Wilkinson's boring
+mill:
+
+     ... it seems tolerably true, but is an inch thick and weighs about
+     10 cwt. Its diameter is about as much above 18 inches as the tin
+     one was under, and therefore it is become necessary to add a brass
+     hoop to the piston, which is made almost two inches broad.[4]
+
+[Footnote 4: _Ibid._, vol. 2, p. 84.]
+
+This cylinder indeed marked the turning point in the discouragingly long
+development of the Watt steam engine, which for 10 years had occupied
+nearly all of Watt's thoughts and all the time he could spare from the
+requirements of earning a living. Although there were many trials ahead
+for the firm of Boulton and Watt in further developing and perfecting
+the steam engine, the crucial problem of leakage of steam past the
+piston in the cylinder had now been solved by Wilkinson's new boring
+mill, which was the first large machine tool capable of boring a
+cylinder both round and straight.
+
+The boring mill is pertinent to the development of linkages "in great,"
+being the first of a new class of machine tools that over the next 50 or
+60 years came to include nearly all of the basic types of heavy
+chip-removing tools that are in use today. The development of tools was
+accelerated by the inherent accuracy required of the linkages that were
+originated by Watt. Once it had been demonstrated that a large and
+complex machine, such as the steam engine, could be built accurately
+enough so that its operation would be relatively free of trouble, many
+outstanding minds became engaged in the development of machines and
+tools. It is interesting, however, to see how Watt and others grappled
+with the solutions of problems that resulted from the advance of the
+steam engine.
+
+During the 1770's the demand for continuous, dependable power applied to
+a rotating shaft was becoming insistent, and much of Boulton's and
+Watt's effort was directed toward meeting this demand. Mills of all
+kinds used water or horses to turn "wheel-work," but, while these
+sources of power were adequate for small operations, the quantity of
+water available was often limited, and the use of enormous horse-whims
+was frequently impracticable.
+
+The only type of steam engine then in existence was the Newcomen beam
+engine, which had been introduced in 1712 by Thomas Newcomen, also an
+Englishman. This type of engine was widely used, mostly for pumping
+water out of mines but occasionally for pumping water into a reservoir
+to supply a waterwheel. It was arranged with a vertical steam cylinder
+located beneath one end of a large pivoted working beam and a vertical
+plunger-type pump beneath the other end. Heavy, flat chains were secured
+to a sector at each end of the working beam and to the engine and pump
+piston rods in such a way that the rods were always tangent to a circle
+whose center was at the beam pivot. The weight of the reciprocating pump
+parts pulled the pump end of the beam down; the atmosphere, acting on
+the open top of the piston in the steam cylinder, caused the engine end
+of the beam to be pulled down when the steam beneath the piston was
+condensed. The chains would of course transmit force from piston to beam
+only in tension.
+
+It is now obvious that a connecting rod, a crank, and a sufficiently
+heavy flywheel might have been used in a conventional Newcomen engine in
+order to supply power to a rotating shaft, but contemporary evidence
+makes it clear that this solution was by no means obvious to Watt nor to
+his contemporaries.
+
+At the time of his first engine patent, in 1769, Watt had devised a
+"steam wheel," or rotary engine, that used liquid mercury in the lower
+part of a toroidal chamber to provide a boundary for steam spaces
+successively formed by flap gates within the chamber. The practical
+difficulties of construction finally ruled out this solution to the
+problem of a rotating power source, but not until after Boulton and
+Watt had spent considerable effort and money on it.[5]
+
+[Footnote 5: Henry W. Dickinson and Rhys Jenkins, _James Watt and the
+Steam Engine_, Oxford, Clarendon Press, 1927, pp. 146-148, pls. 14, 31.
+This work presents a full and knowledgeable discussion, based on primary
+material, of the development of Watt's many contributions to mechanical
+technology. It is ably summarized in Dickinson, _op. cit._ (footnote
+2).]
+
+In 1777 a speaker before the Royal Society in London observed that in
+order to obtain rotary output from a reciprocating steam engine, a crank
+"naturally occurs in theory," but that in fact the crank is impractical
+because of the irregular rate of going of the engine and its variable
+length of stroke. He said that on the first variation of length of
+stroke the machine would be "either broken to pieces, or turned
+back."[6] John Smeaton, in the front rank of English steam engineers of
+his time, was asked in 1781 by His Majesty's Victualling-Office for his
+opinion as to whether a steam-powered grain mill ought to be driven by a
+crank or by a waterwheel supplied by a pump. Smeaton's conclusion was
+that the crank was quite unsuited to a machine in which regularity of
+operation was a factor. "I apprehend," he wrote, "that no motion
+communicated from the reciprocating beam of a fire engine can ever act
+perfectly equal and steady in producing a circular motion, like the
+regular efflux of water in turning a waterwheel." He recommended,
+incidentally, that a Boulton and Watt steam engine be used to pump water
+to supply the waterwheel.[7] Smeaton had thought of a flywheel, but he
+reasoned that a flywheel large enough to smooth out the halting, jerky
+operation of the steam engines that he had observed would be more of an
+encumbrance than a pump, reservoir, and waterwheel.[8]
+
+[Footnote 6: John Farey, _A Treatise on the Steam Engine_, London, 1827,
+pp. 408-409.]
+
+[Footnote 7: _Reports of the Late John Smeaton, F.R.S._, London, 1812,
+vol. 2, pp. 378-380.]
+
+[Footnote 8: Farey, _op. cit._ (footnote 6), p. 409.]
+
+The simplicity of the eventual solution of the problem was not clear to
+Watt at this time. He was not, as tradition has it, blocked merely by
+the existence of a patent for a simple crank and thus forced to invent
+some other device as a substitute.
+
+Matthew Wasbrough, of Bristol, the engineer commonly credited with the
+crank patent, made no mention of a crank in his patent specification,
+but rather intended to make use of "racks with teeth," or "one or more
+pullies, wheels, segments of wheels, to which are fastened rotchets and
+clicks or palls...." He did, however, propose to "add a fly or flys, in
+order to render the motion more regular and uniform." Unfortunately for
+us, he submitted no drawings with his patent specification.[9]
+
+[Footnote 9: British Patent 1213, March 10, 1779.]
+
+James Pickard, of Birmingham, like Boulton, a buttonmaker, in 1780
+patented a counterweighted crank device (fig. 6) that was expected to
+remove the objection to a crank, which operated with changing leverage
+and thus irregular power. In figure 6, the counterweighted wheel,
+revolving twice for each revolution of the crank (A), would allow the
+counterweight to descend while the crank passed the dead-center position
+and would be raised while the crank had maximum leverage. No mention of
+a flywheel was made in this patent.[10]
+
+[Footnote 10: British Patent 1263, August 23, 1780.]
+
+[Illustration: Figure 6.--One of the steam engine "Crank Patents" that
+hindered James Watt's progress. This patent, granted to James Pickard in
+1780, claimed only the arrangement of counterweights, not the crank. The
+crank pin to which the connecting rod was attached is at _Aa_. From
+British Patent 1263, August 23, 1780.]
+
+Wasbrough, finding that his "rotchets and clicks" did not serve,
+actually used, in 1780, a crank with a flywheel. Watt was aware of this,
+but he remained unconvinced of the superiority of the crank over other
+devices and did not immediately appreciate the regulating ability of a
+flywheel.[11] In April 1781 Watt wrote to Boulton, who was then out of
+town: "I know from experiment that the other contrivance, which you saw
+me try, performs at least as well, and has in fact many advantages over
+the crank."[12] The "other contrivance" probably was his swash wheel
+which he built and which appeared on his next important patent
+specification (fig. 7a). Also in this patent were four other devices,
+one of which was easily recognizable as a crank, and two of which were
+eccentrics (fig. 7a, b). The fourth device was the well-known
+sun-and-planet gearing (fig. 7e).[13] In spite of the similarity of the
+simple crank to the several variations devised by Watt, this patent drew
+no fire from Wasbrough or Pickard, perhaps because no reasonable person
+would contend that the crank itself was a patentable feature, or perhaps
+because the similarity was not at that time so obvious. However, Watt
+steered clear of directly discernible application of cranks because he
+preferred to avoid a suit that might overthrow his or other patents. For
+example, if the Wasbrough and Pickard patents had been voided, they
+would have become public property; and Watt feared that they might
+"get into the hands of men more ingenious," who would give Boulton and
+Watt more competition than Wasbrough and Pickard.[14]
+
+[Footnote 11: Dickinson and Jenkins, _op. cit._ (footnote 5), pp. 150,
+154.]
+
+[Footnote 12: _Ibid._, p. 154.]
+
+[Footnote 13: William Murdock, at this time a Boulton and Watt erector,
+may have suggested this arrangement. _Ibid._, p. 56.]
+
+[Footnote 14: Muirhead, _op. cit._ (footnote 3), vol. 3, note on p. 39.]
+
+[Illustration: Figure 7.--James Watt's five alternative devices for the
+conversion of reciprocating motion to rotary motion in a steam engine.
+(British Patent 1306, October 25, 1781). From James P. Muirhead, _The
+Origin and Progress of the Mechanical Inventions of James Watt_ (London,
+1854, vol. 3, pls. 3-5, 7).]
+
+[Illustration: (a) "Inclined wheel." The vertical shaft at _D_ is
+rotated by action of wheels _H_ and _J_ on cam, or swash plate, _ABC_.
+Boulton and Watt tried this device but discarded it.]
+
+[Illustration: (b) Counterweighted crank wheel.]
+
+[Illustration: (c) "Eccentric wheel" with external yoke hung from
+working beam. The wheel pivots at _C_.]
+
+[Illustration: (d) "Eccentric wheel" with internal driving wheel hung
+from working beam. Wheel _B_ is pivoted at center of shaft _A_.]
+
+[Illustration: (e) Sun-and-planet gearing. This is the idea actually
+employed in Boulton and Watt engines. As the optional link _JK_ held the
+gearwheel centers always equidistant, the annular guide _G_ was not
+used.]
+
+The sun-and-planet arrangement, with gears of equal size, was adopted by
+Watt for nearly all the rotative engines that he built during the term
+of the "crank patents." This arrangement had the advantage of turning
+the flywheel through two revolutions during a single cycle of operation
+of the piston, thus requiring a flywheel only one-fourth the size of the
+flywheel needed if a simple crank were used. The optional link (JK of
+fig. 7e) was used in the engines as built.
+
+From the first, the rotative engines were made double-acting--that is,
+work was done by steam alternately in each end of the cylinder. The
+double-acting engine, unlike the single-acting pumping engine, required
+a piston rod that would push as well as pull. It was in the solution of
+this problem that Watt's originality and sure judgment were most clearly
+demonstrated.
+
+A rack and sector arrangement (fig. 8) was used on some engines. The
+first one, according to Watt, "has broke out several teeth of the rack,
+but works steady."[15] A little later he told a correspondent that his
+double-acting engine "acts so powerfully that it has broken all its
+tackling repeatedly. We have now tamed it, however."[16]
+
+[Footnote 15: James Watt, March 31, 1783, quoted in Dickinson and
+Jenkins, _op. cit._ (footnote 5), p. 140.]
+
+[Footnote 16: Watt to De Luc, April 26, 1783, quoted in Muirhead, _op.
+cit._ (footnote 3), vol. 2, p. 174.]
+
+[Illustration: Figure 8.--Watt engine of 1782 (British Patent 1321,
+March 12, 1782) showing the rack and sector used to guide the upper end
+of the piston rod and to transmit force from piston to working beam.
+This engine, with a 30-inch cylinder and an 8-foot stroke, was arranged
+for pumping. Pump rod _SS_ is hung from sector of the working beam. From
+James P. Muirhead, _The Origin and Progress of the Mechanical Inventions
+of James Watt_ (London, 1854, vol. 3, pl. 15).]
+
+It was about a year later that the straight-line linkage[17] was thought
+out. "I have started a new hare," Watt wrote to his partner. "I have
+got a glimpse of a method of causing the piston-rod to move up and down
+perpendicularly, by only fixing it to a piece of iron upon the beam,
+without chains, or perpendicular guides, or untowardly frictions,
+arch-heads, or other pieces of clumsiness.... I have only tried it in a
+slight model yet, so cannot build upon it, though I think it a very
+probable thing to succeed, and one of the most ingenious simple pieces
+of mechanism I have contrived...."[18]
+
+[Footnote 17: Watt's was a four-bar linkage. All four-bar straight-line
+linkages that have no sliding pairs trace only an approximately straight
+line. The exact straight-line linkage in a single plane was not known
+until 1864 (see p. 204). In 1853 Pierre-Frédéric Sarrus (1798-1861), a
+French professor of mathematics at Strasbourg, devised an accordion-like
+spatial linkage that traced a true straight line. Described but not
+illustrated (Académie des Sciences, Paris, _Comptes rendus_, 1853, vol.
+36, pp. 1036-1038, 1125), the mechanism was forgotten and twice
+reinvented; finally, the original invention was rediscovered by an
+English writer in 1905. For chronology, see Florian Cajori, _A History
+of Mathematics_, ed. 2, New York, 1919, p. 301.]
+
+[Footnote 18: Muirhead, _op. cit._ (footnote 3), vol. 2, pp. 191-192.]
+
+Watt's marvelously simple straight-line linkage was incorporated into a
+large beam engine almost immediately, and the usually pessimistic and
+reserved inventor was close to a state of elation when he told Boulton
+that the "new central perpendicular motion answers beyond expectation,
+and does not make the shadow of a noise."[19] This linkage, which was
+included in an extensive patent of 1784, and two alternative devices are
+illustrated here (fig. 9). One of the alternatives is a guided crosshead
+(fig. 9, top right).
+
+[Footnote 19: _Ibid._, p. 202.]
+
+[Illustration: Figure 9.--Watt's mechanisms for guiding the upper end of
+the piston rod of a double-acting engine (British Patent 1432, April 28,
+1784). _Top left_, straight-line linkage; _top right_, crosshead and
+guide arrangement; _lower left_, piston rod _A_ is guided by sectors _D_
+and _E_, suspended by flexible cords. From James P. Muirhead, _The
+Origin and Progress of the Mechanical Inventions of James Watt_ (London,
+1854, vol. 3, pls. 21, 22).]
+
+Brilliant as was the conception of this linkage, it was followed up by a
+synthesis that is very little short of incredible. In order to make the
+linkage attached to the beam of his engines more compact, Watt had
+plumbed his experience for ideas; his experience had yielded up the work
+done much earlier on a drafting machine that made use of a
+pantograph.[20] Watt combined his straight-line linkage with a
+pantograph, one link becoming a member of the pantograph.
+
+[Footnote 20: "It has only one fault," he had told a friend on December
+24, 1773, after describing the drafting machine to him, "which is, that
+it will not do, because it describes conic sections instead of straight
+lines." _Ibid._, p. 71.]
+
+The length of each oscillating link of the straight-line linkage was
+thus reduced to one-fourth instead of one-half the beam length, and the
+entire mechanism could be constructed so that it would not extend
+beyond the end of the working beam. This arrangement soon came to be
+known as Watt's "parallel motion" (fig. 10).[21] Years later Watt told
+his son: "Though I am not over anxious after fame, yet I am more proud
+of the parallel motion than of any other mechanical invention I have
+ever made."[22]
+
+[Footnote 21: Throughout the 19th century the term "parallel motion" was
+used indiscriminately to refer to any straight-line linkage. I have not
+discovered the origin of the term. Watt did not use it in his patent
+specification, and I have not found it in his writings or elsewhere
+before 1808 (see footnote 22). _The Cyclopaedia_ (Abraham Rees, ed.,
+London, 1819, vol. 26) defined parallel motion as "a term used among
+practical mechanics to denote the rectilinear motion of a piston-rod,
+&c. in the direction of its length; and contrivances, by which such
+alternate rectilinear motions are converted into continuous rotatory
+ones, or _vice versa_...." Robert Willis in his _Principles of
+Mechanism_ (London, 1841, p. 399) described parallel motion as "a term
+somewhat awkwardly applied to a combination of jointed rods, the purpose
+of which is to cause a point to describe a straight line...." A. B.
+Kempe in _How to Draw a Straight Line_ (London, 1877, p. 49) wrote: "I
+have been more than once asked to get rid of the objectionable term
+'parallel motion.' I do not know how it came to be employed, and it
+certainly does not express what is intended. The expression, however,
+has now become crystallised, and I for one cannot undertake to find a
+solvent."]
+
+[Footnote 22: Muirhead, _op. cit._ (footnote 3), vol. 3, note on p. 89.]
+
+[Illustration: Figure 10.--Watt's "parallel motion." Engine's working
+beam is pivoted at _A_. Pivot _F_ is attached to the engine frame. From
+Dyonysius Lardner, _The Steam Engine_ (Philadelphia, 1852), pl. 5
+(American ed. 5 from London ed. 5).]
+
+The Watt four-bar linkage was employed 75 years after its inception by
+the American Charles B. Richards when, in 1861, he designed his first
+high-speed engine indicator (fig. 11). Introduced into England the
+following year, the Richards Indicator was an immediate success, and
+many thousands were sold over the next 20 or 30 years.[23]
+
+[Footnote 23: Charles T. Porter, _Engineering Reminiscences_, New York,
+1908, pp. 58-59, 90.]
+
+[Illustration: Figure 11.--Richards high-speed engine indicator of 1861,
+showing application of the Watt straight-line linkage. (_USNM 307515_;
+_Smithsonian photo 46570_).]
+
+In considering the order of synthetic ability required to design the
+straight-line linkage and to combine it with a pantograph, it should be
+kept in mind that this was the first one of a long line of such
+mechanisms.[24] Once the idea was abroad, it was only to be expected
+that many variations and alternative solutions should appear. One
+wonders, however, what direction the subsequent work would have taken
+if Watt had not so clearly pointed the way.
+
+[Footnote 24: At least one earlier straight-line linkage, an arrangement
+later ascribed to Richard Roberts, had been depicted before Watt's
+patent (Pierre Patte, _Mémoirs sur les objets les plus importants de
+l'architecture_, Paris, 1769, p. 229 and pl. 11). However, this linkage
+(reproduced here in figure 18) had no detectable influence on Watt or on
+subsequent practice.]
+
+In 1827 John Farey, in his exhaustive study of the steam engine, wrote
+perhaps the best contemporary view of Watt's work. Farey as a young man
+had several times talked with the aging Watt, and he had reflected upon
+the nature of the intellect that had caused Watt to be recognized as a
+genius, even within his own lifetime. In attempting to explain Watt's
+genius, Farey set down some observations that are pertinent not only to
+kinematic synthesis but to the currently fashionable term "creativity."
+
+In Farey's opinion Watt's inventive faculty was far superior to that of
+any of his contemporaries; but his many and various ideas would have
+been of little use if he had not possessed a very high order of
+judgment, that "faculty of distinguishing between ideas; decomposing
+compound ideas into more simple elements; arranging them into classes,
+and comparing them together...."
+
+Farey was of the opinion that while a mind like Watt's could produce
+brilliant new ideas, still the "common stock of ideas which are current
+amongst communities and professions, will generally prove to be of a
+better quality than the average of those new ideas, which can be
+produced by any individual from the operation of his own mind, without
+assistance from others." Farey concluded with the observation that "the
+most useful additions to that common stock, usually proceed from the
+individuals who are well acquainted with the whole series."[25]
+
+[Footnote 25: Farey, _op. cit._ (footnote 6), pp. 651, 652.]
+
+
+To Draw a Straight Line
+
+During most of the century after James Watt had produced his parallel
+motion, the problem of devising a linkage, one point of which would
+describe a straight line, was one that tickled the fancies of
+mathematicians, of ingenious mechanics, and of gentlemanly dabblers in
+ideas. The quest for a straight-line mechanism more accurate than that
+of Watt far outlasted the pressing practical need for such a device.
+Large metal planing machines were well known by 1830, and by midcentury
+crossheads and crosshead guides were used on both sides of the Atlantic
+in engines with and without working beams.
+
+By 1819 John Farey had observed quite accurately that, in England at
+least, many other schemes had been tried and found wanting and that "no
+methods have been found so good as the original engine; and we
+accordingly find, that all the most established and experienced
+manufacturers make engines which are not altered in any great feature
+from Mr. Watt's original engine...."[26]
+
+[Footnote 26: In Rees, _op. cit._ (footnote 21), vol. 34 ("Steam
+Engine"). John Farey was the writer of this article (see Farey, _op.
+cit._, p. vi).]
+
+Two mechanisms for producing a straight line were introduced before the
+Boulton and Watt monopoly ended in 1800. Perhaps the first was by Edmund
+Cartwright (1743-1823), who is said to have had the original idea for a
+power loom. This geared device (fig. 12), was characterized
+patronizingly by a contemporary American editor as possessing "as much
+merit as can possibly be attributed to a gentleman engaged in the
+pursuit of mechanical studies for his own amusement."[27] Only a few
+small engines were made under the patent.[28]
+
+[Footnote 27: _Emporium of Arts and Sciences_, December 1813, new ser.,
+vol. 2, no. 1, p. 81.]
+
+[Footnote 28: Farey, _op. cit._ (footnote 6), p. 666.]
+
+[Illustration: Figure 12.--Cartwright's geared straight-line mechanism
+of about 1800. From Abraham Rees, _The Cyclopaedia_ (London, 1819,
+"Steam Engine," pl. 5).]
+
+The properties of a hypocycloid were recognized by James White, an
+English engineer, in his geared design which employed a pivot located on
+the pitch circle of a spur gear revolving inside an internal gear. The
+diameter of the pitch circle of the spur gear was one-half that of the
+internal gear, with the result that the pivot, to which the piston rod
+was connected, traced out a diameter of the large pitch circle (fig.
+13). White in 1801 received from Napoleon Bonaparte a medal for this
+invention when it was exhibited at an industrial exposition in
+Paris.[29] Some steam engines employing White's mechanism were built,
+but without conspicuous commercial success. White himself rather agreed
+that while his invention was "allowed to possess curious properties, and
+to be a _pretty_ thing, opinions do not all concur in declaring it,
+essentially and generally, a _good_ thing."[30]
+
+[Footnote 29: H. W. Dickinson, "James White and His 'New Century of
+Inventions,'" _Transactions of the Newcomen Society_, 1949-1951, vol.
+27, pp. 175-179.]
+
+[Footnote 30: James White, _A New Century of Inventions_, Manchester,
+1822, pp. 30-31, 338. A hypocycloidal engine used in Stourbridge,
+England, is in the Henry Ford Museum.]
+
+[Illustration: Figure 13.--James White's hypocycloidal straight-line
+mechanism, about 1800. The fly-weights (at the ends of the diagonal arm)
+functioned as a flywheel. From James White, _A New Century of
+Inventions_ (Manchester, 1822, pl. 7).]
+
+The first of the non-Watt four-bar linkages appeared shortly after 1800.
+The origin of the grasshopper beam motion is somewhat obscure, although
+it came to be associated with the name of Oliver Evans, the American
+pioneer in the employment of high-pressure steam. A similar idea,
+employing an isosceles linkage, was patented in 1803 by William
+Freemantle, an English watchmaker (fig. 14).[31] This is the linkage
+that was attributed much later to John Scott Russell (1808-1882), the
+prominent naval architect.[32] An inconclusive hint that Evans had
+devised his straight-line linkage by 1805 appeared in a plate
+illustrating his _Abortion of the Young Steam Engineer's Guide_
+(Philadelphia, 1805), and it was certainly used on his Columbian engine
+(fig. 15), which was built before 1813. The Freemantle linkage, in
+modified form, appeared in Rees's _Cyclopaedia_ of 1819 (fig. 16), but
+it is doubtful whether even this would have been readily recognized as
+identical with the Evans linkage, because the connecting rod was at the
+opposite end of the working beam from the piston rod, in accordance with
+established usage, while in the Evans linkage the crank and connecting
+rod were at the same end of the beam. It is possible that Evans got his
+idea from an earlier English periodical, but concrete evidence is
+lacking.
+
+[Footnote 31: British Patent 2741, November 17, 1803.]
+
+[Footnote 32: William J. M. Rankine, _Manual of Machinery and Millwork_,
+ed. 6, London, 1887, p. 275.]
+
+[Illustration: Figure 14.--Freemantle straight-line linkage, later
+called the Scott Russell linkage. From British Patent 2741, November 17,
+1803.]
+
+[Illustration: Figure 15.--Oliver Evans' "Columbian" engine, 1813,
+showing the Evans, or "grasshopper," straight-line linkage. From
+_Emporium of Arts and Sciences_ (new ser., vol. 2, no. 3, April 1814,
+pl. opposite p. 380).]
+
+[Illustration: Figure 16.--Modified Freemantle linkage, 1819, which is
+kinematically the same as the Evans linkage. Pivots _D_ and _E_ are
+attached to engine frame. From Abraham Rees, _The Cyclopaedia_ (London,
+1819, "Parallel Motions," pl. 3).]
+
+If the idea did in fact originate with Evans, it is strange that he did
+not mention it in his patent claims, or in the descriptions that he
+published of his engines.[33] The practical advantage of the Evans
+linkage, utilizing as it could a much lighter working beam than the Watt
+or Freemantle engines, would not escape Oliver Evans, and he was not a
+man of excessive modesty where his own inventions were concerned.
+
+[Footnote 33: Greville and Dorothy Bathe, _Oliver Evans_, Philadelphia,
+1935, pp. 88, 196, and _passim_.]
+
+Another four-bar straight-line linkage that became well known was
+attributed to Richard Roberts of Manchester (1789-1864), who around 1820
+had built one of the first metal planing machines, which machines helped
+make the quest for straight-line linkages largely academic. I have not
+discovered what occasioned the introduction of the Roberts linkage, but
+it dated from before 1841. Although Roberts patented many complex
+textile machines, an inspection of all of his patent drawings has failed
+to provide proof that he was the inventor of the Roberts linkage.[34]
+The fact that the same linkage is shown in an engraving of 1769 (fig.
+18) further confuses the issue.[35]
+
+[Footnote 34: Robert Willis (_op. cit._ [Footnote 21] p. 411) credited
+Richard Roberts with the linkage. Roberts' 15 British patent drawings
+exhibit complex applications of cams, levers, guided rods, cords, and so
+forth, but no straight-line mechanism. In his patent no. 6258 of April
+13, 1832, for a steam engine and locomotive carriage, Roberts used
+Watt's "parallel motion" on a beam driven by a vertical cylinder.]
+
+[Footnote 35: This engraving appeared as plate 11 in Pierre Patte's 1769
+work (_op. cit._ footnote 24). Patte stated that the machine depicted in
+his plate 11 was invented by M. de Voglie and was actually used in
+1756.]
+
+[Illustration: Figure 17.--Straight-line linkage (before 1841)
+attributed to Richard Roberts by Robert Willis. From A. B. Kempe, _How
+to Draw a Straight Line_ (London, 1877, p. 10).]
+
+[Illustration: Figure 18.--Machine for sawing off pilings under water,
+about 1760, designed by De Voglie. The Roberts linkage operates the bar
+(_Q_ in detailed sketch) at the rear of the machine below the operators.
+The significance of the linkage apparently was not generally recognized.
+A similar machine depicted in Diderot's _Encyclopédie_, published
+several years later, did not employ the straight-line linkage. From
+Pierre Patte, _Memoirs sur les objets plus importants de l'architecture_
+(Paris, 1769, pl. 11).]
+
+The appearance in 1864 of Peaucellier's exact straight-line linkage went
+nearly unnoticed. A decade later, when news of its invention crossed
+the Channel to England, this linkage excited a flurry of interest, and
+variations of it occupied mathematical minds for several years. For at
+least 10 years before and 20 years after the final solution of the
+problem, Professor Chebyshev,[36] a noted mathematician of the
+University of St. Petersburg, was interested in the matter. Judging by
+his published works and his reputation abroad, Chebyshev's interest
+amounted to an obsession.
+
+[Footnote 36: This is the Library of Congress spelling]
+
+Pafnutï[)i] L'vovich Chebyshev was born in 1821, near Moscow, and
+entered the University of Moscow in 1837. In 1853, after visiting France
+and England and observing carefully the progress of applied mechanics in
+those countries, he read his first paper on approximate straight-line
+linkages, and over the next 30 years he attacked the problem with new
+vigor at least a dozen times. He found that the two principal
+straight-line linkages then in use were Watt's and Evans'. Chebyshev
+noted the departure of these linkages from a straight line and
+calculated the deviation as of the fifth degree, or about 0.0008 inch
+per inch of beam length. He proposed a modification of the Watt linkage
+to refine its accuracy but found that he would have to more than double
+the length of the working beam. Chebyshev concluded ruefully that his
+modification would "present great practical difficulties."[37]
+
+[Footnote 37: _Oeuvres de P. L. Tchebychef_, 2 vols., St. Petersburg,
+1899-1907, vol. 1, p. 538; vol. 2, pp. 57, 85.]
+
+At length an idea occurred to Chebyshev that would enable him to
+approach if not quite attain a true straight line. If one mechanism was
+good, he reasoned, two would be better, _et cetera, ad infinitum_. The
+idea was simply to combine, or compound, four-link approximate linkages,
+arranging them in such a way that the errors would be successively
+reduced. Contemplating first a combination of the Watt and Evans
+linkages (fig. 19), Chebyshev recognized that if point D of the Watt
+linkage followed nearly a straight line, point A of the Evans linkage
+would depart even less from a straight line. He calculated the deviation
+in this case as of the 11th degree. He then replaced Watt's linkage by
+one that is usually called the Chebyshev straight-line mechanism (fig.
+20), with the result that precision was increased to the 13th
+degree.[38] The steam engine that he displayed at the Vienna Exhibition
+in 1873 employed this linkage--the Chebyshev mechanism compounded with
+the Evans, or approximate isosceles, linkage. An English visitor to the
+exhibition commented that "the motion is of little or no practical use,
+for we can scarcely imagine circumstances under which it would be more
+advantageous to use such a complicated system of levers, with so many
+joints to be lubricated and so many pins to wear, than a solid guide of
+some kind; but at the same time the arrangement is very ingenious and in
+this respect reflects great credit on its designer."[39]
+
+[Footnote 38: _Ibid._, vol. 2, pp. 93, 94.]
+
+[Footnote 39: _Engineering_, October 3, 1873, vol. 16, p. 284.]
+
+[Illustration: Figure 19.--Pafnutï[)i] L'vovich Chebyshev (1821-1894),
+Russian mathematician active in analysis and synthesis of straight-line
+mechanisms. From _Ouvres de P. L. Tchebychef_ (St. Petersburg, 1907,
+vol. 2, frontispiece).]
+
+[Illustration: Figure 20.--Chebyshev's combination (about 1867) of
+Watt's and Evans' linkages to reduce errors inherent in each. Points
+_C_, _C'_, and _C"_ are fixed; _A_ is the tracing point. From _Oeuvres
+de P. L. Tchebychef_ (St. Petersburg, 1907, vol. 2, p. 93).]
+
+[Illustration: Figure 21.--_Top_: Chebyshev straight-line linkage, 1867;
+from A. B. Kempe, _How to Draw a Straight Line_ (London, 1877, p. 11).
+_Bottom_: Chebyshev-Evans combination, 1867; from _Oeuvres de P. L.
+Tchebychef_ (St. Petersburg, 1907, vol. 2, p. 94). Points _C_, _C'_, and
+_C"_ are fixed. _A_ is the tracing point.]
+
+There is a persistent rumor that Professor Chebyshev sought to
+demonstrate the impossibility of constructing any linkage, regardless of
+the number of links, that would generate a straight line; but I have
+found only a dubious statement in the _Grande Encyclopédie_[40] of the
+late 19th century and a report of a conversation with the Russian by an
+Englishman, James Sylvester, to the effect that Chebyshev had "succeeded
+in proving the nonexistence of a five-bar link-work capable of producing
+a perfect parallel motion...."[41] Regardless of what tradition may have
+to say about what Chebyshev said, it is of course well known that
+Captain Peaucellier was the man who finally synthesized the exact
+straight-line mechanism that bears his name.
+
+[Footnote 40: _La Grande Encyclopédie_, Paris, 1886 ("Peaucellier").]
+
+[Footnote 41: James Sylvester, "Recent Discoveries in Mechanical
+Conversion of Motion," _Notices of the Proceedings of the Royal
+Institution of Great Britain_, 1873-1875, vol. 7, p. 181. The fixed link
+was not counted by Sylvester; in modern parlance this would be a
+six-link mechanism.]
+
+[Illustration: Figure 22.--Peaucellier exact straight-line linkage,
+1873. From A. B. Kempe, _How to Draw a Straight Line_ (London, 1877, p.
+12).]
+
+[Illustration: Figure 23.--Model of the Peaucellier "Compas Composé,"
+deposited in Conservatoire National des Arts et Métiers, Paris, 1875.
+Photo courtesy of the Conservatoire.] [Illustration: Figure 24.--James
+Joseph Sylvester (1814-1897), mathematician and lecturer on
+straight-line linkages. From _Proceedings of the Royal Society of
+London_ (1898, vol. 63, opposite p. 161).]
+
+Charles-Nicolas Peaucellier, a graduate of the Ecole Polytechnique and a
+captain in the French corps of engineers, was 32 years old in 1864 when
+he wrote a short letter to the editor of _Nouvelles Annales de
+mathématiques_ (ser. 2, vol. 3, pp. 414-415) in Paris. He called
+attention to what he termed "compound compasses," a class of linkages
+that included Watt's parallel motion, the pantograph, and the polar
+planimeter. He proposed to design linkages to describe a straight line,
+a circle of any radius no matter how large, and conic sections, and he
+indicated in his letter that he had arrived at a solution.
+
+This letter stirred no pens in reply, and during the next 10 years the
+problem merely led to the filling of a few academic pages by Peaucellier
+and Amédée Mannheim (1831-1906), also a graduate of Ecole Polytechnique,
+a professor of mathematics, and the designer of the Mannheim slide rule.
+Finally, in 1873, Captain Peaucellier gave his solution to the readers
+of the _Nouvelles Annales_. His reasoning, which has a distinct flavor
+of discovery by hindsight, was that since a linkage generates a curve
+that can be expressed algebraically, it must follow that any algebraic
+curve can be generated by a suitable linkage--it was only necessary to
+find the suitable linkage. He then gave a neat geometric proof,
+suggested by Mannheim, for his straight-line "compound compass."[42]
+
+[Footnote 42: Charles-Nicholas Peaucellier, "Note sur une question de
+geométrie de compas," _Nouvelles Annales de mathématiques_, 1873, ser.
+2, vol. 12, pp. 71-78. A sketch of Mannheim's work is in Florian Cajori,
+_A History of the Logarithmic Slide Rule_, New York, about 1910,
+reprinted in _String Figures and Other Monographs_, New York, Chelsea
+Publishing Company, 1960.]
+
+On a Friday evening in January 1874 Albemarle Street in London was
+filled with carriages, each maneuvering to unload its charge of
+gentlemen and their ladies at the door of the venerable hall of the
+Royal Institution. Amidst a "mighty rustling of silks," the elegant
+crowd made its way to the auditorium for one of the famous weekly
+lectures. The speaker on this occasion was James Joseph Sylvester, a
+small intense man with an enormous head, sometime professor of
+mathematics at the University of Virginia, in America, and more recently
+at the Royal Military Academy in Woolwich. He spoke from the same
+rostrum that had been occupied by Davy, Faraday, Tyndall, Maxwell, and
+many other notable scientists. Professor Sylvester's subject was "Recent
+Discoveries in Mechanical Conversion of Motion."[43]
+
+[Footnote 43: Sylvester, _op. cit._ (footnote 41), pp. 179-198. It
+appears from a comment in this lecture that Sylvester was responsible
+for the word "linkage." According to Sylvester, a linkage consists of an
+even number of links, a "link-work" of an odd number. Since the fixed
+member was not considered as a link by Sylvester, this distinction
+became utterly confusing when Reuleaux's work was published in 1876.
+Although "link" was used by Watt in a patent specification, it is not
+probable that he ever used the term "link-work"--at any rate, my search
+for his use of it has been fruitless. "Link work" is used by Willis
+(_op. cit._ footnote 21), but the term most likely did not originate
+with him. I have not found the word "linkage" used earlier than
+Sylvester.]
+
+Remarking upon the popular appeal of most of the lectures, a
+contemporary observer noted that while many listeners might prefer to
+hear Professor Tyndall expound on the acoustic opacity of the
+atmosphere, "those of a higher and drier turn of mind experience
+ineffable delight when Professor Sylvester holds forth on the conversion
+of circular into parallel motion."[44]
+
+[Footnote 44: Bernard H. Becker, _Scientific London_, London, 1874, pp.
+45, 50, 51.]
+
+Sylvester's aim was to bring the Peaucellier linkage to the notice of
+the English-speaking world, as it had been brought to his attention by
+Chebyshev--during a recent visit of the Russian to England--and to give
+his listeners some insight into the vastness of the field that he saw
+opened by the discovery of the French soldier.[45]
+
+[Footnote 45: Sylvester, _op. cit._ (footnote 41), p. 183; _Nature_,
+November 13, 1873, vol. 9, p. 33.]
+
+"The perfect parallel motion of Peaucellier looks so simple," he
+observed, "and moves so easily that people who see it at work almost
+universally express astonishment that it waited so long to be
+discovered." But that was not his reaction at all. The more one reflects
+upon the problem, Sylvester continued, he "wonders the more that it was
+ever found out, and can see no reason why it should have been
+discovered for a hundred years to come. Viewed _a priori_ there was
+nothing to lead up to it. It bears not the remotest analogy (except in
+the fact of a double centring) to Watt's parallel motion or any of its
+progeny."[46]
+
+[Footnote 46: Sylvester, _op. cit._ (footnote 41), p. 181.]
+
+It must be pointed out, parenthetically at least, that James Watt had
+not only had to solve the problem as best he could, but that he had no
+inkling, so far as experience was concerned, that a solvable problem
+existed.
+
+Sylvester interrupted his panegyric long enough to enumerate some of the
+practical results of the Peaucellier linkage. He said that Mr. Penrose,
+the eminent architect and surveyor to St. Paul's Cathedral, had "put up
+a house-pump worked by a negative Peaucellier cell, to the great
+wonderment of the plumber employed, who could hardly believe his senses
+when he saw the sling attached to the piston-rod moving in a true
+vertical line, instead of wobbling as usual from side to side."
+Sylvester could see no reason "why the perfect parallel motion should
+not be employed with equal advantage in the construction of ordinary
+water-closets." The linkage was to be employed by "a gentleman of
+fortune" in a marine engine for his yacht, and there was talk of using
+it to guide a piston rod "in certain machinery connected with some new
+apparatus for the ventilation and filtration of the air of the Houses of
+Parliament." In due course, Mr. Prim, "engineer to the Houses," was
+pleased to show his adaptation of the Peaucellier linkage to his new
+blowing engines, which proved to be exceptionally quiet in their
+operation (fig. 25).[47] A bit on the ludicrous side, also, was
+Sylvester's 78-bar linkage that traced a straight line along the line
+connecting the two fixed centers of the linkage.[48]
+
+[Footnote 47: _Ibid._, pp. 182, 183, 188, 193.]
+
+[Footnote 48: Kempe, _op. cit._ (footnote 21), p. 17.]
+
+[Illustration: Figure 25.--Mr. Prim's blowing engine used for
+ventilating the House of Commons, 1877. The crosshead of the
+reciprocating air pump is guided by a Peaucellier linkage shown at the
+center. The slate-lined air cylinders had rubber-flap inlet and exhaust
+valves and a piston whose periphery was formed by two rows of brush
+bristles. Prim's machine was driven by a steam engine. Photograph by
+Science Museum, London.]
+
+Before dismissing with a smile the quaint ideas of our Victorian
+forbears, however, it is well to ask, 88 years later, whether some
+rather elaborate work reported recently on the synthesis of
+straight-line mechanisms is more to the point, when the principal
+objective appears to be the moving of an indicator on a "pleasing,
+expanded" (i.e., squashed flat) radio dial.[49]
+
+[Footnote 49: _Machine Design_, December 1954, vol. 26, p. 210.]
+
+But Professor Sylvester was more interested, really, in the mathematical
+possibilities of the Peaucellier linkage, as no doubt our modern
+investigators are. Through a compounding of Peaucellier mechanisms, he
+had already devised square-root and cube-root extractors, an angle
+trisector, and a quadratic-binomial root extractor, and he could see no
+limits to the computing abilities of linkages as yet undiscovered.[50]
+
+[Footnote 50: Sylvester, _op. cit._ (footnote 41), p. 191.]
+
+Sylvester recalled fondly, in a footnote to his lecture, his experience
+with a little mechanical model of the Peaucellier linkage at an earlier
+dinner meeting of the Philosophical Club of the Royal Society. The
+Peaucellier model had been greeted by the members with lively
+expressions of admiration "when it was brought in with the dessert, to
+be seen by them after dinner, as is the laudable custom among members of
+that eminent body in making known to each other the latest scientific
+novelties." And Sylvester would never forget the reaction of his
+brilliant friend Sir William Thomson (later Lord Kelvin) upon being
+handed the same model in the Athenaeum Club. After Sir William had
+operated it for a time, Sylvester reached for the model, but he was
+rebuffed by the exclamation "No! I have not had nearly enough of it--it
+is the most beautiful thing I have ever seen in my life."[51]
+
+[Footnote 51: _Ibid._, p. 183.]
+
+The aftermath of Professor Sylvester's performance at the Royal
+Institution was considerable excitement amongst a limited company of
+interested mathematicians. Many alternatives to the Peaucellier
+straight-line linkage were suggested by several writers of papers for
+learned journals.[52]
+
+[Footnote 52: For a summary of developments and references, see Kempe,
+_op. cit._ (footnote 21), pp. 49-51. Two of Hart's six-link exact
+straight-line linkages referred to by Kempe are illustrated in Henry M.
+Cundy and A. P. Rollett, _Mathematical Models_, Oxford, Oxford
+University Press, 1952, pp. 204-205. Peaucellier's linkage was of eight
+links.]
+
+In the summer of 1876, after Sylvester had departed from England to take
+up his post as professor of mathematics in the new Johns Hopkins
+University in Baltimore, Alfred Bray Kempe, a young barrister who
+pursued mathematics as a hobby, delivered at London's South Kensington
+Museum a lecture with the provocative title "How to Draw a Straight
+Line."[53]
+
+[Footnote 53: Kempe, _op. cit._ (footnote 21), p. 26.]
+
+In order to justify the Peaucellier linkage, Kempe belabored the point
+that a perfect circle could be generated by means of a pivoted bar and a
+pencil, while the generation of a straight line was most difficult if
+not impossible until Captain Peaucellier came along. A straight line
+could be drawn along a straight edge; but how was one to determine
+whether the straight edge was straight? He did not weaken his argument
+by suggesting the obvious possibility of using a piece of string. Kempe
+had collaborated with Sylvester in pursuing the latter's first thoughts
+on the subject, and one result, that to my mind exemplifies the general
+direction of their thinking, was the Sylvester-Kempe "parallel motion"
+(fig. 26).
+
+[Illustration: Figure 26.--Sylvester-Kempe translating linkage, 1877.
+The upper and lower plates remain parallel and equidistant. From A. B.
+Kempe, _How to Draw a Straight Line_ (London, 1877, p. 37).]
+
+[Illustration: Figure 27.--Gaspard Monge (1746-1818), professor of
+mathematics at the Ecole Polytechnique from 1794 and founder of the
+academic discipline of machine kinematics, From _Livre du Centenaire,
+1794-1894, Ecole Polytechnique_ (Paris, 1895, vol. 1, frontispiece).]
+
+Enthusiastic as Kempe was, however, he injected an apologetic note in
+his lecture. "That these results are valuable cannot I think be
+doubted," he said, "though it may well be that their great beauty has
+led some to attribute to them an importance which they do not really
+possess...." He went on to say that 50 years earlier, before the great
+improvements in the production of true plane surfaces, the straight-line
+mechanisms would have been more important than in 1876, but he added
+that "linkages have not at present, I think, been sufficiently put
+before the mechanician to enable us to say what value should really be
+set upon them."[54]
+
+[Footnote 54: _Ibid._, pp. 6-7. I have not pursued the matter of cognate
+linkages (the Watt and Evans linkages are cognates) because the
+Roberts-Chebyshev theorem escaped my earlier search, as it had
+apparently escaped most others until 1958. See R. S. Hartenberg and J.
+Denavit, "The Fecund Four-Bar," _Transactions of the Fifth Conference on
+Mechanisms_, Cleveland, Penton Publishing Company, 1958, pp. 194-206,
+reprinted in _Machine Design_, April 16, 1959, vol. 31, pp. 149-152. See
+also A. E. R. de Jonge, "The Correlation of Hinged Four-Bar
+Straight-Line Motion Devices by Means of the Roberts Theorem and a New
+Proof of the Latter," _Annals of the New York Academy of Sciences_,
+March 18, 1960, vol. 84, art. 3, pp. 75-145 (published separately).]
+
+It was during this same summer of 1876, at the Loan Exhibition of
+Scientific Apparatus in the South Kensington Museum, that the work of
+Franz Reuleaux, which was to have an important and lasting influence on
+kinematics everywhere, was first introduced to English engineers. Some
+300 beautifully constructed teaching aids, known as the Berlin kinematic
+models, were loaned to the exhibition by the Royal Industrial School in
+Berlin, of which Reuleaux was the director. These models were used by
+Prof. Alexander B. W. Kennedy of University College, London, to help
+explain Reuleaux's new and revolutionary theory of machines.[55]
+
+[Footnote 55: Alexander B. W. Kennedy, "The Berlin Kinematic Models,"
+_Engineering_, September 15, 1876, vol. 22, pp. 239-240.]
+
+
+Scholars and Machines
+
+When, in 1829, André-Marie Ampère (1775-1836) was called upon to prepare
+a course in theoretical and experimental physics for the Collège de
+France, he first set about determining the limits of the field of
+physics. This exercise suggested to his wide-ranging intellect not only
+the definition of physics but the classification of all human knowledge.
+He prepared his scheme of classification, tried it out on his physics
+students, found it incomplete, returned to his study, and produced
+finally a two-volume work wherein the province of kinematics was first
+marked out for all to see and consider.[56] Only a few lines could be
+devoted to so specialized a branch as kinematics, but Ampère managed to
+capture the central idea of the subject.
+
+[Footnote 56: André-Marie Ampère, _Essai sur la philosophie des
+sciences, une exposition analytique d'une classification naturelle de
+toutes les connaissances humaines_, 2 vols., Paris, 1838 (for origin of
+the project, see vol. 1, pp. v, xv).]
+
+Cinématique (from the Greek word for movement) was, according to Ampère,
+the science "in which movements are considered in themselves
+[independent of the forces which produce them], as we observe them in
+solid bodies all about us, and especially in the assemblages called
+machines."[57] Kinematics, as the study soon came to be known in
+English,[58] was one of the two branches of elementary mechanics, the
+other being statics.
+
+[Footnote 57: _Ibid._, vol. 1, pp. 51-52.]
+
+[Footnote 58: Willis (_op. cit._ footnote 21) adopted the word
+"kinematics," and this Anglicization subsequently became the standard
+term for this branch of mechanics.]
+
+In his definition of kinematics, Ampère stated what the faculty of
+mathematics at the Ecole Polytechnique, in Paris, had been groping
+toward since the school's opening some 40 years earlier. The study of
+mechanisms as an intellectual discipline most certainly had its origin
+on the left bank of the Seine, in this school spawned, as suggested by
+one French historian,[59] by the great _Encyclopédie_ of Diderot and
+d'Alembert.
+
+[Footnote 59: G. Pinet, _Histoire de l'Ecole Polytechnique_, Paris,
+1887, pp. viii-ix. In their forthcoming book on kinematic synthesis, R.
+S. Hartenberg and J. Denavit will trace the germinal ideas of Jacob
+Leupold and Leonhard Euler of the 18th century.]
+
+Because the Ecole Polytechnique had such a far-reaching influence upon
+the point of view from which mechanisms were contemplated by scholars
+for nearly a century after the time of Watt, and by compilers of
+dictionaries of mechanical movements for an even longer time, it is
+well to look for a moment at the early work that was done there. If one
+is interested in origins, it might be profitable for him to investigate
+the military school in the ancient town of Mézières, about 150 miles
+northeast of Paris. It was here that Lazare Carnot, one of the principal
+founders of the Ecole Polytechnique, in 1783 published his essay on
+machines,[60] which was concerned, among other things, with showing the
+impossibility of "perpetual motion"; and it was from Mézières that
+Gaspard Monge and Jean Hachette[61] came to Paris to work out the system
+of mechanism classification that has come to be associated with the
+names of Lanz and Bétancourt.
+
+[Footnote 60: Lazare N. M. Carnot, _Essai sur les machines en général_,
+Mézières, 1783 (later published as _Principes fondamentaux de
+l'equilibre et du mouvement_, Paris, 1803).]
+
+[Footnote 61: Biographical notices of Monge and Hachette appear in
+_Encyclopaedia Britannica_, ed. 11. See also _L'Ecole Polytechnique,
+Livre du Centenaire_, Paris, 1895, vol. 1, p. 11ff.]
+
+Gaspard Monge (1746-1818), who while a draftsman at Mézières originated
+the methods of descriptive geometry, came to the Ecole Polytechnique as
+professor of mathematics upon its founding in 1794, the second year of
+the French Republic. According to Jean Nicolas Pierre Hachette
+(1769-1834), who was junior to Monge in the department of descriptive
+geometry, Monge planned to give a two-months' course devoted to the
+elements of machines. Having barely gotten his department under way,
+however, Monge became involved in Napoleon's ambitious scientific
+mission to Egypt and, taking leave of his family and his students,
+embarked for the distant shores.
+
+"Being left in charge," wrote Hachette, "I prepared the course of which
+Monge had given only the first idea, and I pursued the study of machines
+in order to analyze and classify them, and to relate geometrical and
+mechanical principles to their construction." Changes of curriculum
+delayed introduction of the course until 1806, and not until 1811 was
+his textbook ready, but the outline of his ideas was presented to his
+classes in chart form (fig. 28). This chart was the first of the widely
+popular synoptical tables of mechanical movements.[62]
+
+[Footnote 62: Jean N. P. Hachette, _Traité élémentaire des machines_,
+Paris, 1811, p. v.]
+
+[Illustration: Figure 28.--Hachette's synoptic chart of elementary
+mechanisms, 1808. This was the first of many charts of mechanical
+movements that enjoyed wide popularity for over 100 years.
+
+From Jean N. P. Hachette, _Traité Élémentaire des Machines_ (Paris,
+1811, pl. 1).]
+
+Hachette classified all mechanisms by considering the conversion of one
+motion into another. His elementary motions were continuous circular,
+alternating circular, continuous rectilinear, and alternating
+rectilinear. Combining one motion with another--for example, a treadle
+and crank converted alternating circular to continuous circular
+motion--he devised a system that supplied a frame of reference for the
+study of mechanisms. In the U.S. Military Academy at West Point,
+Hachette's treatise, in the original French, was used as a textbook in
+1824, and perhaps earlier.[63]
+
+[Footnote 63: This work was among the books sent back by Sylvanus Thayer
+when he visited France in 1816 to observe the education of the French
+army cadets. Thayer's visit resulted in his adopting the philosophy of
+the Ecole Polytechnique in his reorganization of the U.S. Military
+Academy and, incidentally, in his inclusion of Hachette's course in the
+Academy's curriculum (U.S. Congress, _American State Papers_,
+Washington, 1832-1861, Class v, Military Affairs, vol. 2, p. 661: Sidney
+Forman, _West Point_, New York, 1950, pp. 36-60). There is a collection
+of miscellaneous papers (indexed under Sylvanus Thayer and William
+McRee, U.S. National Archives, RG 77, Office, Chief of Engineers, Boxes
+1 and 6) pertaining to the U.S. Military Academy of this period, but I
+found no mention of kinematics in this collection.]
+
+Lanz and Bétancourt, scholars from Spain at the Ecole Polytechnique,
+plugged some of the gaps in Hachette's system by adding continuous and
+alternating curvilinear motion, which doubled the number of combinations
+to be treated, but the advance of their work over that of Hachette was
+one of degree rather than of kind.[64]
+
+[Footnote 64: Phillipe Louis Lanz and Augustin de Bétancourt, _Essai sur
+la composition des machines_, Paris, 1808. Hachette's chart and an
+outline of his elementary course on machines is bound with the Princeton
+University Library copy of the Lanz and Bétancourt work. This copy
+probably represents the first textbook of kinematics. Bétancourt was
+born in 1760 in Teneriffe, attended the military school in Madrid, and
+became inspector-general of Spanish roads and canals. He was in England
+before 1789, learning how to build Watt engines, and he introduced the
+engines to Paris in 1790 (see Farey, _op. cit._, p. 655). He entered
+Russian service in 1808 and died in St. Petersburg in 1826 J. C.
+Poggendorff, _Biographisches-literarisches Handwörterbuch für Mathematik
+..._, Leipzig, 1863, vol. 1.]
+
+[Illustration: Figure 29.--Robert Willis (1800-1875), Jacksonian
+Professor, Cambridge University, and author of _Principles of
+Mechanism_, one of the landmark books in the development of kinematics
+of mechanisms. Photo courtesy Gonville and Caius College, Cambridge
+University.]
+
+Giuseppe Antonio Borgnis, an Italian "engineer and member of many
+academies" and professor of mechanics at the University of Pavia in
+Italy, in his monumental, nine-volume _Traité complet de méchanique
+appliquée aux arts_, caused a bifurcation of the structure built upon
+Hachette's foundation of classification when he introduced six orders of
+machine elements and subdivided these into classes and species. His six
+orders were _récepteurs_ (receivers of motion from the prime mover),
+_communicateurs_, _modificateurs_ (modifiers of velocity), _supports_
+(e.g., bearings), _regulateurs_ (e.g., governors), and _operateurs_,
+which produced the final effect.[65]
+
+[Footnote 65: Giuseppe Antonio Borgnis, _Théorie de la mécanique
+usuelle_ in _Traité complet de mécanique appliquée aux arts_, Paris,
+1818, vol. 1, pp. xiv-xvi.]
+
+The brilliant Gaspard-Gustave de Coriolis (1792-1843)--remembered mainly
+for a paper of a dozen pages explaining the nature of the acceleration
+that bears his name[66]--was another graduate of the Ecole Polytechnique
+who wrote on the subject of machines. His book,[67] published in 1829,
+was provoked by his recognition that the designer of machines needed
+more knowledge than his undergraduate work at the Ecole Polytechnique
+was likely to give him. Although he embraced a part of Borgnis'
+approach, adopting _récepteurs_, _communicateurs_, and _operateurs_,
+Coriolis indicated by the title of his book that he was more concerned
+with forces than with relative displacements. However, the attractively
+simple three-element scheme of Coriolis became well fixed in French
+thinking.[68]
+
+[Footnote 66: Gaspard-Gustave de Coriolis, "Memoire sur les equations du
+mouvement relatif des systèmes de corps," _Journal de l'Ecole
+Polytechnique_, 1835, vol. 15, pp. 142-154.]
+
+[Footnote 67: Gaspard-Gustave de Coriolis, _De Calcul de l'effet des
+machines_, Paris, 1829. In this book Coriolis proposed the now generally
+accepted equation, work = force × distance (pp. iii, 2).]
+
+[Footnote 68: The renowned Jean Victor Poncelet lent weight to this
+scheme. (See Franz Reuleaux, _Theoretische Kinematik: Grundzüge einer
+Theorie des Maschinenwesens_, Braunschweig, 1875, translated by
+Alexander B. W. Kennedy as _The Kinematics of Machinery: Outlines of a
+Theory of Machines_, London, 1876, pp. 11, 487. I have used the Kennedy
+translation in the Reuleaux references throughout the present work.)]
+
+Michel Chasles (1793-1880), another graduate of the Ecole Polytechnique,
+contributed some incisive ideas in his papers on instant centers[69]
+published during the 1830's, but their tremendous importance in
+kinematic analysis was not recognized until much later.
+
+[Footnote 69: The instant center was probably first recognized by Jean
+Bernoulli (1667-1748) in his "De Centro Spontaneo Rotationis" (_Johannis
+Bernoulli ... Opera Omnia ..._, Lausanne, 1742, vol. 4, p. 265ff.).]
+
+[Illustration: Figure 30.--Franz Reuleaux (1829-1905). His _Theoretische
+Kinematik_, published in 1875, provided the basis for modern kinematic
+analysis. Photo courtesy Deutsches Museum, Munich.]
+
+Acting upon Ampère's clear exposition of the province of kinematics and
+excluding, as Ampère had done, the consideration of forces, an
+Englishman, Robert Willis, made the next giant stride forward in the
+analysis of mechanisms. Willis was 37 years old in 1837 when he was
+appointed professor of natural and experimental philosophy at Cambridge.
+In the same year Professor Willis--a man of prodigious energy and
+industry and an authority on archeology and architectural history as
+well as mechanisms--read his important paper "On the Teeth of Wheels"
+before the Institution of Civil Engineers[70] and commenced at Cambridge
+his lectures on kinematics of mechanisms that culminated in his 1841
+book _Principles of Mechanism_.[71]
+
+[Footnote 70: Robert Willis, "On the Teeth of Wheels," _Transactions of
+the Institution of Civil Engineers of London_, 1838, vol. 2, pp.
+89-112.]
+
+[Footnote 71: Willis, _op. cit._ (footnote 21). Through the kindness of
+its owner (Mr. Warren G. Ogden of North Andover, Massachusetts), I have
+had access to Willis' own copy of his 1841 edition of _Principles of
+Mechanism_. The book is interleaved, and it contains notes made by
+Willis from time to time until at least 1870, when the second edition
+was issued. Corrections, emendations, notations of some of his sources
+(for example, the De Voglie linkage mentioned in footnote 35 above),
+notes to himself to "examine the general case" and "examine the modern
+forms" of straight-line devices are interspersed with references to
+authors that had borrowed from his work without acknowledgment. Of one
+author Willis writes an indignant "He ignores my work."]
+
+It seemed clear to Willis that the problem of devising a mechanism for a
+given purpose ought to be attacked systematically, perhaps
+mathematically, in order to determine "all the forms and arrangements
+that are applicable to the desired purpose," from which the designer
+might select the simplest or most suitable combination. "At present," he
+wrote, "questions of this kind can only be solved by that species of
+intuition which long familiarity with a subject usually confers upon
+experienced persons, but which they are totally unable to communicate to
+others."
+
+In analyzing the process by which a machine was designed, Willis
+observed: "When the mind of a mechanician is occupied with the
+contrivance of a machine, he must wait until, in the midst of his
+meditations, some happy combination presents itself to his mind which
+may answer his purpose." He ventured the opinion that at this stage of
+the design process "the motions of the machine are the principal subject
+of contemplation, rather than the forces applied to it, or the work it
+has to do." Therefore he was prepared to adopt without reservation
+Ampère's view of kinematics, and, if possible, to make the science
+useful to engineers by stating principles that could be applied without
+having to fit the problem at hand into the framework of the systems of
+classification and description that had gone before. He appraised the
+"celebrated system" of Lanz and Bétancourt as "a merely popular
+arrangement, notwithstanding the apparently scientific simplicity of the
+scheme." He rejected this scheme because "no attempt is made to subject
+the motions to calculation, or to reduce these laws to general formulas,
+for which indeed the system is totally unfitted."
+
+Borgnis had done a better job, Willis thought, in actually describing
+machinery, with his "orders" based upon the functions of machine
+elements or mechanisms within the machine, but again there was no means
+suggested by which the kinematics of mechanisms could be systematically
+investigated.
+
+Although Willis commenced his treatise with yet another "synoptical
+table of the elementary combinations of pure mechanism," his view
+shifted quickly from description to analysis. He was consistent in his
+pursuit of analytical methods for "pure mechanism," eschewing any
+excursions into the realm of forces and absolute velocities. He grasped
+the important concept of relative displacements of machine elements, and
+based his treatment upon "the proportions and relations between the
+velocities and directions of the pieces, and not upon their actual and
+separate motions."[72]
+
+[Footnote 72: _Ibid._, pp. iv, x-xii, xxi, 15.]
+
+That he did not succeed in developing the "formulas" that would enable
+the student to determine "all the forms and arrangements that are
+applicable to the desired purpose"--that he did not present a rational
+approach to synthesis--is not to be wondered at. Well over a century
+later we still are nibbling at the fringes of the problem. Willis did,
+nonetheless, give the thoughtful reader a glimpse of the most powerful
+tool for kinematic synthesis that has yet been devised; namely,
+kinematic analysis, in which the argument is confined to the relative
+displacements of points on links of a mechanism, and through which the
+designer may grasp the nature of the means at his disposal for the
+solution of any particular problem.
+
+As remarked by Reuleaux a generation later, there was much in Professor
+Willis's book that was wrong, but it was an original, thoughtful work
+that departed in spirit if not always in method from its predecessors.
+_Principles of Mechanism_ was a prominent landmark along the road to a
+rational discipline of machine-kinematics.
+
+A phenomenal engineer of the 19th century was the Scottish professor of
+civil engineering at the University of Glasgow, William John MacQuorn
+Rankine. Although he was at the University for only 17 years--he died at
+the age of 52, in 1872--he turned out during that time four thick
+manuals on such diverse subjects as civil engineering, ship-building,
+thermodynamics, and machinery and mill-work, in addition to literally
+hundreds of papers, articles, and notes for scientific journals and the
+technical press. Endowed with apparently boundless energy, he found time
+from his studies to command a battalion of rifle volunteers and to
+compose and sing comic and patriotic songs. His manuals, often used as
+textbooks, were widely circulated and went through many editions.
+Rankine's work had a profound effect upon the practice of engineering by
+setting out principles in a form that could be grasped by people who
+were dismayed by the treatment usually found in the learned journals.
+
+When Rankine's book titled _A Manual of Machinery and Millwork_ was
+published in 1869 it was accurately characterized by a reviewer as
+"dealing with the _principles_ of machinery and millworks, and as such
+it is entirely distinct from [other works on the same subject] which
+treat more of the practical applications of such principles than of the
+principles themselves."[73]
+
+[Footnote 73: _Engineering_, London, August 13, 1869, vol. 8, p. 111.]
+
+Rankine borrowed what appeared useful from Willis' _Principles of
+Mechanism_ and from other sources. His treatment of kinematics was not
+as closely reasoned as the later treatises of Reuleaux and Kennedy,
+which will be considered below. Rankine did, however, for the first time
+show the utility of instant centers in velocity analysis, although he
+made use only of the instant centers involving the fixed link of a
+linkage. Like others before him, he considered the fixed link of a
+mechanism as something quite different from the movable links, and he
+did not perceive the possibilities opened up by determining the instant
+center of two movable links.
+
+Many other books dealing with mechanisms were published during the
+middle third of the century, but none of them had a discernible
+influence upon the advance of kinematical ideas.[74] The center of
+inquiry had by the 1860's shifted from France to Germany. Only by
+scattered individuals in England, Italy, and France was there any
+impatience with the well-established, general understanding of the
+machine-building art.
+
+[Footnote 74: Several such books are referred to by Reuleaux, _op. cit._
+(footnote 68), pp. 12-16.]
+
+In Germany, on the other hand, there was a surge of industrial activity
+that attracted some very able men to the problems of how machines ought
+to be built. Among the first of these was Ferdinand Redtenbacher
+(1809-1863), professor of mechanical engineering in the polytechnic
+school in Karlsruhe, not far from Heidelberg. Redtenbacher, although he
+despaired of the possibility of finding a "true system on which to base
+the study of mechanisms," was nevertheless a factor in the development
+of such a system. He had young Franz Reuleaux in his classes for two
+years, from 1850. During that time the older man's commanding presence,
+his ability as a lecturer, and his infectious impatience with the
+existing order influenced Reuleaux to follow the scholar's trail that
+led him to eminence as an authority of the first rank.[75]
+
+[Footnote 75: See Carl Weihe, "Franz Reuleaux und die Grundlagen seiner
+Kinematik," Deutsches Museum, Munich, _Abhandlung und Berichte_, 1942,
+p. 2; Friedrich Klemm, _Technik: Eine Geschichte ihrer Probleme_,
+Freiburg and Munich, Verlag Karl Alber, 1954, translated by Dorothea W.
+Singer as _A History of Western Technology_, New York, Charles
+Scribner's Sons, 1959, p. 317.]
+
+Before he was 25 years old Franz Reuleaux published, in collaboration
+with a classmate, a textbook whose translated title would be
+_Constructive Lessons for the Machine Shop_.[76] His several years in
+the workshop, before and after coming under Redtenbacher's influence,
+gave his works a practical flavor, simple and direct. According to one
+observer, Reuleaux's book exhibited "a recognition of the claims of
+practice such as Englishmen do not generally associate with the writings
+of a German scientific professor."[77]
+
+[Footnote 76: See Weihe, _op. cit._ (footnote 75), p. 3; Hans Zopke,
+"Professor Franz Reuleaux," _Cassier's Magazine_, December 1896, vol.
+11, pp. 133-139; _Transactions of the American Society of Mechanical
+Engineers_, 1904-1905, vol. 26, pp. 813-817.]
+
+[Footnote 77: _Engineering_, London, September 8, 1876, vol. 22, p.
+197.]
+
+Reuleaux's original ideas on kinematics, which are responsible for the
+way in which we look at mechanisms today, were sufficiently formed in
+1864 for him to lecture upon them.[78] Starting in 1871, he published
+his findings serially in the publication of the Verein zur Beförderung
+des Gewerbefleisses in Preussen (Society for the Advancement of Industry
+in Prussia), of which he was editor. In 1875 these articles were brought
+together in the book that established his fame--_Theoretische
+Kinematik...._[79]
+
+[Footnote 78: A. E. Richard de Jonge, "What is Wrong with Kinematics and
+Mechanisms?" _Mechanical Engineering_, April 1942, vol. 64, pp. 273-278
+(comments on this paper are in _Mechanical Engineering_, October 1942,
+vol. 64, pp. 744-751); Zopke, _op. cit._ (footnote 76), p. 135.]
+
+[Footnote 79: Reuleaux, _op. cit._ (footnote 68). This was not the last
+of Reuleaux's books. His trilogy on kinematics and machine design is
+discussed by De Jonge, _op. cit._ (footnote 78).]
+
+In the introduction of this book, Reuleaux wrote:
+
+     In the development of every exact science, its substance having
+     grown sufficiently to make generalization possible, there is a time
+     when a series of changes bring it into clearness. This time has
+     most certainly arrived for the science of kinematics. The number of
+     mechanisms has grown almost out of measure, and the number of ways
+     in which they are applied no less. It has become absolutely
+     impossible still to hold the thread which can lead in any way
+     through this labyrinth by the existing methods.[80]
+
+[Footnote 80: Reuleaux, _op. cit._ (footnote 68), p. 23.]
+
+Reuleaux's confidence that it would be his own work that would bring
+order out of confusion was well founded. His book had already been
+translated into Italian and was being translated into French when, only
+a year after its publication, it was presented by Prof. Alexander B. W.
+Kennedy in English translation.[81]
+
+[Footnote 81: _Ibid._, p. iii.]
+
+The book was enthusiastically reviewed by the weekly London journal
+_Engineering_,[82] and it was given lengthy notice by the rival journal,
+_The Engineer_. The editor of _The Engineer_ thought that the
+mechanician would find in it many new ideas, that he would be "taught to
+detect hitherto hidden resemblances, and that he must part--reluctantly,
+perhaps--with many of his old notions." "But," added the editor with
+considerable justice, "that he [the mechanician] would suddenly
+recognize in Professor Reuleaux's 'kinematic notation,' 'analysis,' and
+'synthesis,' the long-felt want of his professional existence we do not
+for a moment believe."[83] Indeed, the fresh and sharp ideas of Reuleaux
+were somewhat clouded by a long (600-page) presentation; and his
+kinematic notation, which required another attempt at classification,
+did not simplify the presentation of radically new ideas.[84]
+
+[Footnote 82: _Engineering_, _loc. cit._ (footnote 77).]
+
+[Footnote 83: _The Engineer_, London, March 30 and April 13, 1877, vol.
+43, pp. 211-212, 247-248.]
+
+[Footnote 84: It is perhaps significant that the first paper of the
+First Conference on Mechanisms at Purdue University was Allen S. Hall's
+"Mechanisms and Their Classification," which appeared in _Machine
+Design_, December 1953, vol. 25, pp. 174-180. The place of
+classification in kinematic synthesis is suggested in Ferdinand
+Freudenstein's "Trends in Kinematics of Mechanisms," _Applied Mechanics
+Reviews_, September 1959, vol. 12, pp. 587-590.]
+
+[Illustration: Figure 31.--Alexander Blackie William Kennedy
+(1847-1928), translator of Reuleaux' _Theoretische Kinematik_ and
+discoverer of Kennedy's "Law of Three Centers." From _Minutes of the
+Proceedings of the Institution of Civil Engineers_ (1907, vol. 167,
+frontispiece).]
+
+Nevertheless, no earlier author had seen the problem of kinematic
+analysis so clearly or had introduced so much that was fresh, new, and
+of lasting value.
+
+Reuleaux was first to state the concept of the pair; by his concept of
+the expansion of pairs he was able to show similarities in mechanisms
+that had no apparent relation. He was first to recognize that the fixed
+link of a mechanism was kinematically the same as the movable links.
+This led him to the important notion of inversion of linkages, fixing
+successively the various links and thus changing the function of the
+mechanism. He devoted 40 pages to showing, with obvious delight, the
+kinematic identity of one design after another of rotary steam engines,
+demolishing for all time the fond hopes of ingenious but ill-informed
+inventors who think that improvements and advances in mechanism design
+consist in contortion and complexity.
+
+The chapter on synthesis was likewise fresh, but it consisted of a
+discussion, not a system; and Reuleaux stressed the idea that I have
+mentioned above in connection with Willis' book, that synthesis will be
+successful in proportion to the designer's understanding and
+appreciation of analysis. Reuleaux tried to put the designer on the
+right track by showing him clearly "the essential simplicity of the
+means with which we have to work" and by demonstrating to him "that the
+many things which have to be done can be done with but few means, and
+that the principles underlying them all lie clearly before us."[85]
+
+[Footnote 85: Reuleaux, _op. cit._ (footnote 68), p. 582.]
+
+It remained for Sir Alexander Blackie William Kennedy (1847-1928) and
+Robert Henry Smith (1852-1916) to add to Reuleaux's work the elements
+that would give kinematic analysis essentially its modern shape.
+
+Kennedy, the translator of Reuleaux's book, became professor of
+engineering at the University College in London in 1874, and eventually
+served as president both of the Institution of Mechanical Engineers and
+of the Institution of Civil Engineers. Smith, who had taught in the
+Imperial University of Japan, was professor of engineering at Mason
+College, now a part of Birmingham University, in England.
+
+While Reuleaux had used instant centers almost exclusively for the
+construction of centrodes (paths of successive positions of an instant
+center), Professor Kennedy recognized that instant centers might be used
+in velocity analysis. His book, _Mechanics of Machinery_, was published
+in 1886 ("partly through pressure of work and partly through ill-health,
+this book appears only now"). In it he developed the law of three
+centers, now known as Kennedy's theorem. He noted that his law of three
+centers "was first given, I believe, by Aronhold, although its previous
+publication was unknown to me until some years after I had given it in
+my lectures."[86] In fact, the law had been published by Siegfried
+Heinrich Aronhold (1819-1884) in his "Outline of Kinematic Geometry,"
+which appeared in 1872 alongside Reuleaux's series in the journal that
+Reuleaux edited. Apparently Reuleaux did not perceive its particular
+significance at that time.[87]
+
+[Footnote 86: Alexander B. W. Kennedy, _The Mechanics of Machinery_, ed.
+3, London, 1898, pp. vii, x.]
+
+[Footnote 87: Siegfried Heinrich Aronhold, "Outline of Kinematic
+Geometry," _Verein zur Beförderung des Gewerbefleisses in Preussen_,
+1872, vol. 51, pp. 129-155. Kennedy's theorem is on pp. 137-138.]
+
+[Illustration: Figure 32.--Robert Henry Smith (1852-1916), originator of
+velocity and acceleration polygons for kinematic analysis. Photo
+courtesy the Librarian, Birmingham Reference Library, England.]
+
+Kennedy, after locating instant centers, determined velocities by
+calculation and accelerations by graphical differentiation of
+velocities, and he noted in his preface that he had been unable, for a
+variety of reasons, to make use in his book of Smith's recent work.
+Professor Kennedy at least was aware of Smith's surprisingly advanced
+ideas, which seem to have been generally ignored by Americans and
+Englishmen alike.
+
+Professor Smith, in a paper before the Royal Society of Edinburgh in
+1885, stated clearly the ideas and methods for construction of velocity
+and acceleration diagrams of linkages.[88] For the first time, velocity
+and acceleration "images" of links (fig. 33) were presented. It is
+unfortunate that Smith's ideas were permitted to languish for so long a
+time.
+
+[Footnote 88: Robert H. Smith, "A New Graphic Analysis of the Kinematics
+of Mechanisms," _Transactions of the Royal Society of Edinburgh_,
+1882-1885, vol. 32, pp. 507-517, and pl. 82. Smith used this paper as
+the basis for a chapter in his _Graphics or the Art of Calculating by
+Drawing Lines_, London, 1889, pp. 144-162. In a footnote of his paper,
+Smith credited Fleeming Jenkin (1833-1885) with suggesting the term
+"image." After discarding as "practically useless" Kennedy's graphical
+differentiation, Smith complained that he had "failed to find any
+practical use" for Reuleaux's "method of centroids, more properly called
+axoids." Such statements were not calculated to encourage Kennedy and
+Reuleaux to advertise Smith's fame; however, I found no indication that
+either one took offense at the criticism. Smith's velocity and
+acceleration diagrams were included (apparently embalmed, so far as
+American engineers were concerned) in _Encyclopaedia Britannica_, ed.
+11, 1910, vol. 17, pp. 1008-1009.]
+
+[Illustration: Figure 33.--Smith's velocity image (the two figures at
+top), and his velocity, mechanism, and acceleration diagrams, 1885. The
+image of link BACD is shown as figure _bacd_. The lines _pa_, _pb_,
+_pc_, and _pd_ are velocity vectors. This novel, original, and powerful
+analytical method was not generally adopted in English or American
+schools until nearly 50 years after its inception. From _Transactions of
+the Royal Society of Edinburgh_ (1882-1885, vol. 32, pl. 82).]
+
+By 1885 nearly all the tools for modern kinematic analysis had been
+forged. Before discussing subsequent developments in analysis and
+synthesis, however, it will be profitable to inquire what the
+mechanician--designer and builder of machines--was doing while all of
+this intellectual effort was being expended.
+
+
+Mechanicians and Mechanisms
+
+While the inductive process of recognizing and stating true principles
+of the kinematics of mechanisms was proceeding through three generations
+of French, English, and finally German scholars, the actual design of
+mechanisms went ahead with scant regard for what the scholars were doing
+and saying.
+
+After the demonstration by Boulton and Watt that large mechanisms could
+be wrought with sufficient precision to be useful, the English tool
+builders Maudslay, Roberts, Clement, Nasmyth, and Whitworth developed
+machine tools of increasing size and truth. The design of other
+machinery kept pace with--sometimes just behind, sometimes just ahead
+of--the capacity and capability of machine tools. In general, there was
+an increasing sophistication of mechanisms that could only be accounted
+for by an increase of information with which the individual designer
+could start.
+
+Reuleaux pointed out in 1875 that the "almost feverish progress made in
+the regions of technical work" was "not a consequence of any increased
+capacity for intellectual action in the race, but only the perfecting
+and extending of the tools with which the intellect works." These tools,
+he said, "have increased in number just like those in the modern
+mechanical workshop--the men who work them remain the same." Reuleaux
+went on to say that the theory and practice of machine-kinematics had
+"carried on a separate existence side by side." The reason for this
+failure to apply theory to practice, and vice versa, must be sought in
+the defects of the theory, he thought, because "the mechanisms
+themselves have been quietly developed in practical machine-design, by
+invention and improvement, regardless of whether or not they were
+accorded any direct and proper theoretical recognition." He pointed out
+that the theories had thus far "furnished no new mechanisms."[89]
+
+[Footnote 89: Reuleaux, _op. cit._ (footnote 68), p. 8.]
+
+It is reasonable, therefore, to ask what was responsible for the
+appearance of new mechanisms, and then to see what sort of mechanisms
+had their origins in this period.
+
+It is immediately evident to a designer that the progress in mechanisms
+came about through the spread of knowledge of what had already been
+done; but designers of the last century had neither the leisure nor
+means to be constantly visiting other workshops, near and far, to
+observe and study the latest developments. In the 1800's, as now, word
+must in the main be spread by the printed page.
+
+Hachette's chart (fig. 28) had set the pattern for display of mechanical
+contrivances in practical journals and in the large number of mechanical
+dictionaries that were compiled to meet an apparent demand for such
+information. It is a little surprising, however, to find how persistent
+were some of Hachette's ideas that could only have come from the
+uppermost superficial layer of his cranium. See, for example, his
+"anchored ferryboat" (fig. 34). This device, employed by Hachette to
+show conversion of continuous rectilinear motion into alternating
+circular motion, appeared in one publication after another throughout
+the 19th century. As late as 1903 the ferryboat was still anchored in
+Hiscox's _Mechanical Movements_, although the tide had changed (fig.
+35).[90]
+
+[Footnote 90: Gardner D. Hiscox, ed., _Mechanical Movements_, ed. 10,
+New York, 1903, p. 151. The ferryboat did not appear in the 1917
+edition.]
+
+[Illustration: Figure 34.--Hachette's ferryboat of 1808, a "machine" for
+converting continuous rectilinear motion into alternating circular
+motion. From Phillipe Louis Lanz and Augustin de Bétancourt, _Essai sur
+la composition des machines_ (Paris, 1808, pl. 2).]
+
+[Illustration: Figure 35.--Ferryboat from Gardner D. Hiscox, ed.,
+_Mechanical Movements_ (ed. 10, New York, 1903, p. 151).]
+
+During the upsurge of the Lyceum--or working-man's institute--movement
+in the 1820's, Jacob Bigelow, Rumford professor of applied science at
+Harvard University, gave his popular lectures on the "Elements of
+Technology" before capacity audiences in Boston. In preparing his
+lecture on the elements of machinery, Bigelow used as his authorities
+Hachette, Lanz and Bétancourt, and Olinthus Gregory's mechanical
+dictionary, an English work in which Hachette's classification scheme
+was copied and his chart reproduced.[91]
+
+[Footnote 91: Jacob Bigelow, _Elements of Technology_, ed. 2, Boston,
+1831, pp. 231-256; Olinthus Gregory, _A Treatise of Mechanics_, 3 vols.,
+ed. 3, London, 1815.]
+
+A translation of the work of Lanz and Bétancourt[92] under the title
+_Analytical Essay on the Construction of Machines_, was published about
+1820 at London by Rudolph Ackermann (for whom the Ackermann steering
+linkage was named), and their synoptic chart was reprinted again in 1822
+in Durham.[93] In the United States, _Appleton's Dictionary of
+Machines_[94] (1851) adopted the same system and used the same figures.
+Apparently the wood engraver traced directly onto his block the figures
+from one of the reprints of Lanz and Bétancourt's chart because the
+figures are in every case exact mirror images of the originals.
+
+[Footnote 92: Rudolph Ackermann, _Analytical Essay on the Construction
+of Machines_, London, about 1820, a translation of Lanz and Bétancourt,
+_op. cit._ (footnote 64).]
+
+[Footnote 93: Thomas Fenwick, _Essays on Practical Mechanics_, ed. 3,
+Durham, England, 1822.]
+
+[Footnote 94: _Appleton's Dictionary of Machines, Mechanics,
+Engine-Work, and Engineering_, 2 vols., New York, 1851 ("Motion").]
+
+In the _Dictionary of Engineering_[95] (London, 1873), the figures were
+redrawn and dozens of mechanisms were added to the repertory of
+mechanical motions; the result was a fair catalog of sound ideas. The
+ferryboat still tugged at its anchor cable, however.[96] _Knight's
+American Mechanical Dictionary_,[97] a classic of detailed pictorial
+information compiled by a U.S. patent examiner, contained well over
+10,000 finely detailed figures of various kinds of mechanical
+contrivances. Knight did not have a separate section on mechanisms, but
+there was little need for one of the Hachette variety, because his whole
+dictionary was a huge and fascinating compendium of ideas to be filed
+away in the synthetic mind. One reason for the popularity and usefulness
+of the various pictorial works was the peculiar ability of a wood or
+steel engraving to convey precise mechanical information, an advantage
+not possessed by modern halftone processes.
+
+[Footnote 95: E. F. and N. Spon, _Dictionary of Engineering_, London
+1873, pp. 2421-2452.]
+
+[Footnote 96: _Ibid._, p. 2447.]
+
+[Footnote 97: Edward H. Knight, _Knight's American Mechanical
+Dictionary_, 3 vols., New York 1874-1876.]
+
+[Illustration: Figure 36.--Typical mechanisms from E. F. and N. Spon,
+_Dictionary of Engineering_ (London, 1873, pp. 2426, 2478).]
+
+Many patent journals and other mechanical periodicals concerned with
+mechanics were available in English from the beginning of the 19th
+century, but few of them found their way into the hands of American
+mechanicians until after 1820. Oliver Evans (1755-1819) had much to say
+about "the difficulties inventive mechanics labored under for want of
+published records of what had preceded them, and for works of reference
+to help the beginner."[98] In 1817 the _North American Review_ also
+remarked upon the scarcity of engineering books in America.[99]
+
+[Footnote 98: George Escol Sellers in _American Machinist_, July 12,
+1884, vol. 7, p. 3.]
+
+[Footnote 99: _North-American Review and Miscellaneous Journal_, 1819,
+new ser., vol. 8, pp. 13-15, 25.]
+
+The _Scientific American_, which appeared in 1845 as a patent journal
+edited by the patent promoter Rufus Porter, carried almost from its
+beginning a column or so entitled "Mechanical Movements," in which one
+or two mechanisms--borrowed from an English work that had borrowed from
+a French work--were illustrated and explained. The _American Artisan_
+began a similar series in 1864, and in 1868 it published a compilation
+of the series as _Five Hundred and Seven Mechanical Movements_,
+"embracing all those which are most important in dynamics, hydraulics,
+hydrostatics, pneumatics, steam engines ... and miscellaneous
+machinery."[100] This collection went through many editions; it was last
+revived in 1943 under the title _A Manual of Mechanical Movements_.
+This 1943 edition included photographs of kinematic models.[101]
+
+[Footnote 100: Henry T. Brown, ed., _Five Hundred and Seven Mechanical
+Movements_, New York, 1868.]
+
+[Footnote 101: Will M. Clark, _A Manual of Mechanical Movements_, Garden
+City, New York, 1943.]
+
+Many readers are already well acquainted with the three volumes of
+_Ingenious Mechanisms for Designers and Inventors_,[102] a work that
+resulted from a contest, announced by _Machinery_ (vol. 33, p. 405) in
+1927, in which seven prizes were offered for the seven best articles on
+unpublished ingenious mechanisms.
+
+[Footnote 102: _Ingenious Mechanisms for Designers and Inventors_ (vols.
+1 and 2 edited by F. D. Jones, vol. 3 edited by H. L. Horton), New York,
+Industrial Press, 1930-1951.]
+
+There was an interesting class of United States patents called
+"Mechanical Movements" that comprised scores of patents issued
+throughout the middle decades of the 19th century. A sampling of these
+patents shows that while some were for devices used in particular
+machines--such as a ratchet device for a numbering machine, a locking
+index for gunmaking machinery, and a few gear trains--the great majority
+were for converting reciprocating motion to rotary motion. Even a
+cursory examination of these patents reveals an appalling absence of
+sound mechanical sense, and many of them appear to be attempts at
+"perpetual motion," in spite of an occasional disclaimer of such intent.
+
+Typical of many of these patented devices was a linkage for
+"multiplying" the motion of a flywheel, proposed in 1841 by Charles
+Johnson of Amity, Illinois (fig. 37). "It is not pretended that there is
+any actual gain of power," wrote Mr. Johnson; and probably he meant it.
+The avowed purpose of his linkage was to increase the speed of a
+flywheel and thus decrease its size.[103]
+
+[Footnote 103: U.S. Patent 2295, October 11, 1841.]
+
+[Illustration: Figure 37.--Johnson's "converting motion," 1841. The
+linkage causes the flywheel to make two revolutions for each
+double-stroke of the engine piston rod B. From U.S. Patent 2295, October
+11, 1841.]
+
+An Englishman who a few years earlier had invented a "new Motion" had
+claimed that his device would supersede the "ordinary crank in steam
+engines," the beam, parallel motion, and "external flywheel," reduce
+friction, neutralize "all extra contending power," and leave nothing for
+the piston to do "but the work intended to be done."
+
+A correspondent of the _Repertory of Patent Inventions_ made short work
+of this device: "There is hardly one assertion that can be supported by
+proof," he wrote, "and most of them are palpable misstatements." The
+writer attacked "the 'beetle impetus wheel,' which he [the inventor]
+thinks us all so beetle-headed, as not to perceive to be a flywheel,"
+and concluded with the statement: "In short the whole production evinces
+gross ignorance either of machinery, if the patentee really believed
+what he asserted, or of mankind, if he did not."[104]
+
+[Footnote 104: _Repertory of Patent Inventions_, ser. 3, October 1828,
+vol. 7, pp. 196-200, and December 1828, vol. 7, pp. 357-361.]
+
+Although many of the mechanisms for which patents were taken out were
+designed by persons who would make no use of the principles involved
+even if such principles could at that time have been clearly stated, it
+is a regrettable fact that worthless mechanisms often got as much space
+as sound ones in patent journals, and objections such as the one above
+were infrequent. The slanted information thus conveyed to the young
+mechanician, who was just accumulating his first kinematic repertory,
+was at times sadly misleading.
+
+From even this sketchy outline of the literature on the subject, it
+should be fairly evident that there has been available to the
+mechanician an enormous quantity of information about mechanical
+linkages and other devices. Whatever one may think of the quality of the
+literature, it has undoubtedly had influence not only in supplying
+designers with information but in forming a tradition of how one ought
+to supply the background that will enable the mind to assemble and
+synthesize the necessary mechanism for a given purpose.[105]
+
+[Footnote 105: Some additional catalogs of "mechanical movements" are
+listed in the selected references at the end of this paper.]
+
+Some of the mechanisms that have been given names--such as the Watt
+straight-line linkage and the Geneva stop--have appeared in textbook
+after textbook. Their only excuse for being seems to be that the authors
+must include them or risk censure by colleagues. Such mechanisms are
+more interesting to a reader, certainly, when he has some idea of what
+the name has to do with the mechanism, and who originated it. One such
+mechanism is the drag link.
+
+After I had learned of the drag link (as most American engineering
+students do), I wondered for awhile, and eventually despaired of making
+any sense out of the term. What, I wanted to know, was being dragged?
+Recently, in Nicholson's _Operative Mechanic and British Machinist_
+(1826), I ran across the sketch reproduced here as figure 38. This
+figure, explained Mr. Nicholson (in vol. 1, p. 32) "represents the
+coupling link used by Messrs. Boulton and Watt in their portable steam
+engines. A, a strong iron pin, projecting from one of the arms of the
+fly-wheel B; D, a crank connected with the shaft C; and E, a link to
+couple the pin A and the crank D together, so the motion may be
+communicated to the shaft C." So the drag link was actually a link of a
+coupling. Nothing could be more logical. A drag link mechanism now makes
+sense to me.
+
+[Illustration: Figure 38.--Drag link coupling used on Boulton and Watt
+portable engines. The link E drags one shaft when the other turns. From
+John Nicholson, _The Operative Mechanic, and British Machinist_
+(Philadelphia, 1826, vol. I, pl. 5).]
+
+Directly related to the drag link coupling were the patents of John
+Oldham (1779-1840), an Irish engineer who is remembered mainly for the
+coupling that bears his name (fig. 39). His three patents, which were
+for various forms of steamboat feathering paddle wheels, involved
+linkages kinematically similar to the drag link coupling, although it is
+quite unlikely that Oldham recognized the similarity. However, for his
+well-known coupling, which employs an inversion of the elliptical
+trammel mechanism, I have found no evidence of a patent. Probably it was
+part of the machinery that he designed for the Bank of Ireland's
+printing house, of which Oldham was manager for many years. "Mr. Oldham
+and his beautiful system" were brought to the Bank of England in 1836,
+where Oldham remained until his death in 1840.[106]
+
+[Footnote 106: Oldham's paddle-wheel patents were British Patents 4169
+(October 10, 1817), 4429 (January 15, 1820), and 5445 (February 1,
+1827). Robert Willis (_op. cit._ footnote 21, p. 167) noticed the
+existence of the coupling. Drawings or descriptions of the banknote
+machinery apparently have not been published though they probably still
+exist in the banks' archives. The quotation is from Frederick G. Hall,
+_The Bank of Ireland 1783-1946_, Dublin, 1949. John Francis in his
+_History of the Bank of England_ (London, 1848, vol. 2, p. 232) wrote:
+"The new machinery for printing the notes, which was introduced by Mr.
+Oldham ... is well worthy of a visit, but would be uninteresting to
+delineate."]
+
+[Illustration: Figure 39.--_Top_, Original Oldham coupling built before
+1840, using a cross (instead of a center disk), as sketched by Robert
+Willis in personal copy of his _Principles of Mechanism_ (London, 1841,
+p. 167). _Bottom_, Oldham coupling as illustrated in Alexander B. W.
+Kennedy, _Kinematics of Machinery_, a translation of Franz Reuleaux'
+_Theoretische Kinematik_ (London, 1876, pp. 315-316).]
+
+The Geneva stop mechanism (fig. 40) was properly described by Willis as
+a device to permit less than a full revolution of the star wheel and
+thus to prevent overwinding of a watch spring. It was called Geneva stop
+because it was used in Geneva watches. The Geneva wheel mechanism, which
+permits full rotation of the star wheel and which is frequently used
+for intermittent drives, was improperly called a Geneva stop in a
+recent textbook probably because the logical origin of the term had been
+lost.
+
+[Illustration: Figure 40.--Geneva stop mechanism first used in Geneva
+watches to prevent overwinding. The starwheel B had one convex surface
+(_g-f_, dotted) so the wheel could be turned less than a full
+revolution. After Robert Willis, _Principles of Mechanism_ (London,
+1841, p. 266).]
+
+The name for the Scotch yoke seems to be of fairly recent origin, the
+linkage being called by a Scotsman in 1869 a "crank and slot-headed
+sliding rod" (fig. 41). I suppose that it is now known as a Scotch yoke
+because, in America at least, a "Scotch" was a slotted bar that was
+slipped under a collar on a string of well-drilling tools to support
+them while a section was being added (fig. 42).
+
+[Illustration: Figure 41.--Scotch yoke, described as a "crank and
+slot-headed sliding rod." From W. J. M. Rankine, _A Manual of Machinery
+and Millwork_ (ed. 6, London, 1887, p. 169).]
+
+[Illustration: Figure 42.--A "Scotch" supporting the top member of a
+string of well-drilling tools while a section is being added, 1876. From
+Edward H. Knight, _Knight's American Mechanical Dictionary_ (New York,
+1876, p. 2057).]
+
+It was surprising to me to find that the Ackermann steering linkage,
+used today on most automobiles, was patented in 1818 when Detroit was
+still a frontier town.[107] Furthermore, the man who took out the patent
+described himself as Rudolph Ackermann, publisher and printseller. I
+thought I had the necessary clue to the linkage's origin when I noticed
+that the first English translation of the Lanz and Bétancourt treatise
+was published by Ackermann, but the connection finally proved to be more
+logical, if less direct. Ackermann (1764-1834), son of a Bavarian coach
+builder, had spent a number of years designing coaches for English
+gentlemen in London, where he made his home. One of his more notable
+commissions was for the design of Admiral Nelson's funeral car in 1805.
+The Ackermann steering linkage was not actually Ackermann's invention,
+although he took out the British patent in his name and promoted the
+introduction of the running gear of which the linkage was a part (fig.
+43). The actual inventor was Ackermann's friend George Lankensperger of
+Munich, coachmaker to the King of Bavaria. The advantage of being able
+to turn a carriage around in a limited area without danger of
+oversetting was immediately obvious, and while there was considerable
+opposition by English coachmakers to an innovation for which a premium
+had to be paid, the invention soon "made its way from its own intrinsic
+merit," as Ackermann predicted it would.[108]
+
+[Footnote 107: British Patent 4212, January 27, 1818.]
+
+[Footnote 108: Rudolph Ackermann, _Observations on Ackermann's Patent
+Moveable Axles_, London, 1819. It was interesting to me to note an
+abstract of W. A. Wolfe's paper "Analytical Design of an Ackermann
+Steering Linkage" in _Mechanical Engineering_, September 1958, vol. 80,
+p. 92.]
+
+[Illustration: Figure 43.--Ackermann steering linkage of 1818, currently
+used in automobiles. This linkage was invented by George Lankensperger,
+coachmaker to the King of Bavaria. From _Dinglers Polytechnisches
+Journal_ (1820, vol. 1, pl. 7).]
+
+The Whitworth quick-return mechanism (fig. 44) was first applied to a
+slotter, or vertical shaper, in 1849, and was exhibited in 1851 at the
+Great Exhibition in London.[109] Willis' comments on the mechanism are
+reproduced in figure 44. I hope that Sir Joseph Whitworth (1803-1887)
+will be remembered for sounder mechanical contrivances than this.
+
+[Footnote 109: The quick-return mechanism (British Patent 12907,
+December 19, 1849) was perhaps first publicly described in Charles
+Tomlinson, ed., _Cyclopaedia of Useful Arts and Manufactures_, London,
+1854, vol. 1, p. cxliv.]
+
+[Illustration: Figure 44.--Quick-return mechanism. _Top_, Early
+representation of the quick-return mechanism patented by Whitworth in
+1849, from William Johnson, ed., _The Imperial Cyclopaedia of machinery_
+(Glasgow, about 1855, pl. 88). _Middle_, Sketch by Robert Willis from
+his copy of _Principles of Mechanism_ (London, 1841, p. 264), which
+"shews Whitworth dissected into a simpler form"; it is as obscure as
+most subsequent attempts have been to explain this mechanism without a
+schematic diagram. _Bottom_, Linkage that is kinematically equivalent to
+Whitworth's, from Robert Willis, _Principles of Mechanism_ (London,
+1841, p. 264).]
+
+
+Mechanisms in America, 1875-1955
+
+Engineering colleges in the United States were occupied until the late
+1940's with extending, refining, and sharpening the tools of analysis
+that had been suggested by Willis, Rankine, Reuleaux, Kennedy, and
+Smith. The actual practice of kinematic synthesis went on apace, but
+designers often declined such help as the analytical methods might give
+them and there was little exchange of ideas between scholars and
+practitioners.
+
+The capability and precision of machine tools were greatly enhanced
+during this period, although, with the exception of the centerless
+grinder, no significant new types of tools appeared. The machines that
+were made with machine tools increased in complexity and, with the
+introduction of ideas that made mass production of complex mechanical
+products economically feasible, there was an accelerating increase in
+quantity. The adoption of standards for all sorts of component parts
+also had an important bearing upon the ability of a designer
+economically to produce mechanisms that operated very nearly as he hoped
+they would.
+
+The study of kinematics has been considered for nearly 80 years as a
+necessary part of the mechanical engineer's training, as the dozens of
+textbooks that have been published over the years make amply clear.
+Until recently, however, one would look in vain for original work in
+America in the analysis or rational synthesis of mechanisms.
+
+One of the very earliest American textbooks of kinematics was the 1883
+work of Charles W. MacCord (1836-1915), who had been appointed professor
+of mechanical drawing at Stevens Institute of Technology in Hoboken
+after serving John Ericsson, designer of the _Monitor_, as chief
+draftsman during the Civil War.[110] Based upon the findings of Willis
+and Rankine, MacCord's _Kinematics_ came too early to be influenced by
+Kennedy's improvements upon Reuleaux's work.
+
+[Footnote 110: A biographical notice and a bibliography of MacCord
+appears in _Morton Memorial: A History of the Stevens Institute of
+Technology_, Hoboken, 1905, pp. 219-222.]
+
+When the faculty at Washington University in St. Louis introduced in
+1885 a curriculum in "dynamic engineering," reflecting a
+dissatisfaction with the traditional branches of engineering, kinematics
+was a senior subject and was taught from Rankine's _Machinery and
+Millwork_.[111]
+
+[Footnote 111: _Transactions of the American Society of Mechanical
+Engineers_, 1885-1886, vol. 7, p. 757.]
+
+At Massachusetts Institute of Technology, Peter Schwamb, professor of
+machine design, put together in 1885 a set of printed notes on the
+kinematics of mechanisms, based on Reuleaux's and Rankine's works. Out
+of these notes grew one of the most durable of American textbooks, first
+published in 1904.[112] In the first edition of this work, acceleration
+was mentioned only once in passing (on p. 4). Velocities in linkages
+were determined by orthogonal components transferred from link to link.
+Instant centers were used only to determine velocities of various points
+on the same link. Angular velocity ratios were frequently noted. In the
+third edition, published in 1921, linear and angular accelerations were
+defined, but no acceleration analyses were made. Velocity analyses were
+altered without essential change. The fourth edition (1930) was
+essentially unchanged from the previous one. Treatment of velocity
+analysis was improved in the fifth edition (1938) and acceleration
+analysis was added. A sixth edition, further revised by Prof. V. L.
+Doughtie of the University of Texas, appeared in 1947.
+
+[Footnote 112: Peter Schwamb and Allyne L. Merrill, _Elements of
+Mechanism_, New York, 1904. In addition to the work of Reuleaux and
+Rankine, the authors acknowledged their use of the publications of
+Charles MacCord, Stillman W. Robinson, Thomas W. Goodeve, and William C.
+Unwin. For complete titles see the list of selected references.]
+
+Before 1900, several other books on mechanisms had been published, and
+all followed one or another of the patterns of their predecessors.
+Professors Woods and Stahl, at the Universities of Illinois and Purdue,
+respectively, who published their _Elementary Mechanism_ in 1885, said
+in their preface what has been said by many other American authors and
+what should have been said by many more. "We make little claim to
+originality of the subject-matter," wrote Woods and Stahl, "free use
+having been made of all available matter on the subject.... Our claim to
+consideration is based almost entirely on the manner in which the
+subject has been presented." Not content with this disclaimer, they
+continued: "There is, in fact, very little room for such originality,
+the ground having been almost completely covered by previous
+writers."[113]
+
+[Footnote 113: Arthur T. Woods and Albert W. Stahl, _Elementary
+Mechanism_, New York, 1885.]
+
+The similarity and aridity of kinematics textbooks in this country from
+around 1910 are most striking. The generation of textbook writers
+following MacCord, Woods and Stahl, Barr of Cornell, Robinson of Ohio
+State, and Schwamb and Merrill managed to squeeze out any remaining
+juice in the subject, and the dessication and sterilization of textbooks
+was nearly complete when my generation used them in the 1930's.
+Kinematics was then, in more than one school, very nearly as it was
+characterized by an observer in 1942--"on an intellectual par with
+mechanical drafting."[114] I can recall my own naïve belief that a
+textbook contained all that was known of the subject; and I was not
+disabused of my belief by my own textbook or by my teacher. I think I
+detect in several recent books a fresh, less final, and less tidy
+treatment of the kinematics of mechanisms, but I would yet recommend
+that anyone who thinks of writing a textbook take time to review,
+carefully and at first hand, not only the desk copies of books that he
+has accumulated but a score or more of earlier works, covering the last
+century at least. Such a study should result in a better appreciation of
+what constitutes a contribution to knowledge and what constitutes merely
+the ringing of another change.
+
+[Footnote 114: _Mechanical Engineering_, October 1942, vol. 64, p. 745.]
+
+The author of the contentious article that appeared in _Mechanical
+Engineering_ in 1942 under the title "What is Wrong with Kinematics and
+Mechanisms?" made several pronouncements that were questioned by various
+readers, but his remarks on the meagerness of the college courses of
+kinematics and the "curious fact" that the textbooks "are all strangely
+similar in their incompleteness" went unchallenged and were, in fact,
+quite timely.[115]
+
+[Footnote 115: De Jonge, _op. cit._ (footnote 78).]
+
+It appears that in the early 1940's the general classroom treatment of
+accelerations was at a level well below the existing knowledge of the
+subject, for in a series of articles by two teachers at Purdue attention
+was called to the serious consequences of errors in acceleration
+analysis occasioned by omitting the Coriolis component.[116] These
+authors were reversing a trend that had been given impetus by an article
+written in 1920 by one of their predecessors, Henry N. Bonis. The
+earlier article, appearing in a practical-and-proud-of-it technical
+magazine, demonstrated how the acceleration of a point on a flywheel
+governor might be determined "without the use of the fictitious
+acceleration of Coriolis." The author's analysis was right enough, and
+he closed his article with the unimpeachable statement that "it is
+better psychologically for the student and practically for the engineer
+to understand the fundamentals thoroughly than to use a complex formula
+that may be misapplied." However, many readers undoubtedly read only the
+lead paragraph, sagely nodded their heads when they reached the word
+"fictitious," which confirmed their half-formed conviction that anything
+as abstruse as the Coriolis component could have no bearing upon a
+practical problem, and turned the page to the "practical kinks"
+section.[117]
+
+[Footnote 116: A. S. Hall and E. S. Ault, "How Acceleration Analysis Can
+Be Improved," _Machine Design_, February 1943, vol. 15, pp. 100-102,
+162, 164; and March 1943, vol. 15, pp. 90-92, 168, 170. See also A. S.
+Hall, "Teaching Coriolis' Law," _Journal of Engineering Education_, June
+1948, vol. 38, pp. 757-765.]
+
+[Footnote 117: Henry N. Bonis, "The Law of Coriolis," _American
+Machinist_, November 18, 1920, vol. 53, pp. 928-930. See also
+"Acceleration Determinations," _American Machinist_, November 25 and
+December 2, 1920, vol. 53, pp. 977-981 and 1027-1029.]
+
+Less than 20 years ago one might have read in _Mechanical Engineering_
+that "Practical machinery does not originate in mathematical formulas
+nor in beautiful vector diagrams." While this remark was in a letter
+evoked by an article, and was not a reflection of editorial policy, it
+was nevertheless representative of an element in the American tradition
+of engineering. The unconscious arrogance that is displayed in this
+statement of the "practical" designer's creed is giving way to
+recognition of the value of scholarly work. Lest the scholar develop
+arrogance of another sort, however, it is well to hear the author of
+the statement out. "A drafting machine is a useful tool," he wrote. "It
+is not a substitute for a draftsman."[118]
+
+[Footnote 118: _Mechanical Engineering_, October 1942, vol. 64, p. 746.]
+
+The scholarly interest in a subject is fairly represented by the papers
+that are published in the transactions of professional societies and,
+more recently, by original papers that appear in specialized magazines.
+From 1900 to 1930 there were few papers on mechanisms, and most of those
+that did appear were concerned with descriptions of new "mechanical
+motions." In the 1930's the number of papers reported in _Engineering
+Index_ increased sharply, but only because the editors had begun to
+include foreign-language listings.
+
+There has been in Germany a thread of continuity in the kinematics of
+mechanisms since the time of Reuleaux. While most of the work has had to
+do with analysis, the teasing question of synthesis that Reuleaux raised
+in his work has never been ignored. The developments in Germany and
+elsewhere have been ably reviewed by others,[119] and it is only to be
+noted here that two of the German papers, published in 1939 in
+_Maschinenbau_, appear to have been the sparks for the conflagration
+that still is increasing in extent and intensity. According to summaries
+in _Engineering Index_, R. Kraus, writing on the synthesis of the
+double-crank mechanism, drew fire from the Russian Z. S. Bloch, who, in
+1940, discussed critically Kraus's articles and proceeded to give the
+outline of the "correct analysis of the problem" and a general numerical
+solution for the synthesis of "any four-bar linkage."[120] Russian work
+in mechanisms, dating back to Chebyshev and following the "Chebyshev
+theory of synthesis" in which algebraic methods are used to determine
+paths of minimum deviation from a given curve, has also been reviewed
+elsewhere,[121] and I can add nothing of value.
+
+[Footnote 119: Grodzinski, Bottema, De Jonge, and Hartenberg and
+Denavit. For complete titles see list of selected references.]
+
+[Footnote 120: My source, as noted, is _Engineering Index_. Kraus's
+articles are reported in 1939 and Bloch's in 1940, both under the
+section heading "Mechanisms."]
+
+[Footnote 121: A. E. Richard de Jonge, "Are the Russians Ahead in
+Mechanism Analysis?" _Machine Design_, September 1951, vol. 23, pp. 127,
+200-208; O. Bottema, "Recent Work on Kinematics," _Applied Mechanics
+Reviews_, April 1953, vol. 6, pp. 169-170.]
+
+When, after World War II, some of the possibilities of kinematic
+synthesis were recognized in the United States, a few perceptive
+teachers fanned the tinder into an open flame.
+
+The first publication of note in this country on the synthesis of
+linkages was a practical one, but in conception and undertaking it was a
+bold enterprise. In a book by John A. Hrones and G. L. Nelson,
+_Analysis of the Four Bar Linkage_ (1951), the four-bar crank-and-rocker
+mechanism was exhaustively analyzed mechanically and the results were
+presented graphically. This work was faintly praised by a Dutch scholar,
+O. Bottema, who observed that the "complicated analytical theory of the
+three-bar [sic] curve has undoubtedly kept the engineer from using it"
+and who went on to say that "we fully understand the publication of an
+atlas by Hrones and Nelson containing thousands of trajectories which
+must be very useful in many design problems."[122] Nevertheless, the
+authors furnished designers with a tool that could be readily, almost
+instantly, understood (fig. 45), and the atlas has enjoyed wide
+circulation.[123] The idea of a geometrical approach to synthesis has
+been exploited by others in more recent publications,[124] and it is
+likely that many more variations on this theme will appear.
+
+[Footnote 122: Bottema, _op. cit._ (footnote 121).]
+
+[Footnote 123: In 1851 Robert Willis had designed a coupler-point
+path-generating machine (fig. 46) that could have been used to produce a
+work similar to that of Hrones and Nelson.]
+
+[Footnote 124: R. S. Hartenberg and J. Denavit, "Systematic Mechanism
+Design," _Machine Design_, September 1954, vol. 26, pp. 167-175, and
+October 1954, vol. 26, pp. 257-265; A. S. Hall, A. R. Holowenko, and H.
+G. Laughlin, "Four-Bar Lever Crank Mechanism," _Design News_, September
+15, 1957, vol. 12, pp. 130-139, October 1, 1957, vol. 12, pp. 145-154,
+and October 15, 1957, vol. 12, pp. 132-141. For a nomographic approach,
+with particular application to computers, see Antonin Svoboda,
+_Computing Mechanisms and Linkages_, New York, 1948.]
+
+[Illustration: Figure 45.--Paths of 11 points on the coupler
+(horizontal) link are plotted through one cycle. Dashes indicate equal
+time intervals. From John A. Hrones and G. L. Nelson, _Analysis of the
+Four Bar Linkage_ (New York, 1951, p. 635).]
+
+[Illustration: Figure 46.--Coupler-point path-generating machine for
+four-bar linkage. This device, built by Professor Willis as a teaching
+aid for demonstrating straight-line linkages, could have been adapted to
+produce a plate like the one shown in figure 45. From Robert Willis, _A
+System of Apparatus for the Use of Lecturers and Experimenters_ ...
+(London 1851, pl. 3).]
+
+Pursuit of solutions to the "complicated analytical theory" of linkages
+was stimulated by publication of Ferdinand Freudenstein's "Analytical
+Approach to the Design of Four-Link Mechanisms" in 1954,[125] and an
+increasing interest in the problem is indicated by the extensive
+literature that has appeared in the last five years.
+
+[Footnote 125: _Transactions of the American Society of Mechanical
+Engineers_, 1954, vol. 76, pp. 483-492. See also _Transactions of the
+American Society of Mechanical Engineers_, 1955, vol. 77, pp. 853-861,
+and 1956, vol. 78, pp. 779-787.]
+
+The proper role of rational methods in the synthesis of mechanisms is
+not yet clear. "While we may talk about kinematic synthesis," wrote two
+of today's leaders in the field, "we are really talking about a hope for
+the future rather than a great reality of the present."[126] When the
+mental equipment and the enthusiasm of scholars who are devoting their
+time to the problems of kinematic synthesis are considered, however, it
+is difficult to see how important new ideas can fail to be produced.
+
+[Footnote 126: R. S. Hartenberg and J. Denavit, "Kinematic Synthesis,"
+_Machine Design_, September 6, 1956, vol. 28, pp. 101-105.]
+
+An annual Conference on Mechanisms, sponsored by Purdue University and
+_Machine Design_, was inaugurated in 1953 and has met with a lively
+response. Among other manifestations of current interest in mechanisms,
+the contributions of Americans to international conferences on
+mechanisms reflects the growing recognition of the value of scholarly
+investigation of the kind that can scarcely hope to yield immediately
+tangible results.
+
+While we look to the future, one may ask how a lengthy view of the past
+can be justified. It seems to me that there is inherent in the almost
+feverish activity of the present the danger of becoming so preoccupied
+with operational theory that the goals may become clouded and the
+synthesis (let us put it less elegantly: the design) of mechanisms may
+never quite come into focus. If one knows nothing of the past, I wonder
+how he can with any confidence decide in what direction he must turn in
+order to face the future.
+
+
+Acknowledgment
+
+I am grateful to Professors Richard S. Hartenberg and Allen S. Hall,
+Jr., for reading the manuscript, making helpful comments, and suggesting
+material that I had not found. The errors, however, are mine.
+
+
+Additional References
+
+The following list of additional reference material on kinematics may be
+of help to readers who desire to do independent research. The material
+is listed according to the section headings in the text of the present
+article.
+
+
+TO DRAW A STRAIGHT LINE
+
+KEMPE, A. B. _How to Draw a Straight Line._ London, 1877.
+
+Contains a useful bibliography. Reprinted in _Squaring the Circle and
+Other Monographs_, New York, Chelsea Publishing Company, 1953.
+
+Much attention has been given to straight-line mechanisms since the time
+of Kempe; at least a half dozen articles have appeared in the United
+States since 1950, but I did not investigate the literature published
+after 1877.
+
+
+SCHOLARS AND MACHINES
+
+BECK, THEODOR. _Beiträge zur Geschichte des Maschinenbaues._ Berlin,
+1899.
+
+Reviews of early works, such as those by Leonardo da Vinci, Biringuccio,
+Besson, Zonca, etc.
+
+BORGNIS, GIUSEPPE ANTONIO. _Traité complet de mécanique appliquée aux
+arts._ Paris, 1818-1821, 9 vols.
+
+Contains several hundred finely detailed plates of machines.
+
+LABOULAYE, CHARLES. _Traité de cinématique ou théorie des mécanismes._
+Paris, 1861 (ed. 2).
+
+This work was quoted frequently by Laboulaye's contemporaries.
+
+ROYAL SOCIETY OF LONDON. _Catalogue of Scientific Papers, 1800-1900,
+Author Index._ London, 1867-1902, and Cambridge, 1914-1925.
+
+----. _Catalogue of Scientific Papers, 1800-1900, Subject Index._
+London, 1909, vol. 2.
+
+This subject index was started in 1908, and by 1914 three volumes (the
+third in two parts) had been published; however, this subject index was
+never completed. Volume 2, titled _Mechanics_, has some 200 entries
+under "Linkages." It is interesting to note that both of the Royal
+Society's monumental catalogs grew out of a suggestion made by Joseph
+Henry at a British Association meeting in Glasgow in 1855.
+
+WEISBACH, JULIUS. _The Mechanics of the Machinery of Transmission_, vol.
+3, pt. 1, sec. 2 of _Mechanics of Engineering and Machinery_, translated
+by J. F. Klein. New York, 1890 (ed. 2).
+
+
+MECHANISMS AND MECHANICIANS
+
+BARBER, THOMAS W. _Engineer's Sketch-Book._ London, 1890 (ed. 2).
+
+HERKIMER, HERBERT. _Engineer's Illustrated Thesaurus._ New York, 1952.
+
+PERIODICALS. _Artizan_, from 1843; _Practical Mechanic and Engineer's
+Magazine_, from 1841; _Repertory of Arts and Manufactures_, from 1794;
+_Newton's London Journal of Arts and Science_, from 1820. (The preceding
+periodicals have many plates of patent specification drawings.) _The
+Engineer_, November 10, 1933, vol. 156, p. 463, and _Engineering_,
+November 10, 1933, vol. 136, p. 525. (Recent English views questioning
+the utility of kinematics.)
+
+TATE, THOMAS. _Elements of Mechanism._ London, 1851.
+
+Contains figures from Lanz and Bétancourt (1808).
+
+WYLSON, JAMES. _Mechanical Inventor's Guide._ London, 1859.
+
+Contains figures from Henry Adcock, _Adcock's Engineers' Pocket-Book,
+1858_.
+
+
+MECHANISMS IN AMERICA, 1875-1955
+
+ALBERT, CALVIN D., AND ROGERS, F. D. _Kinematics of Machinery._ New
+York, 1931.
+
+Contains a bibliography that includes works not mentioned in the present
+paper.
+
+BARR, JOHN H. _Kinematics of Machinery._ New York, 1899.
+
+An early textbook. The author taught at Cornell University.
+
+BEGGS, JOSEPH S. _Mechanism._ New York, 1955.
+
+Contains an extensive and useful bibliography.
+
+BOTTEMA, O. "Recent Work on Kinematics," _Applied Mechanics Reviews_,
+April 1953, vol. 6, pp. 169-170.
+
+
+CONFERENCE ON MECHANISMS.
+
+This conference was sponsored by Purdue University and _Machine Design_.
+Transactions of the first two conferences appeared as special sections
+in _Machine Design_, December 1953, vol. 25, pp. 173-220, December 1954,
+vol. 26, pp. 187-236, and in collected reprints. Papers of the third and
+fourth conferences (May 1956 and October 1957) appeared in _Machine
+Design_ over several months following each conference and in collected
+reprints. Papers of the fifth conference (October 1958) were collected
+and preprinted for conference participants; subsequently, all papers
+appeared in _Machine Design_. Collected reprints and preprints are
+available (May 1960) from Penton Publishing Company, Cleveland, Ohio.
+
+DE JONGE, A. E. RICHARD. "Kinematic Synthesis of Mechanisms,"
+_Mechanical Engineering_, July 1940, vol. 62, pp. 537-542.
+
+----. "A Brief Account of Modern Kinematics," _Transactions of the
+American Society of Mechanical Engineers_, 1943, vol. 65, pp. 663-683.
+
+GOODEVE, THOMAS M. _The Elements of Mechanism._ London, 1903.
+
+An early textbook.
+
+GRODZINSKI, PAUL, AND MCEWEN, EWEN. "Link Mechanisms in Modern
+Kinematics," _Journal and Proceedings of the Institution of Mechanical
+Engineers_, 1954, vol. 168, pp. 877-896.
+
+This article evoked interesting discussion. It is unfortunate that
+Grodzinski's periodical, _Mechanism, An International Bibliography_,
+which was published in London in 1956-1957 and which terminated shortly
+after his death, has not been revived. Grodzinski's incisive views and
+informative essays are valuable and interesting.
+
+HARTENBERG, R. S. "Complex Numbers and Four-Bar Linkages," _Machine
+Design_, March 20, 1958, vol. 30, pp. 156-163.
+
+This is an excellent primer. The author explains complex numbers in his
+usual lucid fashion.
+
+HARTENBERG, R. S., AND DENAVIT, J. "Kinematic Synthesis," _Machine
+Design_, September 6, 1956, vol. 28, pp. 101-105.
+
+MACCORD, CHARLES. _Kinematics._ New York, 1883.
+
+An early textbook.
+
+ROBINSON, STILLMAN W. _Principles of Mechanism._ New York, 1896.
+
+An early textbook. The author taught at Ohio State University.
+
+UNWIN, WILLIAM C. _The Elements of Machine Design._ New York, 1882 (ed.
+4).
+
+An early textbook. The author taught at Royal Indian Engineering
+College, in England.
+
+
+GOVERNMENT PRINTING OFFICE: 1962
+
+For sale by the Superintendent of Documents, U.S. Government Printing
+Office Washington 25, D. C.--Price 40 cents
+
+
+
+
+
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+      The Project Gutenberg eBook of Kinematics Of Mechanisms From The Time Of Watt, by Eugene S. Ferguson.
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+<pre>
+
+The Project Gutenberg EBook of Kinematics of Mechanisms from the Time of
+Watt, by Eugene S. Ferguson
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Kinematics of Mechanisms from the Time of Watt
+
+Author: Eugene S. Ferguson
+
+Release Date: October 31, 2008 [EBook #27106]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK KINEMATICS OF MECHANISMS ***
+
+
+
+
+Produced by Chris Curnow, Viv, Joseph Cooper and the Online
+Distributed Proofreading Team at http://www.pgdp.net
+
+
+
+
+
+
+</pre>
+
+
+
+
+<h1>CONTRIBUTIONS FROM</h1>
+
+<h1>THE MUSEUM OF HISTORY AND TECHNOLOGY</h1>
+
+<h1>PAPER 27</h1>
+
+
+
+<p class="figcenter"><img alt="Front Cover: Paper 27, pages 185-230, from Contributions from the Museum of History and Technology, United States
+National Museum, Bulletin 228, Smithsonian Institution, Washington, D.C., 1962"
+  src="images/icover.jpg" width="500" height="631" /></p>
+<h2>KINEMATICS OF MECHANISMS FROM THE TIME OF WATT</h2>
+
+<p class="textright"><em>Eugene S. Ferguson</em></p>
+<h3>Contents</h3>
+
+<table style="width: 100%" id="table1" summary="Contents">
+	<tr>
+		<td><a href="#James_Watt_Kinematic_Synthesist">JAMES WATT, KINEMATIC SYNTHESIST</a></td>
+		<td>187</td>
+	</tr>
+	<tr>
+		<td><a href="#To_Draw_a_Straight_Line">TO DRAW A STRAIGHT LINE</a></td>
+		<td>199</td>
+	</tr>
+	<tr>
+		<td><a href="#Scholars_and_Machines">SCHOLARS AND MACHINES</a></td>
+		<td>209</td>
+	</tr>
+	<tr>
+		<td><a href="#Mechanicians_and_Mechanisms">MECHANICIANS AND MECHANISMS</a></td>
+		<td>216</td>
+	</tr>
+	<tr>
+		<td><a href="#Mechanisms_in_America_1875-1955">MECHANISMS IN AMERICA, 1875-1955</a></td>
+		<td>223</td>
+	</tr>
+	<tr>
+		<td><a href="#Additional_References">ADDITIONAL REFERENCES</a></td>
+		<td>229</td>
+	</tr>
+</table>
+
+
+<hr style="width: 65%;" />
+<h2><a name="KINEMATICS_OF_MECHANISMS_FROM_THE_TIME_OF_WATT" id="KINEMATICS_OF_MECHANISMS_FROM_THE_TIME_OF_WATT"></a>
+KINEMATICS OF MECHANISMS FROM THE TIME OF WATT</h2>
+
+
+<p><em>In an inventive tour de force that seldom, if ever, has been equalled
+for its brilliance and far-reaching consequences, James Watt radically altered
+the steam engine not only by adding a separate condenser but by creating a whole
+new family of linkages. His approach was largely empirical, as we use the word
+today.</em></p>
+
+<p><em>This study suggests that, despite the glamor of today's sophisticated
+methods of calculation, a highly developed intuitive sense, reinforced by a
+knowledge of the past, is still indispensable to the design of successful
+mechanisms.</em></p>
+
+<p>THE AUTHOR: <em>Eugene S. Ferguson, formerly curator of mechanical and civil
+engineering in the United States National Museum, Smithsonian Institution, is
+now professor of mechanical engineering at Iowa State University of Science and
+Technology.</em></p>
+
+<p>In engineering schools today, a student is introduced to the kinematics of
+mechanisms by means of a course of kinematic analysis, which is concerned with
+principles underlying the motions occurring in mechanisms. These principles are
+demonstrated by a study of mechanisms already in existence, such as the linkage
+of a retractable landing gear, computing mechanisms, mechanisms used in an
+automobile, and the like. A systematic, if not rigorous, approach to the design
+of gears and cams also is usually presented in such a course. Until recently,
+however, no serious attempt was made to apply the principles developed in
+kinematic analysis to the more complex problem of kinematic synthesis of
+linkages. By kinematic synthesis is meant the designing of a linkage to produce
+a given series of motions for a particular purpose.</p>
+
+<p>That a rational&#8212;numerical or geometrical&#8212;approach to kinematic synthesis is
+possible is a relatively recent idea, not yet fully accepted; but it is this
+idea that is responsible for the intense scholarly interest in the kinematics of
+mechanisms that has occurred in this country within the last 10 years.</p>
+
+<p>This scholarly activity has resulted in the rediscovery of many earlier works
+on the subject, and nearly all the scholars now working in this field have
+acknowledged in one way or another their debt to those who arrived on the scene
+at an earlier time than they. There have been occasional reviews of the sequence
+and nature of developments, but the emphasis naturally has been upon the recent
+past. It seems to me that there is something to be gained in looking beyond our
+own generation, or even beyond the time of Franz Reuleaux (1829-1905), who is
+generally credited with originating many of our modern concepts of mechanism
+analysis and design, and to inquire into the ideas that made possible Reuleaux's
+contributions.</p>
+
+<div class="quotation">
+<p><span style="margin-left: 2.5em;"><em>Take to Kinematics. It will repay you. It is
+more fecund than geometry; it adds a fourth dimension to
+space.</em></span><br /></p>
+
+<p><span style="margin-left: 2.5em;">&#8212;Chebyshev to Sylvester, 1873</span><br /></p>
+</div>
+
+<p>While no pretense of completeness is made, I have tried in this paper to
+trace the high points in the development of kinematic analysis and synthesis,
+both in academic circles and in the workshop, noting where possible the
+influence of one upon the other. If I have devoted more space to particular
+people and episodes than is warranted by their contributions to the modern
+treatment of the subject, it is because I have found that the history of
+kinematics of mechanisms, like the history of any other branch of engineering,
+is more interesting and more plausible if it is recognized that its evolutionary
+development is the result of human activity. This history was wrought by people
+like us, no less intelligent and no less subject than we are to environment, to
+a subjective way of looking at things, and to a heritage of ideas and beliefs.</p>
+
+<p>I have selected the period from the time of Watt because modern mechanisms
+originated with him, and I have emphasized the first century of the period
+because by 1885 many of the ideas of modern kinematics of mechanisms were well
+developed. Linkages are discussed, to the virtual exclusion of gears and cams,
+because much of the scholarly work in kinematic synthesis is presently directed
+toward the design of linkages and because linkages provide a convenient thread
+for a narrative that would have become unnecessarily complex if detailed
+treatment of gears and cams had been included. I have brought the narrative down
+to the present by tracing kinematics as taught in American engineering schools,
+closing with brief mention of the scholarly activity in kinematics in this
+country since 1950. An annotated list of additional references is appended as an
+encouragement to further work in the history of the subject.</p>
+
+
+<h3><a name="James_Watt_Kinematic_Synthesist">James Watt, Kinematic Synthesist</a></h3>
+
+<p>James Watt (1736-1819), improver of the steam engine, was a highly gifted
+designer of mechanisms, although his background included no formal study of
+mechanisms. Indeed, the study of mechanisms, without immediate regard to the
+machines in which they were used, was not introduced until after Watt's
+important work had been completed, while the actual design of mechanisms had
+been going on for several centuries before the time of Watt.</p>
+
+<p>Mechanisms that employed screws, cams, and gears were certainly in use by the
+beginning of the Christian era. While I am not aware of unequivocal evidence of
+the existence of four-bar linkages before the 16th century, their widespread
+application by that time indicates that they probably originated much earlier. A
+tantalizing 13th-century sketch of an up-and-down sawmill (fig. 1) suggests, but
+does not prove, that the four-bar linkage was then in use. Leonardo da Vinci
+(1452-1519) delineated, if he did not build, a crank and slider mechanism, also
+for a sawmill (fig. 2). In the 16th century may be found the conversion of
+rotary to reciprocating motion (strictly speaking, an oscillation through a
+small arc of a large circle) and vice versa by use of linkages of rigid members
+(figs. 3 and 4), although the conversion of rotary to reciprocating motion was
+at that time more frequently accomplished by cams and intermittent gearing.
+Nevertheless, the idea of linkages was a firmly established part of the
+repertory of the machine builder before 1600. In fact one might have wondered in
+1588, when Agostino Ramelli published his book on machines,<a name="FNanchor_1_1" id="FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a>
+whether linkages had not indeed reached their ultimate stage of development. To
+illustrate my point, I have selected the plate of Ramelli that most appeals to
+me (fig. 5), although the book exhibits more than 200 other machines of
+comparable complexity and ingenuity.</p>
+
+<div class="footnote"><p><a name="Footnote_1_1" id="Footnote_1_1"></a><a href="#FNanchor_1_1"><span class="label">
+	[1]</span></a> Agostino Ramelli, <em>Le Diverse et Artificiose Machine</em>, Paris,
+	1588.</p></div>
+
+<p class="center">
+<img alt="Figure 1" src="images/fig-01.jpg" width="500" height="435" /></p>
+<p>Figure 1.&#8212;Up-and-down sawmill of the 13th century. The guide
+mechanism at lower left, attached to the saw blade, appears to be a 4-bar
+linkage. After Robert Willis, trans. and ed., <em>Facsimile of the Sketch-Book
+of Wilars de Honecort</em> (London, 1859, pl. 43).</p>
+<p class="center">
+<img alt="Figure 2" src="images/fig-02.jpg" width="171" height="631" /></p>
+
+<p>Figure 2.&#8212;Slider-crank mechanism of Leonardo da Vinci
+(1452-1519), redrawn from his manuscript notebooks. A frame saw is depicted at
+the lower end of the guides. From Theodor Beck, <em>Beiträge zur Geschichte des
+Maschinenbaues</em> (Berlin, 1899, p. 323).</p>
+<p class="center">
+<img alt="Figure 3" src="images/fig-03.jpg" width="500" height="334" /></p>
+
+<p>Figure 3.&#8212;Blowing engine by Vanuccio Biringuccio, about 1540,
+showing conversion of motion of the waterwheel shaft from rotation to
+oscillation. From Theodor Beck, <em>Beiträge zur Geschichte des Maschinenbaues</em>
+(Berlin, 1899. p. 120).</p>
+<p class="center">
+<img alt="Figure 4" src="images/fig-04.jpg" width="400" height="451" /></p>
+
+<p>Figure 4.&#8212;Grain mill, 1588, showing conversion of motion of
+the operating bars from oscillation to rotation. Note the fly-weights,
+predecessors of the flywheel. From Agostino Ramelli, <em>Le Diverse et
+Artificiose Machine</em> (Paris, 1588, pl. opposite p. 199).</p>
+<p class="center">
+<img alt="Figure 5" src="images/fig-05.jpg" width="500" height="332" /></p>
+
+<p>Figure 5.&#8212;Machine for raising water. Such a machine was built
+in Spain during the 16th century and was operated for some 80 years. From Agostino Ramelli, <em>Le Diverse et Artificiose Machine</em>
+(Paris, 1588, p. 199).</p>
+
+<p>There was a vast difference, both in conception and execution, between the
+linkages of Ramelli and those of James Watt some 200 years later. Watt was
+responsible for initiating profound changes in mechanical technology, but it
+should be recognized that the mechanic arts had, through centuries of slow
+development, reached the stage where his genius could flourish. The knowledge
+and ability to provide the materials and tools necessary for Watt's researches
+were at hand, and through the optimism and patient encouragement of his partner,
+Matthew Boulton, they were placed at his disposal.</p>
+
+<p>Watt's genius was nowhere more evident than in his synthesis of linkages. An
+essential ingredient in the success of Watt's linkages, however, was his
+partner's appreciation of the entirely new order of refinement that they called
+for. Matthew Boulton, who had been a successful manufacturer of buttons and
+metal novelties long before his partnership with Watt was formed, had recognized
+at once the need for care in the building of Watt's steam engine. On February 7,
+1769, he had written Watt:<a name="FNanchor_2_2" id="FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a>
+&quot;I presumed that your engine would require money, very accurate workmanship and
+extensive correspondence to make it turn out to the best advantage and that the
+best means of keeping up the reputation and doing the invention justice would be
+to keep the executive part of it out of the hands of the multitude of empirical
+engineers, who from ignorance, want of experience and want of necessary
+convenience, would be very liable to produce bad and inaccurate workmanship; all
+of which deficiencies would affect the reputation of the invention.&quot; Boulton
+expected to build the engines in his shop &quot;with as great a difference of
+accuracy as there is between the blacksmith and the mathematical instrument
+maker.&quot; The Soho Works of Boulton and Watt, in Birmingham, England, solved for
+Watt the problem of producing &quot;in great&quot; (that is, in sizes large enough to be
+useful in steam engines) the mechanisms that he devised.<a name="FNanchor_3_3" id="FNanchor_3_3"></a><a href="#Footnote_3_3" class="fnanchor">[3]</a></p>
+
+<div class="footnote"><p><a name="Footnote_2_2" id="Footnote_2_2"></a><a href="#FNanchor_2_2"><span class="label">
+	[2]</span></a> Henry W. Dickinson, <em>James Watt, Craftsman &amp; Engineer</em>,
+	Cambridge, Cambridge University Press, 1936, pp. 52-53.</p></div>
+
+<div class="footnote"><p><a name="Footnote_3_3" id="Footnote_3_3"></a><a href="#FNanchor_3_3"><span class="label">
+	[3]</span></a> James P. Muirhead, <em>The Origin and Progress of the
+	Mechanical Inventions of James Watt</em>, London, 1854, vol. 1, pp. 56, 64.
+	This work, in three volumes, contains letters, other documents, and plates
+	of patent specification drawings.</p></div>
+
+<p>The contributions of Boulton and Watt to practical mechanics &quot;in great&quot;
+cannot be overestimated. There were in the 18th century instrument makers and
+makers of timekeepers who had produced astonishingly accurate work, but such
+work comprised relatively small items, all being within the scope of a bench
+lathe, hand tools, and superb handwork. The rapid advancement of machine tools,
+which greatly expanded the scope of the machine-building art, began during the
+Boulton and Watt partnership (1775-1800).</p>
+
+<p>In April 1775 the skirmish at Concord between American colonists and British
+redcoats marked the beginning of a war that was to determine for the future the
+course of political events in the Western Hemisphere.</p>
+
+<p>Another event of April 1775 occurring in Birmingham now appears to have been
+one that marked the beginning of a new era of technological advance. It was near
+the end of this month that Boulton, at the Soho Works, wrote to his partner and
+commented upon receiving the cast iron steam engine cylinder that had been
+finished in John Wilkinson's boring mill:</p>
+
+<p><span style="margin-left: 2.5em;">... it seems tolerably true, but is an inch
+thick and weighs about</span><br />
+<span style="margin-left: 2.5em;">10 cwt. Its diameter is about as much above 18
+inches as the tin</span><br />
+<span style="margin-left: 2.5em;">one was under, and therefore it is become
+necessary to add a brass</span><br />
+<span style="margin-left: 2.5em;">hoop to the piston, which is made almost two
+inches broad.<a name="FNanchor_4_4" id="FNanchor_4_4"></a><a href="#Footnote_4_4" class="fnanchor">[4]</a></span><br />
+</p>
+
+<div class="footnote"><p><a name="Footnote_4_4" id="Footnote_4_4"></a><a href="#FNanchor_4_4"><span class="label">
+	[4]</span></a> <em>Ibid.</em>, vol. 2, p. 84.</p></div>
+
+<p>This cylinder indeed marked the turning point in the discouragingly long
+development of the Watt steam engine, which for 10 years had occupied nearly all
+of Watt's thoughts and all the time he could spare from the requirements of
+earning a living. Although there were many trials ahead for the firm of Boulton
+and Watt in further developing and perfecting the steam engine, the crucial
+problem of leakage of steam past the piston in the cylinder had now been solved
+by Wilkinson's new boring mill, which was the first large machine tool capable
+of boring a cylinder both round and straight.</p>
+
+<p>The boring mill is pertinent to the development of linkages &quot;in great,&quot; being
+the first of a new class of machine tools that over the next 50 or 60 years came
+to include nearly all of the basic types of heavy chip-removing tools that are
+in use today. The development of tools was accelerated by the inherent accuracy
+required of the linkages that were originated by Watt. Once it had been
+demonstrated that a large and complex machine, such as the steam engine, could
+be built accurately enough so that its operation would be relatively free of
+trouble, many outstanding minds became engaged in the development of machines
+and tools. It is interesting, however, to see how Watt and others grappled with
+the solutions of problems that resulted from the advance of the steam engine.</p>
+
+<p>During the 1770's the demand for continuous, dependable power applied to a
+rotating shaft was becoming insistent, and much of Boulton's and Watt's effort
+was directed toward meeting this demand. Mills of all kinds used water or horses
+to turn &quot;wheel-work,&quot; but, while these sources of power were adequate for small
+operations, the quantity of water available was often limited, and the use of
+enormous horse-whims was frequently impracticable.</p>
+
+<p>The only type of steam engine then in existence was the Newcomen beam engine,
+which had been introduced in 1712 by Thomas Newcomen, also an Englishman. This
+type of engine was widely used, mostly for pumping water out of mines but
+occasionally for pumping water into a reservoir to supply a waterwheel. It was
+arranged with a vertical steam cylinder located beneath one end of a large
+pivoted working beam and a vertical plunger-type pump beneath the other end.
+Heavy, flat chains were secured to a sector at each end of the working beam and
+to the engine and pump piston rods in such a way that the rods were always
+tangent to a circle whose center was at the beam pivot. The weight of the
+reciprocating pump parts pulled the pump end of the beam down; the atmosphere,
+acting on the open top of the piston in the steam cylinder, caused the engine
+end of the beam to be pulled down when the steam beneath the piston was
+condensed. The chains would of course transmit force from piston to beam only in
+tension.</p>
+
+<p>It is now obvious that a connecting rod, a crank, and a sufficiently heavy
+flywheel might have been used in a conventional Newcomen engine in order to
+supply power to a rotating shaft, but contemporary evidence makes it clear that
+this solution was by no means obvious to Watt nor to his contemporaries.</p>
+
+<p>At the time of his first engine patent, in 1769, Watt had devised a &quot;steam
+wheel,&quot; or rotary engine, that used liquid mercury in the lower part of a
+toroidal chamber to provide a boundary for steam spaces successively formed by
+flap gates within the chamber. The practical difficulties of construction
+finally ruled out this solution to the problem of a rotating power source, but
+not until after Boulton and Watt had spent considerable effort and money on it.<a name="FNanchor_5_5" id="FNanchor_5_5"></a><a href="#Footnote_5_5" class="fnanchor">[5]</a></p>
+
+<div class="footnote"><p><a name="Footnote_5_5" id="Footnote_5_5"></a><a href="#FNanchor_5_5"><span class="label">
+	[5]</span></a> Henry W. Dickinson and Rhys Jenkins, <em>James Watt and the
+	Steam Engine</em>, Oxford, Clarendon Press, 1927, pp. 146-148, pls. 14, 31. This
+	work presents a full and knowledgeable discussion, based on primary
+	material, of the development of Watt's many contributions to mechanical
+	technology. It is ably summarized in Dickinson, <em>op. cit.</em>
+	(footnote 2).</p></div>
+
+<p>In 1777 a speaker before the Royal Society in London observed that in order
+to obtain rotary output from a reciprocating steam engine, a crank &quot;naturally
+occurs in theory,&quot; but that in fact the crank is impractical because of the
+irregular rate of going of the engine and its variable length of stroke. He said
+that on the first variation of length of stroke the machine would be &quot;either
+broken to pieces, or turned back.&quot;<a name="FNanchor_6_6" id="FNanchor_6_6"></a><a href="#Footnote_6_6" class="fnanchor">[6]</a>
+John Smeaton, in the front rank of English steam engineers of his time, was
+asked in 1781 by His Majesty's Victualling-Office for his opinion as to whether
+a steam-powered grain mill ought to be driven by a crank or by a waterwheel
+supplied by a pump. Smeaton's conclusion was that the crank was quite unsuited
+to a machine in which regularity of operation was a factor. &quot;I apprehend,&quot; he
+wrote, &quot;that no motion communicated from the reciprocating beam of a fire engine
+can ever act perfectly equal and steady in producing a circular motion, like the
+regular efflux of water in turning a waterwheel.&quot; He recommended, incidentally,
+that a Boulton and Watt steam engine be used to pump water to supply the
+waterwheel.<a name="FNanchor_7_7" id="FNanchor_7_7"></a><a href="#Footnote_7_7" class="fnanchor">[7]</a>
+Smeaton had thought of a flywheel, but he reasoned that a flywheel large enough
+to smooth out the halting, jerky operation of the steam engines that he had
+observed would be more of an encumbrance than a pump, reservoir, and waterwheel.<a name="FNanchor_8_8" id="FNanchor_8_8"></a><a href="#Footnote_8_8" class="fnanchor">[8]</a></p>
+
+<div class="footnote"><p><a name="Footnote_6_6" id="Footnote_6_6"></a><a href="#FNanchor_6_6"><span class="label">
+	[6]</span></a> John Farey, <em>A Treatise on the Steam Engine</em>,
+	London, 1827, pp. 408-409.</p></div>
+
+<div class="footnote"><p><a name="Footnote_7_7" id="Footnote_7_7"></a><a href="#FNanchor_7_7"><span class="label">
+	[7]</span></a> <em>Reports of the Late John Smeaton, F.R.S.</em>, London,
+	1812, vol. 2, pp. 378-380.</p></div>
+
+<div class="footnote"><p><a name="Footnote_8_8" id="Footnote_8_8"></a><a href="#FNanchor_8_8"><span class="label">
+	[8]</span></a> Farey, <em>op. cit.</em> (footnote 6), p. 409.</p></div>
+
+<p>The simplicity of the eventual solution of the problem was not clear to Watt
+at this time. He was not, as tradition has it, blocked merely by the existence
+of a patent for a simple crank and thus forced to invent some other device as a
+substitute.</p>
+
+<p>Matthew Wasbrough, of Bristol, the engineer commonly credited with the crank
+patent, made no mention of a crank in his patent specification, but rather
+intended to make use of &quot;racks with teeth,&quot; or &quot;one or more pullies, wheels,
+segments of wheels, to which are fastened rotchets and clicks or palls....&quot; He
+did, however, propose to &quot;add a fly or flys, in order to render the motion more
+regular and uniform.&quot; Unfortunately for us, he submitted no drawings with his
+patent specification.<a name="FNanchor_9_9" id="FNanchor_9_9"></a><a href="#Footnote_9_9" class="fnanchor">[9]</a></p>
+
+<div class="footnote"><p><a name="Footnote_9_9" id="Footnote_9_9"></a><a href="#FNanchor_9_9"><span class="label">
+	[9]</span></a> British Patent 1213, March 10, 1779.</p></div>
+
+<p>James Pickard, of Birmingham, like Boulton, a buttonmaker, in 1780 patented a
+counterweighted crank device (fig. 6) that was expected to remove the objection
+to a crank, which operated with changing leverage and thus irregular power. In
+figure 6, the counterweighted wheel, revolving twice for each revolution of the
+crank (A), would allow the counterweight to descend while the crank passed the
+dead-center position and would be raised while the crank had maximum leverage.
+No mention of a flywheel was made in this patent.<a name="FNanchor_10_10" id="FNanchor_10_10"></a><a href="#Footnote_10_10" class="fnanchor">[10]</a></p>
+
+<div class="footnote"><p><a name="Footnote_10_10" id="Footnote_10_10"></a><a href="#FNanchor_10_10"><span class="label">
+	[10]</span></a> British Patent 1263, August 23, 1780.</p></div>
+
+<p class="center">
+<a href="images/big-fig-06.jpg"><img alt="Figure 6" src="images/fig-06.jpg" width="600" height="392" /></a></p>
+<p>Figure 6.&#8212;One of the steam engine &quot;Crank Patents&quot; that
+hindered James Watt's progress. This patent, granted to James Pickard in 1780,
+claimed only the arrangement of counterweights, not the crank. The crank pin to
+which the connecting rod was attached is at <em>Aa</em>. From British Patent
+1263, August 23, 1780.</p>
+
+<p>Wasbrough, finding that his &quot;rotchets and clicks&quot; did not serve, actually
+used, in 1780, a crank with a flywheel. Watt was aware of this, but he remained
+unconvinced of the superiority of the crank over other devices and did not
+immediately appreciate the regulating ability of a flywheel.<a name="FNanchor_11_11" id="FNanchor_11_11"></a><a href="#Footnote_11_11" class="fnanchor">[11]</a>
+In April 1781 Watt wrote to Boulton, who was then out of town: &quot;I know from
+experiment that the other contrivance, which you saw me try, performs at least
+as well, and has in fact many advantages over the crank.&quot;<a name="FNanchor_12_12" id="FNanchor_12_12"></a><a href="#Footnote_12_12" class="fnanchor">[12]</a>
+The &quot;other contrivance&quot; probably was his swash wheel which he built and which
+appeared on his next important patent specification (fig. 7a). Also in this
+patent were four other devices, one of which was easily recognizable as a crank,
+and two of which were eccentrics (fig. 7a, b). The fourth device was the
+well-known sun-and-planet gearing (fig. 7e).<a name="FNanchor_13_13" id="FNanchor_13_13"></a><a href="#Footnote_13_13" class="fnanchor">[13]</a>
+In spite of the similarity of the simple crank to the several variations devised
+by Watt, this patent drew no fire from Wasbrough or Pickard, perhaps because no
+reasonable person would contend that the crank itself was a patentable feature,
+or perhaps because the similarity was not at that time so obvious. However, Watt
+steered clear of directly discernible application of cranks because he preferred
+to avoid a suit that might overthrow his or other patents. For example, if the
+Wasbrough and Pickard patents had been voided, they would have become public
+property; and Watt feared that they might &quot;get into the hands of men more
+ingenious,&quot; who would give Boulton and Watt more competition than Wasbrough and
+Pickard.<a name="FNanchor_14_14" id="FNanchor_14_14"></a><a href="#Footnote_14_14" class="fnanchor">[14]</a></p>
+
+<div class="footnote"><p><a name="Footnote_11_11" id="Footnote_11_11"></a><a href="#FNanchor_11_11"><span class="label">
+	[11]</span></a> Dickinson and Jenkins, <em>op. cit.</em> (footnote 5), pp.
+	150, 154.</p></div>
+
+<div class="footnote"><p><a name="Footnote_12_12" id="Footnote_12_12"></a><a href="#FNanchor_12_12"><span class="label">
+	[12]</span></a> <em>Ibid.</em>, p. 154.</p></div>
+
+<div class="footnote"><p><a name="Footnote_13_13" id="Footnote_13_13"></a><a href="#FNanchor_13_13"><span class="label">
+	[13]</span></a> William Murdock, at this time a Boulton and Watt erector,
+	may have suggested this arrangement. <em>Ibid.</em>, p. 56.</p></div>
+
+<div class="footnote"><p><a name="Footnote_14_14" id="Footnote_14_14"></a><a href="#FNanchor_14_14"><span class="label">
+	[14]</span></a> Muirhead, <em>op. cit.</em> (footnote 3), vol. 3, note on
+	p. 39.</p></div>
+
+<p>Figure 7.&#8212;James Watt's five alternative devices for the
+conversion of reciprocating motion to rotary motion in a steam engine. (British
+Patent 1306, October 25, 1781). From James P. Muirhead, <em>The Origin and Progress
+of the Mechanical Inventions of James Watt</em> (London, 1854, vol. 3, pls. 3-5,
+7).</p>
+<p class="center">
+<img alt="Figure 7a" src="images/fig-07a.jpg" width="500" height="398" /></p>
+
+<p>(a) &quot;Inclined wheel.&quot; The vertical shaft at <em>D</em> is
+rotated by action of wheels <em>H</em> and <em>J</em> on cam, or swash
+plate, <em>ABC</em>. Boulton and Watt tried this device but discarded it.</p>
+<p class="center">
+<img alt="Figure 7b" src="images/fig-07b.jpg" width="500" height="612" /></p>
+
+<p>(b) Counterweighted crank wheel.</p>
+<p class="center">
+<img alt="Figure 7c" src="images/fig-07c.jpg" width="500" height="698" /></p>
+
+<p>(c) &quot;Eccentric wheel&quot; with external yoke hung from working
+beam. The wheel pivots at <em>C</em>.</p>
+<p class="center">
+<img alt="Figure 7d" src="images/fig-07d.jpg" width="389" height="600" /></p>
+
+<p>(d) &quot;Eccentric wheel&quot; with internal driving wheel hung from
+working beam. Wheel <em>B</em> is pivoted at center of shaft <em>A</em>.</p>
+<p class="center">
+<img alt="Figure 7e" src="images/fig-07e.jpg" width="492" height="600" /></p>
+
+<p>(e) Sun-and-planet gearing. This is the idea actually employed
+in Boulton and Watt engines. As the optional link <em>JK</em> held the
+gearwheel centers always equidistant, the annular guide <em>G</em> was not used.</p>
+
+<p>The sun-and-planet arrangement, with gears of equal size, was adopted by Watt
+for nearly all the rotative engines that he built during the term of the &quot;crank
+patents.&quot; This arrangement had the advantage of turning the flywheel through two
+revolutions during a single cycle of operation of the piston, thus requiring a
+flywheel only one-fourth the size of the flywheel needed if a simple crank were
+used. The optional link (JK of fig. 7e) was used in the engines as built.</p>
+
+<p>From the first, the rotative engines were made double-acting&#8212;that is, work
+was done by steam alternately in each end of the cylinder. The double-acting
+engine, unlike the single-acting pumping engine, required a piston rod that
+would push as well as pull. It was in the solution of this problem that Watt's
+originality and sure judgment were most clearly demonstrated.</p>
+
+<p>A rack and sector arrangement (fig. 8) was used on some engines. The first
+one, according to Watt, &quot;has broke out several teeth of the rack, but works
+steady.&quot;<a name="FNanchor_15_15" id="FNanchor_15_15"></a><a href="#Footnote_15_15" class="fnanchor">[15]</a>
+A little later he told a correspondent that his double-acting engine &quot;acts so
+powerfully that it has broken all its tackling repeatedly. We have now tamed it,
+however.&quot;<a name="FNanchor_16_16" id="FNanchor_16_16"></a><a href="#Footnote_16_16" class="fnanchor">[16]</a></p>
+
+<div class="footnote"><p><a name="Footnote_15_15" id="Footnote_15_15"></a><a href="#FNanchor_15_15"><span class="label">
+	[15]</span></a> James Watt, March 31, 1783, quoted in Dickinson and Jenkins,
+	<em>op. cit.</em> (footnote 5), p. 140.</p></div>
+
+<div class="footnote"><p><a name="Footnote_16_16" id="Footnote_16_16"></a><a href="#FNanchor_16_16"><span class="label">
+	[16]</span></a> Watt to De Luc, April 26, 1783, quoted in Muirhead, <em>op.
+	cit.</em> (footnote 3), vol. 2, p. 174.</p></div>
+
+<p class="center">
+<img alt="Figure 8" src="images/fig-08.jpg" width="440" height="600" /></p>
+<p>Figure 8.&#8212;Watt engine of 1782 (British Patent 1321, March 12,
+1782) showing the rack and sector used to guide the upper end of the piston rod
+and to transmit force from piston to working beam. This engine, with a 30-inch
+cylinder and an 8-foot stroke, was arranged for pumping. Pump rod <em>SS</em>
+is hung from sector of the working beam. From James P. Muirhead, <em>The Origin
+and Progress of the Mechanical Inventions of James Watt</em> (London, 1854, vol.
+3, pl. 15).</p>
+
+<p>It was about a year later that the straight-line linkage<a name="FNanchor_17_17" id="FNanchor_17_17"></a><a href="#Footnote_17_17" class="fnanchor">[17]</a>
+was thought out. &quot;I have started a new hare,&quot; Watt wrote to his partner. &quot;I have
+got a glimpse of a method of causing the piston-rod to move up and down
+perpendicularly, by only fixing it to a piece of iron upon the beam, without
+chains, or perpendicular guides, or untowardly frictions, arch-heads, or other
+pieces of clumsiness.... I have only tried it in a slight model yet, so cannot
+build upon it, though I think it a very probable thing to succeed, and one of
+the most ingenious simple pieces of mechanism I have contrived....&quot;<a name="FNanchor_18_18" id="FNanchor_18_18"></a><a href="#Footnote_18_18" class="fnanchor">[18]</a></p>
+
+<div class="footnote"><p><a name="Footnote_17_17" id="Footnote_17_17"></a><a href="#FNanchor_17_17"><span class="label">
+	[17]</span></a> Watt's was a four-bar linkage. All four-bar straight-line
+	linkages that have no sliding pairs trace only an approximately straight
+	line. The exact straight-line linkage in a single plane was not known until
+	1864 (see p. 204). In 1853 Pierre-Frédéric Sarrus (1798-1861), a French
+	professor of mathematics at Strasbourg, devised an accordion-like spatial
+	linkage that traced a true straight line. Described but not illustrated (Académie
+	des Sciences, Paris, <em>Comptes rendus</em>, 1853, vol. 36, pp. 1036-1038, 1125),
+	the mechanism was forgotten and twice reinvented; finally, the original
+	invention was rediscovered by an English writer in 1905. For chronology, see Florian Cajori,
+	<em>A History of Mathematics</em>, ed. 2, New York, 1919, p. 301.</p></div>
+
+<div class="footnote"><p><a name="Footnote_18_18" id="Footnote_18_18"></a><a href="#FNanchor_18_18"><span class="label">
+	[18]</span></a> Muirhead, <em>op. cit.</em> (footnote 3), vol. 2, pp.
+	191-192.</p></div>
+
+<p>Watt's marvelously simple straight-line linkage was incorporated into a large
+beam engine almost immediately, and the usually pessimistic and reserved
+inventor was close to a state of elation when he told Boulton that the &quot;new
+central perpendicular motion answers beyond expectation, and does not make the
+shadow of a noise.&quot;<a name="FNanchor_19_19" id="FNanchor_19_19"></a><a href="#Footnote_19_19" class="fnanchor">[19]</a>
+This linkage, which was included in an extensive patent of 1784, and two
+alternative devices are illustrated here (fig. 9). One of the alternatives is a
+guided crosshead (fig. 9, top right).</p>
+
+<div class="footnote"><p><a name="Footnote_19_19" id="Footnote_19_19"></a><a href="#FNanchor_19_19"><span class="label">
+	[19]</span></a> <em>Ibid.</em>, p. 202.</p></div>
+
+<p class="center">
+<img alt="Figure 9" src="images/fig-09.jpg" width="500" height="434" /></p>
+<p>Figure 9.&#8212;Watt's mechanisms for guiding the upper end of the
+piston rod of a double-acting engine (British Patent 1432, April 28, 1784). <em>
+Top left</em>, straight-line linkage; <em>top right</em>, crosshead and
+guide arrangement; <em>lower left</em>, piston rod <em>A</em> is guided by sectors
+<em>D</em> and
+<em>E</em>,
+suspended by flexible cords. From James P. Muirhead, <em>The Origin and
+Progress of the Mechanical Inventions of James Watt</em> (London, 1854, vol. 3,
+pls. 21, 22).</p>
+
+<p>Brilliant as was the conception of this linkage, it was followed up by a
+synthesis that is very little short of incredible. In order to make the linkage
+attached to the beam of his engines more compact, Watt had plumbed his
+experience for ideas; his experience had yielded up the work done much earlier
+on a drafting machine that made use of a pantograph.<a name="FNanchor_20_20" id="FNanchor_20_20"></a><a href="#Footnote_20_20" class="fnanchor">[20]</a>
+Watt combined his straight-line linkage with a pantograph, one link becoming a
+member of the pantograph.</p>
+
+<div class="footnote"><p><a name="Footnote_20_20" id="Footnote_20_20"></a><a href="#FNanchor_20_20"><span class="label">
+	[20]</span></a> &quot;It has only one fault,&quot; he had told a friend on December
+	24, 1773, after describing the drafting machine to him, &quot;which is, that it
+	will not do, because it describes conic sections instead of straight lines.&quot;
+	<em>Ibid.</em>, p. 71.</p></div>
+
+<p>The length of each oscillating link of the straight-line linkage was thus
+reduced to one-fourth instead of one-half the beam length, and the entire
+mechanism could be constructed so that it would not extend beyond the end of the
+working beam. This arrangement soon came to be known as Watt's &quot;parallel motion&quot;
+(fig. 10).<a name="FNanchor_21_21" id="FNanchor_21_21"></a><a href="#Footnote_21_21" class="fnanchor">[21]</a>
+Years later Watt told his son: &quot;Though I am not over anxious after fame, yet I
+am more proud of the parallel motion than of any other mechanical invention I
+have ever made.&quot;<a name="FNanchor_22_22" id="FNanchor_22_22"></a><a href="#Footnote_22_22" class="fnanchor">[22]</a></p>
+
+<div class="footnote"><p><a name="Footnote_21_21" id="Footnote_21_21"></a><a href="#FNanchor_21_21"><span class="label">
+	[21]</span></a> Throughout the 19th century the term &quot;parallel motion&quot; was
+	used indiscriminately to refer to any straight-line linkage. I have not
+	discovered the origin of the term. Watt did not use it in his patent
+	specification, and I have not found it in his writings or elsewhere before
+	1808 (see footnote 22). <em>The Cyclopaedia</em> (Abraham Rees, ed., London, 1819,
+	vol. 26) defined parallel motion as &quot;a term used among practical mechanics
+	to denote the rectilinear motion of a piston-rod, &amp;c. in the direction of
+	its length; and contrivances, by which such alternate rectilinear motions
+	are converted into continuous rotatory ones, or <em>vice versa</em>....&quot;
+	Robert Willis in his <em>Principles of Mechanism</em> (London, 1841, p.
+	399) described parallel motion as &quot;a term somewhat awkwardly applied to a
+	combination of jointed rods, the purpose of which is to cause a point to
+	describe a straight line....&quot; A. B. Kempe in <em>How to Draw a Straight
+	Line</em> (London, 1877, p. 49) wrote: &quot;I have been more than once asked to
+	get rid of the objectionable term 'parallel motion.' I do not know how it
+	came to be employed, and it certainly does not express what is intended. The
+	expression, however, has now become crystallised, and I for one cannot
+	undertake to find a solvent.&quot;</p></div>
+
+<div class="footnote"><p><a name="Footnote_22_22" id="Footnote_22_22"></a><a href="#FNanchor_22_22"><span class="label">
+	[22]</span></a> Muirhead, <em>op. cit.</em> (footnote 3), vol. 3, note on p. 89.</p></div>
+
+<p class="center">
+<img alt="Figure 10" src="images/fig-10.jpg" width="500" height="305" /></p>
+<p>Figure 10.&#8212;Watt's &quot;parallel motion.&quot; Engine's working beam is
+pivoted at <em>A</em>. Pivot <em>F</em> is attached to the engine frame.
+From Dyonysius Lardner, <em>The Steam Engine</em> (Philadelphia, 1852), pl. 5
+(American ed. 5 from London ed. 5).</p>
+
+<p>The Watt four-bar linkage was employed 75 years after its inception by the
+American Charles B. Richards when, in 1861, he designed his first high-speed
+engine indicator (fig. 11). Introduced into England the following year, the
+Richards Indicator was an immediate success, and many thousands were sold over
+the next 20 or 30 years.<a name="FNanchor_23_23" id="FNanchor_23_23"></a><a href="#Footnote_23_23" class="fnanchor">[23]</a></p>
+
+<div class="footnote"><p><a name="Footnote_23_23" id="Footnote_23_23"></a><a href="#FNanchor_23_23"><span class="label">
+	[23]</span></a> Charles T. Porter, <em>Engineering Reminiscences</em>, New
+	York, 1908, pp. 58-59, 90.</p></div>
+
+<p class="center">
+<img alt="Figure 11" src="images/fig-11.jpg" width="500" height="436" /></p>
+<p>Figure 11.&#8212;Richards high-speed engine indicator of 1861,
+showing application of the Watt straight-line linkage. (<em>USNM 307515</em>;
+<em>Smithsonian photo 46570</em>).</p>
+
+<p>In considering the order of synthetic ability required to design the
+straight-line linkage and to combine it with a pantograph, it should be kept in
+mind that this was the first one of a long line of such mechanisms.<a name="FNanchor_24_24" id="FNanchor_24_24"></a><a href="#Footnote_24_24" class="fnanchor">[24]</a>
+Once the idea was abroad, it was only to be expected that many variations and
+alternative solutions should appear. One wonders, however, what direction the
+subsequent work would have taken if Watt had not so clearly pointed the way.</p>
+
+<div class="footnote"><p><a name="Footnote_24_24" id="Footnote_24_24"></a><a href="#FNanchor_24_24"><span class="label">
+	[24]</span></a> At least one earlier straight-line linkage, an arrangement
+	later ascribed to Richard Roberts, had been depicted before Watt's patent
+	(Pierre Patte, <em>Mémoirs sur les objets les plus importants de
+	l'architecture</em>, Paris, 1769, p. 229 and pl. 11). However, this linkage
+	(reproduced here in figure 18) had no detectable influence on Watt or on
+	subsequent practice.</p></div>
+
+<p>In 1827 John Farey, in his exhaustive study of the steam engine, wrote
+perhaps the best contemporary view of Watt's work. Farey as a young man had
+several times talked with the aging Watt, and he had reflected upon the nature
+of the intellect that had caused Watt to be recognized as a genius, even within
+his own lifetime. In attempting to explain Watt's genius, Farey set down some
+observations that are pertinent not only to kinematic synthesis but to the
+currently fashionable term &quot;creativity.&quot;</p>
+
+<p>In Farey's opinion Watt's inventive faculty was far superior to that of any
+of his contemporaries; but his many and various ideas would have been of little
+use if he had not possessed a very high order of judgment, that &quot;faculty of
+distinguishing between ideas; decomposing compound ideas into more simple
+elements; arranging them into classes, and comparing them together....&quot;</p>
+
+<p>Farey was of the opinion that while a mind like Watt's could produce
+brilliant new ideas, still the &quot;common stock of ideas which are current amongst
+communities and professions, will generally prove to be of a better quality than
+the average of those new ideas, which can be produced by any individual from the
+operation of his own mind, without assistance from others.&quot; Farey concluded with
+the observation that &quot;the most useful additions to that common stock, usually
+proceed from the individuals who are well acquainted with the whole series.&quot;<a name="FNanchor_25_25" id="FNanchor_25_25"></a><a href="#Footnote_25_25" class="fnanchor">[25]</a></p>
+
+<div class="footnote"><p><a name="Footnote_25_25" id="Footnote_25_25"></a><a href="#FNanchor_25_25"><span class="label">
+	[25]</span></a> Farey, <em>op. cit.</em> (footnote 6), pp. 651, 652.</p></div>
+
+
+<h3><a name="To_Draw_a_Straight_Line">To Draw a Straight Line</a></h3>
+
+<p>During most of the century after James Watt had produced his parallel motion,
+the problem of devising a linkage, one point of which would describe a straight
+line, was one that tickled the fancies of mathematicians, of ingenious
+mechanics, and of gentlemanly dabblers in ideas. The quest for a straight-line
+mechanism more accurate than that of Watt far outlasted the pressing practical
+need for such a device. Large metal planing machines were well known by 1830,
+and by midcentury crossheads and crosshead guides were used on both sides of the
+Atlantic in engines with and without working beams.</p>
+
+<p>By 1819 John Farey had observed quite accurately that, in England at least,
+many other schemes had been tried and found wanting and that &quot;no methods have
+been found so good as the original engine; and we accordingly find, that all the
+most established and experienced manufacturers make engines which are not
+altered in any great feature from Mr. Watt's original engine....&quot;<a name="FNanchor_26_26" id="FNanchor_26_26"></a><a href="#Footnote_26_26" class="fnanchor">[26]</a></p>
+
+<div class="footnote"><p><a name="Footnote_26_26" id="Footnote_26_26"></a><a href="#FNanchor_26_26"><span class="label">
+	[26]</span></a> In Rees, <em>op. cit.</em> (footnote 21), vol. 34 (&quot;Steam
+	Engine&quot;). John Farey was the writer of this article (see Farey, <em>op.
+	cit.</em>, p. vi).</p></div>
+
+<p>Two mechanisms for producing a straight line were introduced before the
+Boulton and Watt monopoly ended in 1800. Perhaps the first was by Edmund
+Cartwright (1743-1823), who is said to have had the original idea for a power
+loom. This geared device (fig. 12), was characterized patronizingly by a
+contemporary American editor as possessing &quot;as much merit as can possibly be
+attributed to a gentleman engaged in the pursuit of mechanical studies for his
+own amusement.&quot;<a name="FNanchor_27_27" id="FNanchor_27_27"></a><a href="#Footnote_27_27" class="fnanchor">[27]</a>
+Only a few small engines were made under the patent.<a name="FNanchor_28_28" id="FNanchor_28_28"></a><a href="#Footnote_28_28" class="fnanchor">[28]</a></p>
+
+<div class="footnote"><p><a name="Footnote_27_27" id="Footnote_27_27"></a><a href="#FNanchor_27_27"><span class="label">
+	[27]</span></a> <em>Emporium of Arts and Sciences</em>, December 1813, new
+	ser., vol. 2, no. 1, p. 81.</p></div>
+
+<div class="footnote"><p><a name="Footnote_28_28" id="Footnote_28_28"></a><a href="#FNanchor_28_28"><span class="label">
+	[28]</span></a> Farey, <em>op. cit.</em> (footnote 6), p. 666.</p></div>
+
+<p class="center">
+<img alt="Figure 12" src="images/fig-12.jpg" width="354" height="600" /></p>
+<p>Figure 12.&#8212;Cartwright's geared straight-line mechanism of
+about 1800. From Abraham Rees, <em>The Cyclopaedia</em> (London, 1819, &quot;Steam
+Engine,&quot; pl. 5).</p>
+
+<p>The properties of a hypocycloid were recognized by James White, an English
+engineer, in his geared design which employed a pivot located on the pitch
+circle of a spur gear revolving inside an internal gear. The diameter of the
+pitch circle of the spur gear was one-half that of the internal gear, with the
+result that the pivot, to which the piston rod was connected, traced out a
+diameter of the large pitch circle (fig. 13). White in 1801 received from
+Napoleon Bonaparte a medal for this invention when it was exhibited at an
+industrial exposition in Paris.<a name="FNanchor_29_29" id="FNanchor_29_29"></a><a href="#Footnote_29_29" class="fnanchor">[29]</a>
+Some steam engines employing White's mechanism were built, but without
+conspicuous commercial success. White himself rather agreed that while his
+invention was &quot;allowed to possess curious properties, and to be a <em>pretty</em>
+thing, opinions do not all concur in declaring it, essentially and generally, a
+<em>good</em> thing.&quot;<a name="FNanchor_30_30" id="FNanchor_30_30"></a><a href="#Footnote_30_30" class="fnanchor">[30]</a></p>
+
+<div class="footnote"><p><a name="Footnote_29_29" id="Footnote_29_29"></a><a href="#FNanchor_29_29"><span class="label">
+	[29]</span></a> H. W. Dickinson, &quot;James White and His 'New Century of
+	Inventions,'&quot; <em>Transactions of the Newcomen Society</em>, 1949-1951,
+	vol. 27, pp. 175-179.</p></div>
+
+<div class="footnote"><p><a name="Footnote_30_30" id="Footnote_30_30"></a><a href="#FNanchor_30_30"><span class="label">
+	[30]</span></a> James White, <em>A New Century of Inventions</em>,
+	Manchester, 1822, pp. 30-31, 338. A hypocycloidal engine used in
+	Stourbridge, England, is in the Henry Ford Museum.</p></div>
+
+<p class="center">
+<img alt="Figure 13" src="images/fig-13.jpg" width="500" height="537" /></p>
+<p>Figure 13.&#8212;James White's hypocycloidal straight-line
+mechanism, about 1800. The fly-weights (at the ends of the diagonal arm)
+functioned as a flywheel. From James White, <em>A New Century of Inventions</em>
+(Manchester, 1822, pl. 7).</p>
+
+<p>The first of the non-Watt four-bar linkages appeared shortly after 1800. The
+origin of the grasshopper beam motion is somewhat obscure, although it came to
+be associated with the name of Oliver Evans, the American pioneer in the
+employment of high-pressure steam. A similar idea, employing an isosceles
+linkage, was patented in 1803 by William Freemantle, an English watchmaker (fig.
+14).<a name="FNanchor_31_31" id="FNanchor_31_31"></a><a href="#Footnote_31_31" class="fnanchor">[31]</a>
+This is the linkage that was attributed much later to John Scott Russell
+(1808-1882), the prominent naval architect.<a name="FNanchor_32_32" id="FNanchor_32_32"></a><a href="#Footnote_32_32" class="fnanchor">[32]</a>
+An inconclusive hint that Evans had devised his straight-line linkage by 1805
+appeared in a plate illustrating his <em>Abortion of the Young Steam Engineer's
+Guide</em> (Philadelphia, 1805), and it was certainly used on his Columbian
+engine (fig. 15), which was built before 1813. The Freemantle linkage, in
+modified form, appeared in Rees's <em>Cyclopaedia</em> of 1819 (fig. 16), but
+it is doubtful whether even this would have been readily recognized as identical
+with the Evans linkage, because the connecting rod was at the opposite end of
+the working beam from the piston rod, in accordance with established usage,
+while in the Evans linkage the crank and connecting rod were at the same end of
+the beam. It is possible that Evans got his idea from an earlier English
+periodical, but concrete evidence is lacking.</p>
+
+<div class="footnote"><p><a name="Footnote_31_31" id="Footnote_31_31"></a><a href="#FNanchor_31_31"><span class="label">
+	[31]</span></a> British Patent 2741, November 17, 1803.</p></div>
+
+<div class="footnote"><p><a name="Footnote_32_32" id="Footnote_32_32"></a><a href="#FNanchor_32_32"><span class="label">
+	[32]</span></a> William J. M. Rankine, <em>Manual of Machinery and
+	Millwork</em>, ed. 6, London, 1887, p. 275.</p></div>
+
+<p class="center">
+<img alt="Figure 14" src="images/fig-14.jpg" width="500" height="369" /></p>
+<p>Figure 14.&#8212;Freemantle straight-line linkage, later called the Scott Russell
+linkage. From British Patent 2741, November 17, 1803.</p>
+
+<p class="center">
+<img alt="Figure 15" src="images/fig-15.jpg" width="500" height="364" /></p>
+<p>Figure 15.&#8212;Oliver Evans' &quot;Columbian&quot; engine, 1813, showing the
+Evans, or &quot;grasshopper,&quot; straight-line linkage. From <em>Emporium of Arts and
+Sciences</em> (new ser., vol. 2, no. 3, April 1814, pl. opposite p. 380).</p>
+
+<p class="center">
+<img alt="Figure 16" src="images/fig-16.jpg" width="458" height="376" /></p>
+<p>Figure 16.&#8212;Modified Freemantle linkage, 1819, which is kinematically the same as the Evans linkage. Pivots <em>D</em> and <em>E</em>
+are attached to engine frame. From Abraham Rees, <em>The Cyclopaedia</em>
+(London, 1819, &quot;Parallel Motions,&quot; pl. 3).</p>
+
+<p>If the idea did in fact originate with Evans, it is strange that he did not
+mention it in his patent claims, or in the descriptions that he published of his
+engines.<a name="FNanchor_33_33" id="FNanchor_33_33"></a><a href="#Footnote_33_33" class="fnanchor">[33]</a>
+The practical advantage of the Evans linkage, utilizing as it could a much
+lighter working beam than the Watt or Freemantle engines, would not escape
+Oliver Evans, and he was not a man of excessive modesty where his own inventions
+were concerned.</p>
+
+<div class="footnote"><p><a name="Footnote_33_33" id="Footnote_33_33"></a><a href="#FNanchor_33_33"><span class="label">
+	[33]</span></a> Greville and Dorothy Bathe, <em>Oliver Evans</em>,
+	Philadelphia, 1935, pp. 88, 196, and <em>passim</em>.</p></div>
+
+<p>Another four-bar straight-line linkage that became well known was attributed
+to Richard Roberts of Manchester (1789-1864), who around 1820 had built one of
+the first metal planing machines, which machines helped make the quest for
+straight-line linkages largely academic. I have not discovered what occasioned
+the introduction of the Roberts linkage, but it dated from before 1841. Although
+Roberts patented many complex textile machines, an inspection of all of his
+patent drawings has failed to provide proof that he was the inventor of the
+Roberts linkage.<a name="FNanchor_34_34" id="FNanchor_34_34"></a><a href="#Footnote_34_34" class="fnanchor">[34]</a>
+The fact that the same linkage is shown in an engraving of 1769 (fig. 18)
+further confuses the issue.<a name="FNanchor_35_35" id="FNanchor_35_35"></a><a href="#Footnote_35_35" class="fnanchor">[35]</a></p>
+
+<div class="footnote"><p><a name="Footnote_34_34" id="Footnote_34_34"></a><a href="#FNanchor_34_34"><span class="label">
+	[34]</span></a> Robert Willis (<em>op. cit.</em>
+	[footnote 2] p. 411) credited Richard Roberts with the
+	linkage. Roberts' 15 British patent drawings exhibit complex applications of
+	cams, levers, guided rods, cords, and so forth, but no straight-line
+	mechanism. In his patent no. 6258 of April 13, 1832, for a steam engine and
+	locomotive carriage, Roberts used Watt's &quot;parallel motion&quot; on a beam driven
+	by a vertical cylinder.</p></div>
+
+<div class="footnote"><p><a name="Footnote_35_35" id="Footnote_35_35"></a><a href="#FNanchor_35_35"><span class="label">
+	[35]</span></a> This engraving appeared as plate 11 in Pierre Patte's 1769
+	work (<em>op. cit.</em> footnote 24). Patte stated that the machine depicted in his
+	plate 11 was invented by M. de Voglie and was actually used in 1756.</p></div>
+
+<p class="center">
+<img alt="Figure 17" src="images/fig-17.jpg" width="500" height="521" /></p>
+<p>Figure 17.&#8212;Straight-line linkage (before 1841) attributed to
+Richard Roberts by Robert Willis. From A. B. Kempe, <em>How to Draw a Straight
+Line</em> (London, 1877, p. 10).</p>
+<p class="center">
+<img alt="Detail from Figure 18" src="images/fig-18a.jpg" width="350" height="577" /><img alt="Figure 18" src="images/fig-18.jpg" width="421" height="550" />&nbsp;</p>
+
+<p>Figure 18.&#8212;Machine for sawing off pilings under water, about
+1760, designed by De Voglie. The Roberts linkage operates the bar (<em>Q</em> in
+detailed sketch on left) at the rear of the machine below the operators. The
+significance of the linkage apparently was not generally recognized. A similar
+machine depicted in Diderot's <em>Encyclopédie</em>, published several years later, did
+not employ the straight-line linkage. From Pierre Patte, <em>Memoirs sur les objets
+plus importants de l'architecture</em> (Paris, 1769, pl. 11).</p>
+
+<p>The appearance in 1864 of Peaucellier's exact straight-line linkage went
+nearly unnoticed. A decade later, when news of its invention crossed the Channel
+to England, this linkage excited a flurry of interest, and variations of it
+occupied mathematical minds for several years. For at least 10 years before and
+20 years after the final solution of the problem, Professor Chebyshev,<a name="FNanchor_36_37" id="FNanchor_36_37"></a><a href="#Footnote_36_37" class="fnanchor">[36]</a>
+a noted mathematician of the University of St. Petersburg, was interested in the
+matter. Judging by his published works and his reputation abroad, Chebyshev's
+interest amounted to an obsession.</p>
+
+<div class="footnote"><p><a name="Footnote_36_37" id="Footnote_36_37"></a><a href="#FNanchor_36_37"><span class="label">
+	[36]</span></a> This is the Library of Congress spelling</p></div>
+
+<p>Pafnutï&#301; L'vovich Chebyshev was born in 1821, near Moscow, and entered the
+University of Moscow in 1837. In 1853, after visiting France and England and
+observing carefully the progress of applied mechanics in those countries, he
+read his first paper on approximate straight-line linkages, and over the next 30
+years he attacked the problem with new vigor at least a dozen times. He found
+that the two principal straight-line linkages then in use were Watt's and
+Evans'. Chebyshev noted the departure of these linkages from a straight line and
+calculated the deviation as of the fifth degree, or about 0.0008 inch per inch
+of beam length. He proposed a modification of the Watt linkage to refine its
+accuracy but found that he would have to more than double the length of the
+working beam. Chebyshev concluded ruefully that his modification would &quot;present
+great practical difficulties.&quot;<a name="FNanchor_37_38" id="FNanchor_37_38"></a><a href="#Footnote_37_38" class="fnanchor">[37]</a></p>
+
+<div class="footnote"><p><a name="Footnote_37_38" id="Footnote_37_38"></a><a href="#FNanchor_37_38"><span class="label">
+	[37]</span></a> <em>Oeuvres de P. L. Tchebychef</em>, 2 vols., St. Petersburg,
+	1899-1907, vol. 1, p. 538; vol. 2, pp. 57, 85.</p></div>
+
+<p>At length an idea occurred to Chebyshev that would enable him to approach if
+not quite attain a true straight line. If one mechanism was good, he reasoned,
+two would be better, <em>et cetera, ad infinitum</em>. The idea was simply to combine,
+or compound, four-link approximate linkages, arranging them in such a way that
+the errors would be successively reduced. Contemplating first a combination of
+the Watt and Evans linkages (fig. 19), Chebyshev recognized that if point D of
+the Watt linkage followed nearly a straight line, point A of the Evans linkage
+would depart even less from a straight line. He calculated the deviation in this
+case as of the 11th degree. He then replaced Watt's linkage by one that is
+usually called the Chebyshev straight-line mechanism (fig. 20), with the result
+that precision was increased to the 13th degree.<a name="FNanchor_38_39" id="FNanchor_38_39"></a><a href="#Footnote_38_39" class="fnanchor">[38]</a>
+The steam engine that he displayed at the Vienna Exhibition in 1873 employed
+this linkage&#8212;the Chebyshev mechanism compounded with the Evans, or approximate
+isosceles, linkage. An English visitor to the exhibition commented that &quot;the
+motion is of little or no practical use, for we can scarcely imagine
+circumstances under which it would be more advantageous to use such a
+complicated system of levers, with so many joints to be lubricated and so many
+pins to wear, than a solid guide of some kind; but at the same time the
+arrangement is very ingenious and in this respect reflects great credit on its
+designer.&quot;<a name="FNanchor_39_40" id="FNanchor_39_40"></a><a href="#Footnote_39_40" class="fnanchor">[39]</a></p>
+
+<div class="footnote"><p><a name="Footnote_38_39" id="Footnote_38_39"></a><a href="#FNanchor_38_39"><span class="label">
+	[38]</span></a> <em>Ibid.</em>, vol. 2, pp. 93, 94.</p></div>
+
+<div class="footnote"><p><a name="Footnote_39_40" id="Footnote_39_40"></a><a href="#FNanchor_39_40"><span class="label">
+	[39]</span></a> <em>Engineering</em>, October 3, 1873, vol. 16, p. 284.</p></div>
+
+<p class="center">
+<img alt="figure 19" src="images/fig-19.jpg" width="468" height="600" />&nbsp;</p>
+<p>Figure 19.&#8212;Pafnutï&#301; L'vovich Chebyshev (1821-1894), Russian
+mathematician active in analysis and synthesis of straight-line mechanisms. From
+<em>Ouvres de P. L. Tchebychef</em> (St. Petersburg, 1907, vol. 2,
+frontispiece).</p>
+
+<p class="center">
+<img alt="Figure 20" src="images/fig-20.jpg" width="484" height="600" /></p>
+<p>Figure 20.&#8212;Chebyshev's combination (about 1867) of Watt's and
+Evans' linkages to reduce errors inherent in each. Points <em>C</em>, <em>C'</em>, and
+<em>C&quot;</em>
+are fixed; <em>A</em> is the tracing point. From <em>Oeuvres de P. L. Tchebychef</em>
+(St. Petersburg, 1907, vol. 2, p. 93).</p>
+
+<p class="center">
+<img alt="Figure 21" src="images/fig-21.jpg" width="600" height="312" /></p>
+<p>Figure 21.&#8212;<em>Left</em>: Chebyshev straight-line linkage, 1867; from
+A. B. Kempe, <em>How to Draw a Straight Line</em> (London, 1877, p. 11). <em>
+Right</em>: Chebyshev-Evans combination, 1867; from <em>Oeuvres de P. L. Tchebychef</em> (St.
+Petersburg, 1907, vol. 2, p. 94). Points <em>C</em>, <em>C'</em>, and <em>C&quot;</em> are fixed.
+<em>A</em> is the tracing point.</p>
+
+<p>There is a persistent rumor that Professor Chebyshev sought to demonstrate
+the impossibility of constructing any linkage, regardless of the number of
+links, that would generate a straight line; but I have found only a dubious
+statement in the <em>Grande Encyclopédie</em><a name="FNanchor_40_41" id="FNanchor_40_41"></a><a href="#Footnote_40_41" class="fnanchor">[40]</a>
+of the late 19th century and a report of a conversation with the Russian by an
+Englishman, James Sylvester, to the effect that Chebyshev had &quot;succeeded in
+proving the nonexistence of a five-bar link-work capable of producing a perfect
+parallel motion....&quot;<a name="FNanchor_41_42" id="FNanchor_41_42"></a><a href="#Footnote_41_42" class="fnanchor">[41]</a>
+Regardless of what tradition may have to say about what Chebyshev said, it is of
+course well known that Captain Peaucellier was the man who finally synthesized
+the exact straight-line mechanism that bears his name.</p>
+
+<div class="footnote"><p><a name="Footnote_40_41" id="Footnote_40_41"></a><a href="#FNanchor_40_41"><span class="label">
+	[40]</span></a> <em>La Grande Encyclopédie</em>, Paris, 1886 (&quot;Peaucellier&quot;).</p></div>
+
+<div class="footnote"><p><a name="Footnote_41_42" id="Footnote_41_42"></a><a href="#FNanchor_41_42"><span class="label">
+	[41]</span></a> James Sylvester, &quot;Recent Discoveries in Mechanical
+	Conversion of Motion,&quot; <em>Notices of the Proceedings of the Royal
+	Institution of Great Britain</em>, 1873-1875, vol. 7, p. 181. The fixed link was not counted
+	by Sylvester; in modern parlance this would be a six-link mechanism.</p></div>
+
+<p class="center">
+<img alt="Figure 22" src="images/fig-22.jpg" width="500" height="290" /></p>
+<p>Figure 22.&#8212;Peaucellier exact straight-line linkage, 1873. From
+A. B. Kempe, <em>How to Draw a Straight Line</em> (London, 1877, p. 12).</p>
+
+<p class="center">
+<img alt="Figuer 23" src="images/fig-23.jpg" width="500" height="240" /></p>
+<p>Figure 23.&#8212;Model of the Peaucellier &quot;Compas Composé,&quot;
+deposited in Conservatoire National des Arts et Métiers, Paris, 1875. Photo
+courtesy of the Conservatoire. </p>
+<p class="center">
+<img alt="Figure 24" src="images/fig-24.jpg" width="458" height="500" /></p>
+<p>Figure 24.&#8212;James Joseph Sylvester
+(1814-1897), mathematician and lecturer on straight-line linkages. From
+<em>Proceedings of the Royal Society of London </em>(1898, vol. 63, opposite p.
+161).</p>
+
+<p>Charles-Nicolas Peaucellier, a graduate of the Ecole Polytechnique and a
+captain in the French corps of engineers, was 32 years old in 1864 when he wrote
+a short letter to the editor of <em>Nouvelles Annales de mathématiques</em> (ser. 2,
+vol. 3, pp. 414-415) in Paris. He called attention to what he termed &quot;compound
+compasses,&quot; a class of linkages that included Watt's parallel motion, the
+pantograph, and the polar planimeter. He proposed to design linkages to describe
+a straight line, a circle of any radius no matter how large, and conic sections,
+and he indicated in his letter that he had arrived at a solution.</p>
+
+<p>This letter stirred no pens in reply, and during the next 10 years the
+problem merely led to the filling of a few academic pages by Peaucellier and
+Amédée Mannheim (1831-1906), also a graduate of Ecole Polytechnique, a professor
+of mathematics, and the designer of the Mannheim slide rule. Finally, in 1873,
+Captain Peaucellier gave his solution to the readers of the <em>Nouvelles Annales</em>.
+His reasoning, which has a distinct flavor of discovery by hindsight, was that
+since a linkage generates a curve that can be expressed algebraically, it must
+follow that any algebraic curve can be generated by a suitable linkage&#8212;it was
+only necessary to find the suitable linkage. He then gave a neat geometric
+proof, suggested by Mannheim, for his straight-line &quot;compound compass.&quot;<a name="FNanchor_42_43" id="FNanchor_42_43"></a><a href="#Footnote_42_43" class="fnanchor">[42]</a></p>
+
+<div class="footnote"><p><a name="Footnote_42_43" id="Footnote_42_43"></a><a href="#FNanchor_42_43"><span class="label">
+	[42]</span></a> Charles-Nicholas Peaucellier, &quot;Note sur une question de
+	geométrie de compas,&quot; <em>Nouvelles Annales de mathématiques</em>, 1873, ser. 2,
+	vol. 12, pp. 71-78. A sketch of Mannheim's work is in Florian Cajori, <em>A
+	History of the Logarithmic Slide Rule</em>, New York, about 1910, reprinted in
+	<em>String Figures and Other Monographs</em>, New York, Chelsea Publishing Company,
+	1960.</p></div>
+
+<p>On a Friday evening in January 1874 Albemarle Street in London was filled
+with carriages, each maneuvering to unload its charge of gentlemen and their
+ladies at the door of the venerable hall of the Royal Institution. Amidst a
+&quot;mighty rustling of silks,&quot; the elegant crowd made its way to the auditorium for
+one of the famous weekly lectures. The speaker on this occasion was James Joseph
+Sylvester, a small intense man with an enormous head, sometime professor of
+mathematics at the University of Virginia, in America, and more recently at the
+Royal Military Academy in Woolwich. He spoke from the same rostrum that had been
+occupied by Davy, Faraday, Tyndall, Maxwell, and many other notable scientists.
+Professor Sylvester's subject was &quot;Recent Discoveries in Mechanical Conversion
+of Motion.&quot;<a name="FNanchor_43_44" id="FNanchor_43_44"></a><a href="#Footnote_43_44" class="fnanchor">[43]</a></p>
+
+<div class="footnote"><p><a name="Footnote_43_44" id="Footnote_43_44"></a><a href="#FNanchor_43_44"><span class="label">
+	[43]</span></a> Sylvester, <em>op. cit.</em> (footnote 41), pp. 179-198. It appears
+	from a comment in this lecture that Sylvester was responsible for the word
+	&quot;linkage.&quot; According to Sylvester, a linkage consists of an even number of
+	links, a &quot;link-work&quot; of an odd number. Since the fixed member was not
+	considered as a link by Sylvester, this distinction became utterly confusing
+	when Reuleaux's work was published in 1876. Although &quot;link&quot; was used by Watt
+	in a patent specification, it is not probable that he ever used the term
+	&quot;link-work&quot;&#8212;at any rate, my search for his use of it has been fruitless.
+	&quot;Link work&quot; is used by Willis (<em>op. cit.</em> footnote 21), but the term most
+	likely did not originate with him. I have not found the word &quot;linkage&quot; used
+	earlier than Sylvester.</p></div>
+
+<p>Remarking upon the popular appeal of most of the lectures, a contemporary
+observer noted that while many listeners might prefer to hear Professor Tyndall
+expound on the acoustic opacity of the atmosphere, &quot;those of a higher and drier
+turn of mind experience ineffable delight when Professor Sylvester holds forth
+on the conversion of circular into parallel motion.&quot;<a name="FNanchor_44_45" id="FNanchor_44_45"></a><a href="#Footnote_44_45" class="fnanchor">[44]</a></p>
+
+<div class="footnote"><p><a name="Footnote_44_45" id="Footnote_44_45"></a><a href="#FNanchor_44_45"><span class="label">
+	[44]</span></a>  Bernard H. Becker, <em>Scientific London</em>, London, 1874, pp.
+	45, 50, 51.</p></div>
+
+<p>Sylvester's aim was to bring the Peaucellier linkage to the notice of the
+English-speaking world, as it had been brought to his attention by
+Chebyshev&#8212;during a recent visit of the Russian to England&#8212;and to give his
+listeners some insight into the vastness of the field that he saw opened by the
+discovery of the French soldier.<a name="FNanchor_45_46" id="FNanchor_45_46"></a><a href="#Footnote_45_46" class="fnanchor">[45]</a></p>
+
+<div class="footnote"><p><a name="Footnote_45_46" id="Footnote_45_46"></a><a href="#FNanchor_45_46"><span class="label">
+	[45]</span></a> Sylvester, <em>op. cit.</em>  (footnote 41), p. 183; <em>
+	Nature</em>,
+	November 13, 1873, vol. 9, p. 33.</p></div>
+
+<p>&quot;The perfect parallel motion of Peaucellier looks so simple,&quot; he observed,
+&quot;and moves so easily that people who see it at work almost universally express
+astonishment that it waited so long to be discovered.&quot; But that was not his
+reaction at all. The more one reflects upon the problem, Sylvester continued, he
+&quot;wonders the more that it was ever found out, and can see no reason why it
+should have been discovered for a hundred years to come. Viewed <em>a priori</em> there
+was nothing to lead up to it. It bears not the remotest analogy (except in the
+fact of a double centring) to Watt's parallel motion or any of its progeny.&quot;<a name="FNanchor_46_47" id="FNanchor_46_47"></a><a href="#Footnote_46_47" class="fnanchor">[46]</a></p>
+
+<div class="footnote"><p><a name="Footnote_46_47" id="Footnote_46_47"></a><a href="#FNanchor_46_47"><span class="label">
+	[46]</span></a> Sylvester, <em>op. cit.</em> (footnote 41), p. 181.</p></div>
+
+<p>It must be pointed out, parenthetically at least, that James Watt had not
+only had to solve the problem as best he could, but that he had no inkling, so
+far as experience was concerned, that a solvable problem existed.</p>
+
+<p>Sylvester interrupted his panegyric long enough to enumerate some of the
+practical results of the Peaucellier linkage. He said that Mr. Penrose, the
+eminent architect and surveyor to St. Paul's Cathedral, had &quot;put up a house-pump
+worked by a negative Peaucellier cell, to the great wonderment of the plumber
+employed, who could hardly believe his senses when he saw the sling attached to
+the piston-rod moving in a true vertical line, instead of wobbling as usual from
+side to side.&quot; Sylvester could see no reason &quot;why the perfect parallel motion
+should not be employed with equal advantage in the construction of ordinary
+water-closets.&quot; The linkage was to be employed by &quot;a gentleman of fortune&quot; in a
+marine engine for his yacht, and there was talk of using it to guide a piston
+rod &quot;in certain machinery connected with some new apparatus for the ventilation
+and filtration of the air of the Houses of Parliament.&quot; In due course, Mr. Prim,
+&quot;engineer to the Houses,&quot; was pleased to show his adaptation of the Peaucellier
+linkage to his new blowing engines, which proved to be exceptionally quiet in
+their operation (fig. 25).<a name="FNanchor_47_48" id="FNanchor_47_48"></a><a href="#Footnote_47_48" class="fnanchor">[47]</a>
+A bit on the ludicrous side, also, was Sylvester's 78-bar linkage that traced a
+straight line along the line connecting the two fixed centers of the linkage.<a name="FNanchor_48_49" id="FNanchor_48_49"></a><a href="#Footnote_48_49" class="fnanchor">[48]</a></p>
+
+<div class="footnote"><p><a name="Footnote_47_48" id="Footnote_47_48"></a><a href="#FNanchor_47_48"><span class="label">
+	[47]</span></a> <em>Ibid.</em>, pp. 182, 183, 188, 193.</p></div>
+
+<div class="footnote"><p><a name="Footnote_48_49" id="Footnote_48_49"></a><a href="#FNanchor_48_49"><span class="label">
+	[48]</span></a> Kempe, <em>op. cit.</em> (footnote 21), p. 17.</p></div>
+
+<p class="center">
+<img alt="Figure 25" src="images/fig-25.jpg" width="600" height="184" /></p>
+<p>Figure 25.&#8212;Mr. Prim's blowing engine used for ventilating the
+House of Commons, 1877. The crosshead of the reciprocating air pump is guided by
+a Peaucillier linkage shown at the center. The slate-lined air cylinders had
+rubber-flap inlet and exhaust valves and a piston whose periphery was formed by
+two rows of brush bristles. Prim's machine was driven by a steam engine.
+Photograph by Science Museum, London.</p>
+
+<p>Before dismissing with a smile the quaint ideas of our Victorian forbears,
+however, it is well to ask, 88 years later, whether some rather elaborate work
+reported recently on the synthesis of straight-line mechanisms is more to the
+point, when the principal objective appears to be the moving of an indicator on
+a &quot;pleasing, expanded&quot; (i.e., squashed flat) radio dial.<a name="FNanchor_49_50" id="FNanchor_49_50"></a><a href="#Footnote_49_50" class="fnanchor">[49]</a></p>
+
+<div class="footnote">
+	<p><a name="Footnote_49_50" id="Footnote_49_50"></a>
+	<a href="#FNanchor_49_50"><span class="label">[49]</span></a>  <em>Machine
+	Design</em>, December 1954, vol. 26, p. 210.</p>
+</div>
+
+<p>But Professor Sylvester was more interested, really, in the mathematical
+possibilities of the Peaucellier linkage, as no doubt our modern investigators
+are. Through a compounding of Peaucellier mechanisms, he had already devised
+square-root and cube-root extractors, an angle trisector, and a
+quadratic-binomial root extractor, and he could see no limits to the computing
+abilities of linkages as yet undiscovered.<a name="FNanchor_50_51" id="FNanchor_50_51"></a><a href="#Footnote_50_51" class="fnanchor">[50]</a></p>
+
+<div class="footnote"><p><a name="Footnote_50_51" id="Footnote_50_51"></a><a href="#FNanchor_50_51"><span class="label">
+	[50]</span></a> Sylvester, <em>op. cit.</em> (footnote 41), p. 191.</p></div>
+
+<p>Sylvester recalled fondly, in a footnote to his lecture, his experience with
+a little mechanical model of the Peaucellier linkage at an earlier dinner
+meeting of the Philosophical Club of the Royal Society. The Peaucellier model
+had been greeted by the members with lively expressions of admiration &quot;when it
+was brought in with the dessert, to be seen by them after dinner, as is the
+laudable custom among members of that eminent body in making known to each other
+the latest scientific novelties.&quot; And Sylvester would never forget the reaction
+of his brilliant friend Sir William Thomson (later Lord Kelvin) upon being
+handed the same model in the Athenaeum Club. After Sir William had operated it
+for a time, Sylvester reached for the model, but he was rebuffed by the
+exclamation &quot;No! I have not had nearly enough of it&#8212;it is the most beautiful
+thing I have ever seen in my life.&quot;<a name="FNanchor_51_52" id="FNanchor_51_52"></a><a href="#Footnote_51_52" class="fnanchor">[51]</a></p>
+
+<div class="footnote"><p><a name="Footnote_51_52" id="Footnote_51_52"></a><a href="#FNanchor_51_52"><span class="label">
+	[51]</span></a> <em>Ibid.</em>, p. 183.</p></div>
+
+<p>The aftermath of Professor Sylvester's performance at the Royal Institution
+was considerable excitement amongst a limited company of interested
+mathematicians. Many alternatives to the Peaucellier straight-line linkage were
+suggested by several writers of papers for learned journals.<a name="FNanchor_52_53" id="FNanchor_52_53"></a><a href="#Footnote_52_53" class="fnanchor">[52]</a></p>
+
+<div class="footnote"><p><a name="Footnote_52_53" id="Footnote_52_53"></a><a href="#FNanchor_52_53"><span class="label">
+	[52]</span></a> For a summary of developments and references, see Kempe,
+	<em>op. cit.</em>  (footnote 21), pp. 49-51. Two of Hart's six-link exact
+	straight-line linkages referred to by Kempe are illustrated in Henry M.
+	Cundy and A. P. Rollett, <em>Mathematical Models</em>, Oxford, Oxford University
+	Press, 1952, pp. 204-205. Peaucellier's linkage was of eight links.</p></div>
+
+<p>In the summer of 1876, after Sylvester had departed from England to take up
+his post as professor of mathematics in the new Johns Hopkins University in
+Baltimore, Alfred Bray Kempe, a young barrister who pursued mathematics as a
+hobby, delivered at London's South Kensington Museum a lecture with the
+provocative title &quot;How to Draw a Straight Line.&quot;<a name="FNanchor_53_54" id="FNanchor_53_54"></a><a href="#Footnote_53_54" class="fnanchor">[53]</a></p>
+
+<div class="footnote"><p><a name="Footnote_53_54" id="Footnote_53_54"></a><a href="#FNanchor_53_54"><span class="label">
+	[53]</span></a> Kempe, <em>op. cit.</em> (footnote 21), p. 26.</p></div>
+
+<p>In order to justify the Peaucellier linkage, Kempe belabored the point that a
+perfect circle could be generated by means of a pivoted bar and a pencil, while
+the generation of a straight line was most difficult if not impossible until
+Captain Peaucellier came along. A straight line could be drawn along a straight
+edge; but how was one to determine whether the straight edge was straight? He
+did not weaken his argument by suggesting the obvious possibility of using a
+piece of string. Kempe had collaborated with Sylvester in pursuing the latter's
+first thoughts on the subject, and one result, that to my mind exemplifies the
+general direction of their thinking, was the Sylvester-Kempe &quot;parallel motion&quot;
+(fig. 26).</p>
+
+<p class="center">
+<img alt="Figure 26" src="images/fig-26.jpg" width="500" height="352" /></p>
+<p>Figure 26.&#8212;Sylvester-Kempe translating linkage, 1877. The
+upper and lower plates remain parallel and equidistant. From A. B. Kempe, <em>
+How to Draw a Straight Line</em> (London, 1877, p. 37).</p>
+
+<p class="center">
+<img alt="Figure 27" src="images/fig-27.jpg" width="500" height="602" /></p>
+<p>Figure 27.&#8212;Gaspard Monge (1746-1818), professor of mathematics
+at the Ecole Polytechnique from 1794 and founder of the academic discipline of
+machine kinematics, From <em>Livre du Centenaire, 1794-1894, Ecole Polytechnique</em>
+(Paris, 1895, vol. 1, frontispiece).</p>
+
+<p>Enthusiastic as Kempe was, however, he injected an apologetic note in his
+lecture. &quot;That these results are valuable cannot I think be doubted,&quot; he said,
+&quot;though it may well be that their great beauty has led some to attribute to them
+an importance which they do not really possess....&quot; He went on to say that 50
+years earlier, before the great improvements in the production of true plane
+surfaces, the straight-line mechanisms would have been more important than in
+1876, but he added that &quot;linkages have not at present, I think, been
+sufficiently put before the mechanician to enable us to say what value should
+really be set upon them.&quot;<a name="FNanchor_54_55" id="FNanchor_54_55"></a><a href="#Footnote_54_55" class="fnanchor">[54]</a></p>
+
+<div class="footnote"><p><a name="Footnote_54_55" id="Footnote_54_55"></a><a href="#FNanchor_54_55"><span class="label">
+	[54]</span></a> <em>Ibid.</em>,, pp. 6-7. I have not pursued the matter of cognate
+	linkages (the Watt and Evans linkages are cognates) because the
+	Roberts-Chebyshev theorem escaped my earlier search, as it had apparently
+	escaped most others until 1958. See R. S. Hartenberg and J. Denavit, &quot;The
+	Fecund Four-Bar,&quot; <em>Transactions of the Fifth Conference on
+	Mechanisms</em>,
+	Cleveland, Penton Publishing Company, 1958, pp. 194-206, reprinted in
+	<em>Machine Design</em>, April 16, 1959, vol. 31, pp. 149-152. See also A. E. R. de Jonge, &quot;The Correlation of Hinged Four-Bar Straight-Line Motion Devices by
+	Means of the Roberts Theorem and a New Proof of the Latter,&quot; <em>Annals
+	of the New York Academy of Sciences</em>, March 18, 1960, vol. 84, art. 3, pp. 75-145
+	(published separately).</p></div>
+
+<p>It was during this same summer of 1876, at the Loan Exhibition of Scientific
+Apparatus in the South Kensington Museum, that the work of Franz Reuleaux, which
+was to have an important and lasting influence on kinematics everywhere, was
+first introduced to English engineers. Some 300 beautifully constructed teaching
+aids, known as the Berlin kinematic models, were loaned to the exhibition by the
+Royal Industrial School in Berlin, of which Reuleaux was the director. These
+models were used by Prof. Alexander B. W. Kennedy of University College, London,
+to help explain Reuleaux's new and revolutionary theory of machines.<a name="FNanchor_55_56" id="FNanchor_55_56"></a><a href="#Footnote_55_56" class="fnanchor">[55]</a></p>
+
+<div class="footnote"><p><a name="Footnote_55_56" id="Footnote_55_56"></a><a href="#FNanchor_55_56"><span class="label">
+	[55]</span></a>  Alexander B. W. Kennedy, &quot;The Berlin Kinematic Models,&quot;
+	<em>Engineering</em>, September 15, 1876, vol. 22, pp. 239-240.</p></div>
+
+<h3><a name="Scholars_and_Machines">Scholars and Machines</a></h3>
+
+<p>When, in 1829, André-Marie Ampère (1775-1836) was called upon to prepare a
+course in theoretical and experimental physics for the Collège de France, he
+first set about determining the limits of the field of physics. This exercise
+suggested to his wide-ranging intellect not only the definition of physics but
+the classification of all human knowledge. He prepared his scheme of
+classification, tried it out on his physics students, found it incomplete,
+returned to his study, and produced finally a two-volume work wherein the
+province of kinematics was first marked out for all to see and consider.<a name="FNanchor_56_57" id="FNanchor_56_57"></a><a href="#Footnote_56_57" class="fnanchor">[56]</a>
+Only a few lines could be devoted to so specialized a branch as kinematics, but
+Ampère managed to capture the central idea of the subject.</p>
+
+<div class="footnote"><p><a name="Footnote_56_57" id="Footnote_56_57"></a><a href="#FNanchor_56_57"><span class="label">
+	[56]</span></a>  André-Marie Ampère, <em>Essai sur la philosophie des sciences,
+	une exposition analytique d'une classification naturelle de toutes les
+	connaissances humaines</em>, 2 vols., Paris, 1838 (for origin of the project,
+	see vol. 1, pp. v, xv).</p></div>
+
+<p>Cinématique (from the Greek word for movement) was, according to Ampère, the
+science &quot;in which movements are considered in themselves [independent of the
+forces which produce them], as we observe them in solid bodies all about us, and
+especially in the assemblages called machines.&quot;<a name="FNanchor_57_58" id="FNanchor_57_58"></a><a href="#Footnote_57_58" class="fnanchor">[57]</a>
+Kinematics, as the study soon came to be known in English,<a name="FNanchor_58_59" id="FNanchor_58_59"></a><a href="#Footnote_58_59" class="fnanchor">[58]</a>
+was one of the two branches of elementary mechanics, the other being statics.</p>
+
+<div class="footnote"><p><a name="Footnote_57_58" id="Footnote_57_58"></a><a href="#FNanchor_57_58"><span class="label">
+	[57]</span></a> <em>Ibid.</em>, vol. 1, pp. 51-52.</p></div>
+
+<div class="footnote"><p><a name="Footnote_58_59" id="Footnote_58_59"></a><a href="#FNanchor_58_59"><span class="label">
+	[58]</span></a> Willis (<em>op. cit.</em> footnote 21) adopted the word
+	&quot;kinematics,&quot; and this Anglicization subsequently became the standard term
+	for this branch of mechanics.</p></div>
+
+<p>In his definition of kinematics, Ampère stated what the faculty of
+mathematics at the Ecole Polytechnique, in Paris, had been groping toward since
+the school's opening some 40 years earlier. The study of mechanisms as an
+intellectual discipline most certainly had its origin on the left bank of the
+Seine, in this school spawned, as suggested by one French historian,<a name="FNanchor_59_60" id="FNanchor_59_60"></a><a href="#Footnote_59_60" class="fnanchor">[[59]</a>
+by the great <em>Encyclopédie</em> of Diderot and d'Alembert.</p>
+
+<div class="footnote"><p><a name="Footnote_59_60" id="Footnote_59_60"></a><a href="#FNanchor_59_60"><span class="label">
+	[59]</span></a>  G. Pinet, <em>Histoire de l'Ecole Polytechnique</em>, Paris, 1887,
+	pp. viii-ix. In their forthcoming book on kinematic synthesis, R. S. Hartenberg and J. Denavit will trace the germinal ideas of Jacob Leupold and
+	Leonhard Euler of the 18th century.</p></div>
+
+<p>Because the Ecole Polytechnique had such a far-reaching influence upon the
+point of view from which mechanisms were contemplated by scholars for nearly a
+century after the time of Watt, and by compilers of dictionaries of mechanical
+movements for an even longer time, it is well to look for a moment at the early
+work that was done there. If one is interested in origins, it might be
+profitable for him to investigate the military school in the ancient town of
+Mézières, about 150 miles northeast of Paris. It was here that Lazare Carnot,
+one of the principal founders of the Ecole Polytechnique, in 1783 published his
+essay on machines,<a name="FNanchor_60_61" id="FNanchor_60_61"></a><a href="#Footnote_60_61" class="fnanchor">[60]</a>
+which was concerned, among other things, with showing the impossibility of
+&quot;perpetual motion&quot;; and it was from Mézières that Gaspard Monge and Jean
+Hachette<a name="FNanchor_61_62" id="FNanchor_61_62"></a><a href="#Footnote_61_62" class="fnanchor">[61]</a>
+came to Paris to work out the system of mechanism classification that has come
+to be associated with the names of Lanz and Bétancourt.</p>
+
+<div class="footnote"><p><a name="Footnote_60_61" id="Footnote_60_61"></a><a href="#FNanchor_60_61"><span class="label">
+	[60]</span></a>  Lazare N. M. Carnot, <em>Essai sur les machines en général</em>,
+	Mézières, 1783 (later published as <em>Principes fondamentaux de l'equilibre et
+	du mouvement</em>, Paris, 1803).</p></div>
+
+<div class="footnote"><p><a name="Footnote_61_62" id="Footnote_61_62"></a><a href="#FNanchor_61_62"><span class="label">
+	[61]</span></a>  Biographical notices of Monge and Hachette appear in
+	<em>Encyclopaedia Britannica</em>, ed. 11. See also <em>L'Ecole Polytechnique, Livre
+	du Centenaire</em>, Paris, 1895, vol. 1, p. 11ff.</p></div>
+
+<p>Gaspard Monge (1746-1818), who while a draftsman at Mézières originated the
+methods of descriptive geometry, came to the Ecole Polytechnique as professor of
+mathematics upon its founding in 1794, the second year of the French Republic.
+According to Jean Nicolas Pierre Hachette (1769-1834), who was junior to Monge
+in the department of descriptive geometry, Monge planned to give a two-months'
+course devoted to the elements of machines. Having barely gotten his department
+under way, however, Monge became involved in Napoleon's ambitious scientific
+mission to Egypt and, taking leave of his family and his students, embarked for
+the distant shores.</p>
+
+<p>&quot;Being left in charge,&quot; wrote Hachette, &quot;I prepared the course of which
+Monge
+had given only the first idea, and I pursued the study of machines in order to
+analyze and classify them, and to relate geometrical and mechanical principles
+to their construction.&quot; Changes of curriculum delayed introduction of the course
+until 1806, and not until 1811 was his textbook ready, but the outline of his
+ideas was presented to his classes in chart form (fig. 28). This chart was the
+first of the widely popular synoptical tables of mechanical movements.<a name="FNanchor_62_63" id="FNanchor_62_63"></a><a href="#Footnote_62_63" class="fnanchor">[62]</a></p>
+
+<div class="footnote"><p><a name="Footnote_62_63" id="Footnote_62_63"></a><a href="#FNanchor_62_63"><span class="label">
+	[62]</span></a>  Jean N. P. Hachette, <em>Traité élémentaire des machines</em>,
+	Paris, 1811, p. v.</p></div>
+
+<p class="center">
+<img alt="Figure 28" src="images/fig-28.jpg" width="600" height="329" /></p>
+<p>Figure 28.&#8212;Hachette's synoptic chart of elementary mechanisms,
+1808. This was the first of many charts of mechanical movements that enjoyed
+wide popularity for over 100 years.</p>
+
+<p>From Jean N. P. Hachette, <em>Traité Élémentaire des Machines</em> (Paris,
+1811, pl. 1).</p>
+
+<p>Hachette classified all mechanisms by considering the conversion of one
+motion into another. His elementary motions were continuous circular,
+alternating circular, continuous rectilinear, and alternating rectilinear.
+Combining one motion with another&#8212;for example, a treadle and crank converted
+alternating circular to continuous circular motion&#8212;he devised a system that
+supplied a frame of reference for the study of mechanisms. In the U.S. Military
+Academy at West Point, Hachette's treatise, in the original French, was used as
+a textbook in 1824, and perhaps earlier.<a name="FNanchor_63_64" id="FNanchor_63_64"></a><a href="#Footnote_63_64" class="fnanchor">[63]</a></p>
+
+<div class="footnote"><p><a name="Footnote_63_64" id="Footnote_63_64"></a><a href="#FNanchor_63_64"><span class="label">
+	[63]</span></a>  This work was among the books sent back by Sylvanus Thayer
+	when he visited France in 1816 to observe the education of the French army
+	cadets. Thayer's visit resulted in his adopting the philosophy of the Ecole
+	Polytechnique in his reorganization of the U.S. Military Academy and,
+	incidentally, in his inclusion of Hachette's course in the Academy's
+	curriculum (U.S. Congress, <em>American State Papers</em>, Washington, 1832-1861,
+	Class v, Military Affairs, vol. 2, p. 661: Sidney Forman, <em>West Point</em>, New
+	York, 1950, pp. 36-60). There is a collection of miscellaneous papers
+	(indexed under Sylvanus Thayer and William McRee, U.S. National Archives, RG
+	77, Office, Chief of Engineers, Boxes 1 and 6) pertaining to the U.S.
+	Military Academy of this period, but I found no mention of kinematics in
+	this collection.</p></div>
+
+<p>Lanz and Bétancourt, scholars from Spain at the Ecole Polytechnique, plugged
+some of the gaps in Hachette's system by adding continuous and alternating
+curvilinear motion, which doubled the number of combinations to be treated, but
+the advance of their work over that of Hachette was one of degree rather than of
+kind.<a name="FNanchor_64_65" id="FNanchor_64_65"></a><a href="#Footnote_64_65" class="fnanchor">[64]</a></p>
+
+<div class="footnote"><p><a name="Footnote_64_65" id="Footnote_64_65"></a><a href="#FNanchor_64_65"><span class="label">
+	[64]</span></a>  Phillipe Louis Lanz and Augustin de Bétancourt, <em>Essai sur
+	la composition des machines</em>, Paris, 1808. Hachette's chart and an outline
+	of his elementary course on machines is bound with the Princeton University
+	Library copy of the Lanz and Bétancourt work. This copy probably represents
+	the first textbook of kinematics. Bétancourt was born in 1760 in Teneriffe,
+	attended the military school in Madrid, and became inspector-general of
+	Spanish roads and canals. He was in England before 1789, learning how to
+	build Watt engines, and he introduced the engines to Paris in 1790 (see
+	Farey, <em>op. cit.</em>,, p. 655). He entered Russian service in 1808 and died in
+	St. Petersburg in 1826 (J. C. Poggendorff, <em>Biographisches-literarisches
+	Handwörterbuch für Mathematik ...</em>, Leipzig, 1863, vol. 1.</p></div>
+
+<p class="center">
+<img alt="Figure 29" src="images/fig-29.jpg" width="500" height="640" /></p>
+<p>Figure 29.&#8212;Robert Willis (1800-1875), Jacksonian Professor,
+Cambridge University, and author of <em>Principles of Mechanism</em>, one of the
+landmark books in the development of kinematics of mechanisms. Photo courtesy Gonville
+and Caius College, Cambridge University.</p>
+
+<p>Giuseppe Antonio Borgnis, an Italian &quot;engineer and member of many academies&quot;
+and professor of mechanics at the University of Pavia in Italy, in his
+monumental, nine-volume <em>Traité complet de méchanique appliquée aux arts</em>,
+caused a bifurcation of the structure built upon Hachette's foundation of
+classification when he introduced six orders of machine elements and subdivided
+these into classes and species. His six orders were <em>récepteurs</em> (receivers of
+motion from the prime mover), <em>communicateurs</em>, <em>modificateurs</em> (modifiers of
+velocity), <em>supports</em> (e.g., bearings), <em>regulateurs</em> (e.g., governors), and
+<em>operateurs</em>, which produced the final effect.<a name="FNanchor_65_66" id="FNanchor_65_66"></a><a href="#Footnote_65_66" class="fnanchor">[65]</a></p>
+
+<div class="footnote"><p><a name="Footnote_65_66" id="Footnote_65_66"></a><a href="#FNanchor_65_66"><span class="label">
+	[65]</span></a>  Giuseppe Antonio Borgnis, <em>Théorie de la mécanique usuelle</em>
+	in <em>Traité complet de mécanique appliquée aux arts</em>, Paris, 1818, vol. 1,
+	pp. xiv-xvi.</p></div>
+
+<p>The brilliant Gaspard-Gustave de Coriolis (1792-1843)&#8212;remembered mainly for a
+paper of a dozen pages explaining the nature of the acceleration that bears his
+name<a name="FNanchor_66_67" id="FNanchor_66_67"></a><a href="#Footnote_66_67" class="fnanchor">[66]</a>&#8212;was
+another graduate of the Ecole Polytechnique who wrote on the subject of
+machines. His book,<a name="FNanchor_67_68" id="FNanchor_67_68"></a><a href="#Footnote_67_68" class="fnanchor">[67]</a>
+published in 1829, was provoked by his recognition that the designer of machines
+needed more knowledge than his undergraduate work at the Ecole Polytechnique was
+likely to give him. Although he embraced a part of Borgnis' approach, adopting
+<em>récepteurs</em>, <em>communicateurs</em>, and <em>operateurs</em>, Coriolis indicated by the
+title of his book that he was more concerned with forces than with relative
+displacements. However, the attractively simple three-element scheme of Coriolis
+became well fixed in French thinking.<a name="FNanchor_68_69" id="FNanchor_68_69"></a><a href="#Footnote_68_69" class="fnanchor">[68]</a></p>
+
+<div class="footnote"><p><a name="Footnote_66_67" id="Footnote_66_67"></a><a href="#FNanchor_66_67"><span class="label">
+	[66]</span></a>  Gaspard-Gustave de Coriolis, &quot;Memoire sur les equations du
+	mouvement relatif des systèmes de corps,&quot; <em>Journal de l'Ecole
+	Polytechnique</em>, 1835, vol. 15, pp. 142-154.</p></div>
+
+<div class="footnote"><p><a name="Footnote_67_68" id="Footnote_67_68"></a><a href="#FNanchor_67_68"><span class="label">
+	[67]</span></a>  Gaspard-Gustave de Coriolis, <em>De Calcul de l'effet des
+	machines</em>, Paris, 1829. In this book Coriolis proposed the now generally
+	accepted equation, work = force × distance (pp. iii, 2).</p></div>
+
+<div class="footnote"><p><a name="Footnote_68_69" id="Footnote_68_69"></a><a href="#FNanchor_68_69"><span class="label">
+	[68]</span></a>  The renowned Jean Victor Poncelet lent weight to this
+	scheme. (See Franz Reuleaux, <em>Theoretische Kinematik: Grundzüge einer
+	Theorie des Maschinenwesens</em>, Braunschweig, 1875, translated by Alexander B.
+	W. Kennedy as <em>The Kinematics of Machinery: Outlines of a Theory of
+	Machines</em>, London, 1876, pp. 11, 487. I have used the Kennedy translation in
+	the Reuleaux references throughout the present work.)</p></div>
+
+<p>Michel Chasles (1793-1880), another graduate of the Ecole Polytechnique,
+contributed some incisive ideas in his papers on instant centers<a name="FNanchor_69_70" id="FNanchor_69_70"></a><a href="#Footnote_69_70" class="fnanchor">[69]</a>
+published during the 1830's, but their tremendous importance in kinematic
+analysis was not recognized until much later.</p>
+
+<div class="footnote"><p><a name="Footnote_69_70" id="Footnote_69_70"></a><a href="#FNanchor_69_70"><span class="label">
+	[69]</span></a>  The instant center was probably first recognized by Jean
+	Bernoulli (1667-1748) in his &quot;De Centro Spontaneo Rotationis&quot; (<em>Johannis
+	Bernoulli ... Opera Omnia ...</em>, Lausanne, 1742, vol. 4, p. 265ff.).</p></div>
+
+<p class="center">
+<img alt="Figure 30" src="images/fig-30.jpg" width="500" height="636" /></p>
+<p>Figure 30.&#8212;Franz Reuleaux (1829-1905). His <em>Theoretische
+Kinematik</em>, published in 1875, provided the basis for modern kinematic analysis.
+Photo courtesy Deutsches Museum, Munich.</p>
+
+<p>Acting upon Ampère's clear exposition of the province of kinematics and
+excluding, as Ampère had done, the consideration of forces, an Englishman,
+Robert Willis, made the next giant stride forward in the analysis of mechanisms.
+Willis was 37 years old in 1837 when he was appointed professor of natural and
+experimental philosophy at Cambridge. In the same year Professor Willis&#8212;a man of
+prodigious energy and industry and an authority on archeology and architectural
+history as well as mechanisms&#8212;read his important paper &quot;On the Teeth of Wheels&quot;
+before the Institution of Civil Engineers<a name="FNanchor_70_71" id="FNanchor_70_71"></a><a href="#Footnote_70_71" class="fnanchor">[[70]</a>
+and commenced at Cambridge his lectures on kinematics of mechanisms that
+culminated in his 1841 book <em>Principles of Mechanism</em>.<a name="FNanchor_71_72" id="FNanchor_71_72"></a><a href="#Footnote_71_72" class="fnanchor">[71]</a></p>
+
+<div class="footnote"><p><a name="Footnote_70_71" id="Footnote_70_71"></a><a href="#FNanchor_70_71"><span class="label">
+	[70]</span></a>  Robert Willis, &quot;On the Teeth of Wheels,&quot; <em>
+	Transactions of the Institution of Civil Engineers of London</em>, 1838, vol. 2, pp. 89-112.</p></div>
+
+<div class="footnote"><p><a name="Footnote_71_72" id="Footnote_71_72"></a><a href="#FNanchor_71_72"><span class="label">
+	[71]</span></a> Willis, <em>op. cit.</em>  (footnote 21). Through the kindness of
+	its owner (Mr. Warren G. Ogden of North Andover, Massachusetts), I have had
+	access to Willis' own copy of his 1841 edition of <em>Principles of
+	Mechanism</em>.
+	The book is interleaved, and it contains notes made by Willis from time to
+	time until at least 1870, when the second edition was issued. Corrections,
+	emendations, notations of some of his sources (for example, the De Voglie
+	linkage mentioned in footnote 35 above), notes to himself to &quot;examine the
+	general case&quot; and &quot;examine the modern forms&quot; of straight-line devices are
+	interspersed with references to authors that had borrowed from his work
+	without acknowledgment. Of one author Willis writes an indignant &quot;He ignores
+	my work.&quot;</p></div>
+
+<p>It seemed clear to Willis that the problem of devising a mechanism for a
+given purpose ought to be attacked systematically, perhaps mathematically, in
+order to determine &quot;all the forms and arrangements that are applicable to the
+desired purpose,&quot; from which the designer might select the simplest or most
+suitable combination. &quot;At present,&quot; he wrote, &quot;questions of this kind can only
+be solved by that species of intuition which long familiarity with a subject
+usually confers upon experienced persons, but which they are totally unable to
+communicate to others.&quot;</p>
+
+<p>In analyzing the process by which a machine was designed, Willis observed:
+&quot;When the mind of a mechanician is occupied with the contrivance of a machine,
+he must wait until, in the midst of his meditations, some happy combination
+presents itself to his mind which may answer his purpose.&quot; He ventured the
+opinion that at this stage of the design process &quot;the motions of the machine are
+the principal subject of contemplation, rather than the forces applied to it, or
+the work it has to do.&quot; Therefore he was prepared to adopt without reservation
+Ampère's view of kinematics, and, if possible, to make the science useful to
+engineers by stating principles that could be applied without having to fit the
+problem at hand into the framework of the systems of classification and
+description that had gone before. He appraised the &quot;celebrated system&quot; of Lanz
+and Bétancourt as &quot;a merely popular arrangement, notwithstanding the apparently
+scientific simplicity of the scheme.&quot; He rejected this scheme because &quot;no
+attempt is made to subject the motions to calculation, or to reduce these laws
+to general formulas, for which indeed the system is totally unfitted.&quot;</p>
+
+<p>Borgnis had done a better job, Willis thought, in actually describing
+machinery, with his &quot;orders&quot; based upon the functions of machine elements or
+mechanisms within the machine, but again there was no means suggested by which
+the kinematics of mechanisms could be systematically investigated.</p>
+
+<p>Although Willis commenced his treatise with yet another &quot;synoptical table of
+the elementary combinations of pure mechanism,&quot; his view shifted quickly from
+description to analysis. He was consistent in his pursuit of analytical methods
+for &quot;pure mechanism,&quot; eschewing any excursions into the realm of forces and
+absolute velocities. He grasped the important concept of relative displacements
+of machine elements, and based his treatment upon &quot;the proportions and relations
+between the velocities and directions of the pieces, and not upon their actual
+and separate motions.&quot;<a name="FNanchor_72_73" id="FNanchor_72_73"></a><a href="#Footnote_72_73" class="fnanchor">[72]</a></p>
+
+<div class="footnote"><p><a name="Footnote_72_73" id="Footnote_72_73"></a><a href="#FNanchor_72_73"><span class="label">
+	[72]</span></a> <em>Ibid.</em>, pp. iv, x-xii, xxi, 15.</p></div>
+
+<p>That he did not succeed in developing the &quot;formulas&quot; that would enable the
+student to determine &quot;all the forms and arrangements that are applicable to the
+desired purpose&quot;&#8212;that he did not present a rational approach to synthesis&#8212;is not
+to be wondered at. Well over a century later we still are nibbling at the
+fringes of the problem. Willis did, nonetheless, give the thoughtful reader a
+glimpse of the most powerful tool for kinematic synthesis that has yet been
+devised; namely, kinematic analysis, in which the argument is confined to the
+relative displacements of points on links of a mechanism, and through which the
+designer may grasp the nature of the means at his disposal for the solution of
+any particular problem.</p>
+
+<p>As remarked by Reuleaux a generation later, there was much in Professor
+Willis's book that was wrong, but it was an original, thoughtful work that
+departed in spirit if not always in method from its predecessors. <em>Principles
+of Mechanism</em> was a prominent landmark along the road to a rational discipline of
+machine-kinematics.</p>
+
+<p>A phenomenal engineer of the 19th century was the Scottish professor of civil
+engineering at the University of Glasgow, William John MacQuorn Rankine.
+Although he was at the University for only 17 years&#8212;he died at the age of 52, in
+1872&#8212;he turned out during that time four thick manuals on such diverse subjects
+as civil engineering, ship-building, thermodynamics, and machinery and
+mill-work, in addition to literally hundreds of papers, articles, and notes for
+scientific journals and the technical press. Endowed with apparently boundless
+energy, he found time from his studies to command a battalion of rifle
+volunteers and to compose and sing comic and patriotic songs. His manuals, often
+used as textbooks, were widely circulated and went through many editions.
+Rankine's work had a profound effect upon the practice of engineering by setting
+out principles in a form that could be grasped by people who were dismayed by
+the treatment usually found in the learned journals.</p>
+
+<p>When Rankine's book titled <em>A Manual of Machinery and Millwork</em> was published
+in 1869 it was accurately characterized by a reviewer as &quot;dealing with the
+<em>principles</em> of machinery and millworks, and as such it is entirely distinct
+from [other works on the same subject] which treat more of the practical
+applications of such principles than of the principles themselves.&quot;<a name="FNanchor_73_74" id="FNanchor_73_74"></a><a href="#Footnote_73_74" class="fnanchor">[73]</a></p>
+
+<div class="footnote"><p><a name="Footnote_73_74" id="Footnote_73_74"></a><a href="#FNanchor_73_74"><span class="label">
+	[73]</span></a>  <em>Engineering</em>, London, August 13, 1869, vol. 8, p. 111.</p></div>
+
+<p>Rankine borrowed what appeared useful from Willis' <em>Principles of
+Mechanism</em>
+and from other sources. His treatment of kinematics was not as closely reasoned
+as the later treatises of Reuleaux and Kennedy, which will be considered below.
+Rankine did, however, for the first time show the utility of instant centers in
+velocity analysis, although he made use only of the instant centers involving
+the fixed link of a linkage. Like others before him, he considered the fixed
+link of a mechanism as something quite different from the movable links, and he
+did not perceive the possibilities opened up by determining the instant center
+of two movable links.</p>
+
+<p>Many other books dealing with mechanisms were published during the middle
+third of the century, but none of them had a discernible influence upon the
+advance of kinematical ideas.<a name="FNanchor_74_75" id="FNanchor_74_75"></a><a href="#Footnote_74_75" class="fnanchor">[74]</a>
+The center of inquiry had by the 1860's shifted from France to Germany. Only by
+scattered individuals in England, Italy, and France was there any impatience
+with the well-established, general understanding of the machine-building art.</p>
+
+<div class="footnote"><p><a name="Footnote_74_75" id="Footnote_74_75"></a><a href="#FNanchor_74_75"><span class="label">
+	[74]</span></a> Several such books are referred to by Reuleaux, <em>op. cit.</em>
+	(footnote 68), pp. 12-16.</p></div>
+
+<p>In Germany, on the other hand, there was a surge of industrial activity that
+attracted some very able men to the problems of how machines ought to be built.
+Among the first of these was Ferdinand Redtenbacher (1809-1863), professor of
+mechanical engineering in the polytechnic school in Karlsruhe, not far from
+Heidelberg. Redtenbacher, although he despaired of the possibility of finding a
+&quot;true system on which to base the study of mechanisms,&quot; was nevertheless a
+factor in the development of such a system. He had young Franz Reuleaux in his
+classes for two years, from 1850. During that time the older man's commanding
+presence, his ability as a lecturer, and his infectious impatience with the
+existing order influenced Reuleaux to follow the scholar's trail that led him to
+eminence as an authority of the first rank.<a name="FNanchor_75_76" id="FNanchor_75_76"></a><a href="#Footnote_75_76" class="fnanchor">[75]</a></p>
+
+<div class="footnote"><p><a name="Footnote_75_76" id="Footnote_75_76"></a><a href="#FNanchor_75_76"><span class="label">
+	[75]</span></a>  See Carl Weihe, &quot;Franz Reuleaux und die Grundlagen seiner
+	Kinematik,&quot; Deutsches Museum, Munich, <em>Abhandlung und Berichte</em>, 1942, p. 2;
+	Friedrich Klemm, <em>Technik: Eine Geschichte ihrer Probleme</em>, Freiburg and
+	Munich, Verlag Karl Alber, 1954, translated by Dorothea W. Singer as <em>A
+	History of Western Technology</em>, New York, Charles Scribner's Sons, 1959, p.
+	317.</p></div>
+
+<p>Before he was 25 years old Franz Reuleaux published, in collaboration with a
+classmate, a textbook whose translated title would be <em>Constructive Lessons
+for the Machine Shop</em>.<a name="FNanchor_76_77" id="FNanchor_76_77"></a><a href="#Footnote_76_77" class="fnanchor">[76]</a>
+His several years in the workshop, before and after coming under Redtenbacher's
+influence, gave his works a practical flavor, simple and direct. According to
+one observer, Reuleaux's book exhibited &quot;a recognition of the claims of practice
+such as Englishmen do not generally associate with the writings of a German
+scientific professor.&quot;<a name="FNanchor_77_78" id="FNanchor_77_78"></a><a href="#Footnote_77_78" class="fnanchor">[77]</a></p>
+
+<div class="footnote"><p><a name="Footnote_76_77" id="Footnote_76_77"></a><a href="#FNanchor_76_77"><span class="label">
+	[76]</span></a> See Weihe, <em>op. cit.</em>  (footnote 75), p. 3; Hans Zopke,
+	&quot;Professor Franz Reuleaux,&quot; <em>Cassier's Magazine</em>, December 1896, vol. 11,
+	pp. 133-139; <em>Transactions of the American Society of Mechanical
+	Engineers</em>,
+	1904-1905, vol. 26, pp. 813-817.</p></div>
+
+<div class="footnote"><p><a name="Footnote_77_78" id="Footnote_77_78"></a><a href="#FNanchor_77_78"><span class="label">
+	[77]</span></a>  <em>Engineering</em>, London, September 8, 1876, vol. 22, p. 197.</p></div>
+
+<p>Reuleaux's original ideas on kinematics, which are responsible for the way in
+which we look at mechanisms today, were sufficiently formed in 1864 for him to
+lecture upon them.<a name="FNanchor_78_79" id="FNanchor_78_79"></a><a href="#Footnote_78_79" class="fnanchor">[78]</a>
+Starting in 1871, he published his findings serially in the publication of the
+Verein zur Beförderung des Gewerbefleisses in Preussen (Society for the
+Advancement of Industry in Prussia), of which he was editor. In 1875 these
+articles were brought together in the book that established his
+fame&#8212;<em>Theoretische Kinematik....</em><a name="FNanchor_79_80" id="FNanchor_79_80"></a><a href="#Footnote_79_80" class="fnanchor">[79]</a></p>
+
+<div class="footnote"><p><a name="Footnote_78_79" id="Footnote_78_79"></a><a href="#FNanchor_78_79"><span class="label">
+	[78]</span></a>  A. E. Richard de Jonge, &quot;What is Wrong with Kinematics and
+	Mechanisms?&quot; <em>Mechanical Engineering</em>, April 1942, vol. 64, pp. 273-278
+	(comments on this paper are in <em>Mechanical Engineering,</em> October 1942, vol.
+	64, pp. 744-751); Zopke, <em>op. cit.</em> (footnote 76), p. 135.</p></div>
+
+<div class="footnote"><p><a name="Footnote_79_80" id="Footnote_79_80"></a><a href="#FNanchor_79_80"><span class="label">
+	[79]</span></a> Reuleaux, <em>op. cit.</em> (footnote 68). This was not the last of
+	Reuleaux's books. His trilogy on kinematics and machine design is discussed
+	by De Jonge, <em>op. cit.</em> (footnote 78).</p></div>
+
+<p>In the introduction of this book, Reuleaux wrote:</p>
+
+<p><span style="margin-left: 2.5em;">In the development of every exact science, its
+substance having</span><br />
+<span style="margin-left: 2.5em;">grown sufficiently to make generalization
+possible, there is a time</span><br />
+<span style="margin-left: 2.5em;">when a series of changes bring it into
+clearness. This time has</span><br />
+<span style="margin-left: 2.5em;">most certainly arrived for the science of
+kinematics. The number of</span><br />
+<span style="margin-left: 2.5em;">mechanisms has grown almost out of measure,
+and the number of ways</span><br />
+<span style="margin-left: 2.5em;">in which they are applied no less. It has
+become absolutely</span><br />
+<span style="margin-left: 2.5em;">impossible still to hold the thread which can
+lead in any way</span><br />
+<span style="margin-left: 2.5em;">through this labyrinth by the existing
+methods.<a name="FNanchor_80_81" id="FNanchor_80_81"></a><a href="#Footnote_80_81" class="fnanchor">[80]</a></span><br />
+</p>
+
+<div class="footnote"><p><a name="Footnote_80_81" id="Footnote_80_81"></a><a href="#FNanchor_80_81"><span class="label">
+	[80]</span></a> Reuleaux, <em>op. cit.</em> (footnote 68), p. 23.</p></div>
+
+<p>Reuleaux's confidence that it would be his own work that would bring order
+out of confusion was well founded. His book had already been translated into
+Italian and was being translated into French when, only a year after its
+publication, it was presented by Prof. Alexander B. W. Kennedy in English
+translation.<a name="FNanchor_81_82" id="FNanchor_81_82"></a><a href="#Footnote_81_82" class="fnanchor">[81]</a></p>
+
+<div class="footnote"><p><a name="Footnote_81_82" id="Footnote_81_82"></a><a href="#FNanchor_81_82"><span class="label">
+	[81]</span></a> <em>Ibid.</em>,, p. iii.</p></div>
+
+<p>The book was enthusiastically reviewed by the weekly London journal
+<em>Engineering</em>,<a name="FNanchor_82_83" id="FNanchor_82_83"></a><a href="#Footnote_82_83" class="fnanchor">[82]</a>
+and it was given lengthy notice by the rival journal, <em>The Engineer</em>. The editor
+of <em>The Engineer</em> thought that the mechanician would find in it many new ideas,
+that he would be &quot;taught to detect hitherto hidden resemblances, and that he
+must part&#8212;reluctantly, perhaps&#8212;with many of his old notions.&quot; &quot;But,&quot; added the
+editor with considerable justice, &quot;that he [the mechanician] would suddenly
+recognize in Professor Reuleaux's 'kinematic notation,' 'analysis,' and
+'synthesis,' the long-felt want of his professional existence we do not for a
+moment believe.&quot;<a name="FNanchor_83_84" id="FNanchor_83_84"></a><a href="#Footnote_83_84" class="fnanchor">[83]</a>
+Indeed, the fresh and sharp ideas of Reuleaux were somewhat clouded by a long
+(600-page) presentation; and his kinematic notation, which required another
+attempt at classification, did not simplify the presentation of radically new
+ideas.<a name="FNanchor_84_85" id="FNanchor_84_85"></a><a href="#Footnote_84_85" class="fnanchor">[84]</a></p>
+
+<div class="footnote"><p><a name="Footnote_82_83" id="Footnote_82_83"></a><a href="#FNanchor_82_83"><span class="label">
+	[82]</span></a>  <em>Engineering</em>, <em>loc. cit.</em> (footnote 77).</p></div>
+
+<div class="footnote"><p><a name="Footnote_83_84" id="Footnote_83_84"></a><a href="#FNanchor_83_84"><span class="label">
+	[83]</span></a>  <em>The Engineer</em>, London, March 30 and April 13, 1877, vol.
+	43, pp. 211-212, 247-248.</p></div>
+
+<div class="footnote"><p><a name="Footnote_84_85" id="Footnote_84_85"></a><a href="#FNanchor_84_85"><span class="label">
+	[84]</span></a>  It is perhaps significant that the first paper of the First
+	Conference on Mechanisms at Purdue University was Allen S. Hall's
+	&quot;Mechanisms and Their Classification,&quot; which appeared in <em>
+	Machine Design</em>,
+	December 1953, vol. 25, pp. 174-180. The place of classification in
+	kinematic synthesis is suggested in Ferdinand Freudenstein's &quot;Trends in
+	Kinematics of Mechanisms,&quot; <em>Applied Mechanics Reviews</em>, September 1959, vol.
+	12, pp. 587-590.</p></div>
+
+<p class="center">
+<img alt="Figure 31" src="images/fig-31.jpg" width="430" height="600" /></p>
+<p>Figure 31.&#8212;Alexander Blackie William Kennedy (1847-1928),
+translator of Reuleaux' <em>Theoretische Kinematik</em> and discoverer of Kennedy's
+&quot;Law of Three Centers.&quot; From <em>Minutes of the Proceedings of the
+Institution of Civil Engineers</em> (1907, vol. 167, frontispiece).</p>
+
+<p>Nevertheless, no earlier author had seen the problem of kinematic analysis so
+clearly or had introduced so much that was fresh, new, and of lasting value.</p>
+
+<p>Reuleaux was first to state the concept of the pair; by his concept of the
+expansion of pairs he was able to show similarities in mechanisms that had no
+apparent relation. He was first to recognize that the fixed link of a mechanism
+was kinematically the same as the movable links. This led him to the important
+notion of inversion of linkages, fixing successively the various links and thus
+changing the function of the mechanism. He devoted 40 pages to showing, with
+obvious delight, the kinematic identity of one design after another of rotary
+steam engines, demolishing for all time the fond hopes of ingenious but
+ill-informed inventors who think that improvements and advances in mechanism
+design consist in contortion and complexity.</p>
+
+<p>The chapter on synthesis was likewise fresh, but it consisted of a
+discussion, not a system; and Reuleaux stressed the idea that I have mentioned
+above in connection with Willis' book, that synthesis will be successful in
+proportion to the designer's understanding and appreciation of analysis.
+Reuleaux tried to put the designer on the right track by showing him clearly
+&quot;the essential simplicity of the means with which we have to work&quot; and by
+demonstrating to him &quot;that the many things which have to be done can be done
+with but few means, and that the principles underlying them all lie clearly
+before us.&quot;<a name="FNanchor_85_86" id="FNanchor_85_86"></a><a href="#Footnote_85_86" class="fnanchor">[85]</a></p>
+
+<div class="footnote"><p><a name="Footnote_85_86" id="Footnote_85_86"></a><a href="#FNanchor_85_86"><span class="label">
+	[85]</span></a> Reuleaux, <em>op. cit.</em> (footnote 68), p. 582.</p></div>
+
+<p>It remained for Sir Alexander Blackie William Kennedy (1847-1928) and Robert
+Henry Smith (1852-1916) to add to Reuleaux's work the elements that would give
+kinematic analysis essentially its modern shape.</p>
+
+<p>Kennedy, the translator of Reuleaux's book, became professor of engineering
+at the University College in London in 1874, and eventually served as president
+both of the Institution of Mechanical Engineers and of the Institution of Civil
+Engineers. Smith, who had taught in the Imperial University of Japan, was
+professor of engineering at Mason College, now a part of Birmingham University,
+in England.</p>
+
+<p>While Reuleaux had used instant centers almost exclusively for the
+construction of centrodes (paths of successive positions of an instant center),
+Professor Kennedy recognized that instant centers might be used in velocity
+analysis. His book, <em>Mechanics of Machinery</em>, was published in 1886 (&quot;partly
+through pressure of work and partly through ill-health, this book appears only
+now&quot;). In it he developed the law of three centers, now known as Kennedy's
+theorem. He noted that his law of three centers &quot;was first given, I believe, by
+Aronhold, although its previous publication was unknown to me until some years
+after I had given it in my lectures.&quot;<a name="FNanchor_86_87" id="FNanchor_86_87"></a><a href="#Footnote_86_87" class="fnanchor">[86]</a>
+In fact, the law had been published by Siegfried Heinrich Aronhold (1819-1884)
+in his &quot;Outline of Kinematic Geometry,&quot; which appeared in 1872 alongside
+Reuleaux's series in the journal that Reuleaux edited. Apparently Reuleaux did
+not perceive its particular significance at that time.<a name="FNanchor_87_88" id="FNanchor_87_88"></a><a href="#Footnote_87_88" class="fnanchor">[87]</a></p>
+
+<div class="footnote"><p><a name="Footnote_86_87" id="Footnote_86_87"></a><a href="#FNanchor_86_87"><span class="label">
+	[86]</span></a>  Alexander B. W. Kennedy, <em>The Mechanics of Machinery</em>, ed.
+	3, London, 1898, pp. vii, x.</p></div>
+
+<div class="footnote"><p><a name="Footnote_87_88" id="Footnote_87_88"></a><a href="#FNanchor_87_88"><span class="label">
+	[87]</span></a>  Siegfried Heinrich Aronhold, &quot;Outline of Kinematic
+	Geometry,&quot; <em>Verein zur Beförderung des Gewerbefleisses in Preussen</em>, 1872,
+	vol. 51, pp. 129-155. Kennedy's theorem is on pp. 137-138.</p></div>
+
+<p class="center">
+<img alt="Figure 32" src="images/fig-32.jpg" width="500" height="543" /></p>
+<p>Figure 32.&#8212;Robert Henry Smith (1852-1916), originator of velocity and
+acceleration polygons for kinematic analysis. Photo courtesy the Librarian,
+Birmingham Reference Library, England.</p>
+
+<p>Kennedy, after locating instant centers, determined velocities by calculation
+and accelerations by graphical differentiation of velocities, and he noted in
+his preface that he had been unable, for a variety of reasons, to make use in
+his book of Smith's recent work. Professor Kennedy at least was aware of Smith's
+surprisingly advanced ideas, which seem to have been generally ignored by
+Americans and Englishmen alike.</p>
+
+<p>Professor Smith, in a paper before the Royal Society of Edinburgh in 1885,
+stated clearly the ideas and methods for construction of velocity and
+acceleration diagrams of linkages.<a name="FNanchor_88_89" id="FNanchor_88_89"></a><a href="#Footnote_88_89" class="fnanchor">[88]</a>
+For the first time, velocity and acceleration &quot;images&quot; of links (fig. 33) were
+presented. It is unfortunate that Smith's ideas were permitted to languish for
+so long a time.</p>
+
+<div class="footnote"><p><a name="Footnote_88_89" id="Footnote_88_89"></a><a href="#FNanchor_88_89"><span class="label">
+	[88]</span></a>  Robert H. Smith, &quot;A New Graphic Analysis of the Kinematics
+	of Mechanisms,&quot; <em>Transactions of the Royal Society of Edinburgh</em>, 1882-1885,
+	vol. 32, pp. 507-517, and pl. 82. Smith used this paper as the basis for a
+	chapter in his <em>Graphics or the Art of Calculating by Drawing Lines</em>,
+	London, 1889, pp. 144-162. In a footnote of his paper, Smith credited Fleeming Jenkin (1833-1885) with suggesting the term &quot;image.&quot; After
+	discarding as &quot;practically useless&quot; Kennedy's graphical differentiation,
+	Smith complained that he had &quot;failed to find any practical use&quot; for
+	Reuleaux's &quot;method of centroids, more properly called axoids.&quot; Such
+	statements were not calculated to encourage Kennedy and Reuleaux to
+	advertise Smith's fame; however, I found no indication that either one took
+	offense at the criticism. Smith's velocity and acceleration diagrams were
+	included (apparently embalmed, so far as American engineers were concerned)
+	in <em>Encyclopaedia Britannica</em>, ed. 11, 1910, vol. 17, pp. 1008-1009.</p></div>
+
+<p class="center">
+<img alt="Figure 33" src="images/fig-33.jpg" width="446" height="650" /></p>
+<p>Figure 33.&#8212;Smith's velocity image (the two figures at top),
+and his velocity, mechanism, and acceleration diagrams, 1885. The image of link
+BACD is shown as figure <em>bacd</em>. The lines <em>pa</em>, <em>pb</em>, <em>
+pc</em>, and <em>pd</em> are
+velocity vectors. This novel, original, and powerful analytical method was not
+generally adopted in English or American schools until nearly 50 years after its
+inception. From <em>Transactions of the Royal Society of Edinburgh</em>
+(1882-1885, vol. 32, pl. 82).</p>
+
+<p>By 1885 nearly all the tools for modern kinematic analysis had been forged.
+Before discussing subsequent developments in analysis and synthesis, however, it
+will be profitable to inquire what the mechanician&#8212;designer and builder of
+machines&#8212;was doing while all of this intellectual effort was being expended.</p>
+
+
+<h3><a name="Mechanicians_and_Mechanisms">Mechanicians and Mechanisms</a></h3>
+
+<p>While the inductive process of recognizing and stating true principles of the
+kinematics of mechanisms was proceeding through three generations of French,
+English, and finally German scholars, the actual design of mechanisms went ahead
+with scant regard for what the scholars were doing and saying.</p>
+
+<p>After the demonstration by Boulton and Watt that large mechanisms could be
+wrought with sufficient precision to be useful, the English tool builders
+Maudslay, Roberts, Clement, Nasmyth, and Whitworth developed machine tools of
+increasing size and truth. The design of other machinery kept pace
+with&#8212;sometimes just behind, sometimes just ahead of&#8212;the capacity and capability
+of machine tools. In general, there was an increasing sophistication of
+mechanisms that could only be accounted for by an increase of information with
+which the individual designer could start.</p>
+
+<p>Reuleaux pointed out in 1875 that the &quot;almost feverish progress made in the
+regions of technical work&quot; was &quot;not a consequence of any increased capacity for
+intellectual action in the race, but only the perfecting and extending of the
+tools with which the intellect works.&quot; These tools, he said, &quot;have increased in
+number just like those in the modern mechanical workshop&#8212;the men who work them
+remain the same.&quot; Reuleaux went on to say that the theory and practice of
+machine-kinematics had &quot;carried on a separate existence side by side.&quot; The
+reason for this failure to apply theory to practice, and vice versa, must be
+sought in the defects of the theory, he thought, because &quot;the mechanisms
+themselves have been quietly developed in practical machine-design, by invention
+and improvement, regardless of whether or not they were accorded any direct and
+proper theoretical recognition.&quot; He pointed out that the theories had thus far
+&quot;furnished no new mechanisms.&quot;<a name="FNanchor_89_90" id="FNanchor_89_90"></a><a href="#Footnote_89_90" class="fnanchor">[89]</a></p>
+
+<div class="footnote"><p><a name="Footnote_89_90" id="Footnote_89_90"></a><a href="#FNanchor_89_90"><span class="label">
+	[89]</span></a> Reuleaux, <em>op. cit.</em> (footnote 68), p. 8.</p></div>
+
+<p>It is reasonable, therefore, to ask what was responsible for the appearance
+of new mechanisms, and then to see what sort of mechanisms had their origins in
+this period.</p>
+
+<p>It is immediately evident to a designer that the progress in mechanisms came
+about through the spread of knowledge of what had already been done; but
+designers of the last century had neither the leisure nor means to be constantly
+visiting other workshops, near and far, to observe and study the latest
+developments. In the 1800's, as now, word must in the main be spread by the
+printed page.</p>
+
+<p>Hachette's chart (fig. 28) had set the pattern for display of mechanical
+contrivances in practical journals and in the large number of mechanical
+dictionaries that were compiled to meet an apparent demand for such information.
+It is a little surprising, however, to find how persistent were some of
+Hachette's ideas that could only have come from the uppermost superficial layer
+of his cranium. See, for example, his &quot;anchored ferryboat&quot; (fig. 34). This
+device, employed by Hachette to show conversion of continuous rectilinear motion
+into alternating circular motion, appeared in one publication after another
+throughout the 19th century. As late as 1903 the ferryboat was still anchored in
+Hiscox's <em>Mechanical Movements</em>, although the tide had changed (fig. 35).<a name="FNanchor_90_91" id="FNanchor_90_91"></a><a href="#Footnote_90_91" class="fnanchor">[90]</a></p>
+
+<div class="footnote"><p><a name="Footnote_90_91" id="Footnote_90_91"></a><a href="#FNanchor_90_91"><span class="label">
+	[90]</span></a>  Gardner D. Hiscox, ed., <em>Mechanical Movements</em>, ed. 10, New
+	York, 1903, p. 151. The ferryboat did not appear in the 1917 edition.</p></div>
+
+<p class="center">
+<img alt="Figure 34" src="images/fig-34.jpg" width="500" height="256" /></p>
+<p>Figure 34.&#8212;Hachette's ferryboat of 1808, a &quot;machine&quot; for
+converting continuous rectilinear motion into alternating circular motion. From Phillipe Louis Lanz and Augustin de Bétancourt, <em>Essai sur la composition des
+machines</em> (Paris, 1808, pl. 2).</p>
+
+<p class="center">
+<img alt="Figure 35" src="images/fig-35.jpg" width="500" height="274" /></p>
+<p>Figure 35.&#8212;Ferryboat from Gardner D. Hiscox, ed., <em>
+Mechanical Movements</em> (ed. 10, New York, 1903, p. 151).</p>
+
+<p>During the upsurge of the Lyceum&#8212;or working-man's institute&#8212;movement in the
+1820's, Jacob Bigelow, Rumford professor of applied science at Harvard
+University, gave his popular lectures on the &quot;Elements of Technology&quot; before
+capacity audiences in Boston. In preparing his lecture on the elements of
+machinery, Bigelow used as his authorities Hachette, Lanz and Bétancourt, and
+Olinthus Gregory's mechanical dictionary, an English work in which Hachette's
+classification scheme was copied and his chart reproduced.<a name="FNanchor_91_92" id="FNanchor_91_92"></a><a href="#Footnote_91_92" class="fnanchor">[91]</a></p>
+
+<div class="footnote"><p><a name="Footnote_91_92" id="Footnote_91_92"></a><a href="#FNanchor_91_92"><span class="label">
+	[91]</span></a>  Jacob Bigelow, <em>Elements of Technology</em>, ed. 2, Boston,
+	1831, pp. 231-256; Olinthus Gregory, <em>A Treatise of Mechanics</em>, 3 vols., ed.
+	3, London, 1815.</p></div>
+
+<p>A translation of the work of Lanz and Bétancourt<a name="FNanchor_92_93" id="FNanchor_92_93"></a><a href="#Footnote_92_93" class="fnanchor">[92]</a>
+under the title <em>Analytical Essay on the Construction of Machines</em>, was
+published about 1820 at London by Rudolph Ackermann (for whom the Ackermann
+steering linkage was named), and their synoptic chart was reprinted again in
+1822 in Durham.<a name="FNanchor_93_94" id="FNanchor_93_94"></a><a href="#Footnote_93_94" class="fnanchor">[93]</a>
+In the United States, <em>Appleton's Dictionary of Machines</em><a name="FNanchor_94_95" id="FNanchor_94_95"></a><a href="#Footnote_94_95" class="fnanchor">[94]</a>
+(1851) adopted the same system and used the same figures. Apparently the wood
+engraver traced directly onto his block the figures from one of the reprints of
+Lanz and Bétancourt's chart because the figures are in every case exact mirror
+images of the originals.</p>
+
+<div class="footnote"><p><a name="Footnote_92_93" id="Footnote_92_93"></a><a href="#FNanchor_92_93"><span class="label">
+	[92]</span></a>  Rudolph Ackermann, <em>Analytical Essay on the Construction
+	of Machines</em>, London, about 1820, a translation of Lanz and Bétancourt,
+	<em>op. cit.</em> (footnote 64).</p></div>
+
+<div class="footnote"><p><a name="Footnote_93_94" id="Footnote_93_94"></a><a href="#FNanchor_93_94"><span class="label">
+	[93]</span></a>  Thomas Fenwick, <em>Essays on Practical Mechanics</em>, ed. 3,
+	Durham, England, 1822.</p></div>
+
+<div class="footnote"><p><a name="Footnote_94_95" id="Footnote_94_95"></a><a href="#FNanchor_94_95"><span class="label">
+	[94]</span></a>  <em>Appleton's Dictionary of Machines, Mechanics,
+	Engine-Work, and Engineering</em>, 2 vols., New York, 1851 (&quot;Motion&quot;).</p></div>
+
+<p>In the <em>Dictionary of Engineering</em><a name="FNanchor_95_96" id="FNanchor_95_96"></a><a href="#Footnote_95_96" class="fnanchor">[95]</a>
+(London, 1873), the figures were redrawn and dozens of mechanisms were added to
+the repertory of mechanical motions; the result was a fair catalog of sound
+ideas. The ferryboat still tugged at its anchor cable, however.<a name="FNanchor_96_97" id="FNanchor_96_97"></a><a href="#Footnote_96_97" class="fnanchor">[[96]</a>
+<em>Knight's American Mechanical Dictionary</em>,<a name="FNanchor_97_98" id="FNanchor_97_98"></a><a href="#Footnote_97_98" class="fnanchor">[97]</a>
+a classic of detailed pictorial information compiled by a U.S. patent examiner,
+contained well over 10,000 finely detailed figures of various kinds of
+mechanical contrivances. Knight did not have a separate section on mechanisms,
+but there was little need for one of the Hachette variety, because his whole
+dictionary was a huge and fascinating compendium of ideas to be filed away in
+the synthetic mind. One reason for the popularity and usefulness of the various
+pictorial works was the peculiar ability of a wood or steel engraving to convey
+precise mechanical information, an advantage not possessed by modern halftone
+processes.</p>
+
+<div class="footnote"><p><a name="Footnote_95_96" id="Footnote_95_96"></a><a href="#FNanchor_95_96"><span class="label">
+	[95]</span></a>  E. F. and N. Spon, <em>Dictionary of Engineering</em>, London 1873,
+	pp. 2421-2452.</p></div>
+
+<div class="footnote"><p><a name="Footnote_96_97" id="Footnote_96_97"></a><a href="#FNanchor_96_97"><span class="label">
+	[96]</span></a> <em>Ibid.</em>, p. 2447.</p></div>
+
+<div class="footnote"><p><a name="Footnote_97_98" id="Footnote_97_98"></a><a href="#FNanchor_97_98"><span class="label">
+	[97]</span></a>  Edward H. Knight, <em>Knight's American Mechanical
+	Dictionary</em>,
+	3 vols., New York 1874-1876.</p></div>
+
+<p class="center">
+<img alt="Figure 36" src="images/fig-36.jpg" width="600" height="423" /></p>
+<p>Figure 36.&#8212;Typical mechanisms from E. F. and N. Spon,
+<em>Dictionary of Engineering</em> (London, 1873, pp. 2426, 2478).</p>
+
+<p>Many patent journals and other mechanical periodicals concerned with
+mechanics were available in English from the beginning of the 19th century, but
+few of them found their way into the hands of American mechanicians until after
+1820. Oliver Evans (1755-1819) had much to say about &quot;the difficulties inventive
+mechanics labored under for want of published records of what had preceded them,
+and for works of reference to help the beginner.&quot;<a name="FNanchor_98_99" id="FNanchor_98_99"></a><a href="#Footnote_98_99" class="fnanchor">[98]</a>
+In 1817 the <em>North American Review</em> also remarked upon the scarcity of
+engineering books in America.<a name="FNanchor_99_100" id="FNanchor_99_100"></a><a href="#Footnote_99_100" class="fnanchor">[99]</a></p>
+
+<div class="footnote"><p><a name="Footnote_98_99" id="Footnote_98_99"></a><a href="#FNanchor_98_99"><span class="label">
+	[98]</span></a>  George Escol Sellers in <em>American Machinist</em>, July 12, 1884,
+	vol. 7, p. 3.</p></div>
+
+<div class="footnote"><p><a name="Footnote_99_100" id="Footnote_99_100"></a><a href="#FNanchor_99_100"><span class="label">
+	[99]</span></a>  <em>North-American Review and Miscellaneous Journal</em>, 1819, new
+	ser., vol. 8, pp. 13-15, 25.</p></div>
+
+<p>The <em>Scientific American</em>, which appeared in 1845 as a patent journal edited
+by the patent promoter Rufus Porter, carried almost from its beginning a column
+or so entitled &quot;Mechanical Movements,&quot; in which one or two mechanisms&#8212;borrowed
+from an English work that had borrowed from a French work&#8212;were illustrated and
+explained. The <em>American Artisan</em> began a similar series in 1864, and in 1868 it
+published a compilation of the series as <em>Five Hundred and Seven Mechanical
+Movements</em>, &quot;embracing all those which are most important in dynamics,
+hydraulics, hydrostatics, pneumatics, steam engines ... and miscellaneous
+machinery.&quot;<a name="FNanchor_100_101" id="FNanchor_100_101"></a><a href="#Footnote_100_101" class="fnanchor">[100]</a>
+This collection went through many editions; it was last revived in 1943 under
+the title <em>A Manual of Mechanical Movements</em>. This 1943 edition included
+photographs of kinematic models.<a name="FNanchor_101_102" id="FNanchor_101_102"></a><a href="#Footnote_101_102" class="fnanchor">[101]</a></p>
+
+<div class="footnote"><p><a name="Footnote_100_101" id="Footnote_100_101"></a><a href="#FNanchor_100_101"><span class="label">
+	[100]</span></a>  Henry T. Brown, ed., <em>Five Hundred and Seven Mechanical
+	Movements</em>, New York, 1868.</p></div>
+
+<div class="footnote"><p><a name="Footnote_101_102" id="Footnote_101_102"></a><a href="#FNanchor_101_102"><span class="label">
+	[101]</span></a>  Will M. Clark, <em>A Manual of Mechanical Movements</em>, Garden
+	City, New York, 1943.</p></div>
+
+<p>Many readers are already well acquainted with the three volumes of <em>
+Ingenious Mechanisms for Designers and Inventors</em>,<a name="FNanchor_102_103" id="FNanchor_102_103"></a><a href="#Footnote_102_103" class="fnanchor">[102]</a>
+a work that resulted from a contest, announced by <em>Machinery</em> (vol. 33, p. 405)
+in 1927, in which seven prizes were offered for the seven best articles on
+unpublished ingenious mechanisms.</p>
+
+<div class="footnote"><p><a name="Footnote_102_103" id="Footnote_102_103"></a><a href="#FNanchor_102_103"><span class="label">
+	[102]</span></a>  <em>Ingenious Mechanisms for Designers and Inventors</em> (vols. 1
+	and 2 edited by F. D. Jones, vol. 3 edited by H. L. Horton), New York,
+	Industrial Press, 1930-1951.</p></div>
+
+<p>There was an interesting class of United States patents called &quot;Mechanical
+Movements&quot; that comprised scores of patents issued throughout the middle decades
+of the 19th century. A sampling of these patents shows that while some were for
+devices used in particular machines&#8212;such as a ratchet device for a numbering
+machine, a locking index for unmaking machinery, and a few gear trains&#8212;the
+great majority were for converting reciprocating motion to rotary motion. Even a
+cursory examination of these patents reveals an appalling absence of sound
+mechanical sense, and many of them appear to be attempts at &quot;perpetual motion,&quot;
+in spite of an occasional disclaimer of such intent.</p>
+
+<p>Typical of many of these patented devices was a linkage for &quot;multiplying&quot; the
+motion of a flywheel, proposed in 1841 by Charles Johnson of Amity, Illinois
+(fig. 37). &quot;It is not pretended that there is any actual gain of power,&quot; wrote
+Mr. Johnson; and probably he meant it. The avowed purpose of his linkage was to
+increase the speed of a flywheel and thus decrease its size.<a name="FNanchor_103_104" id="FNanchor_103_104"></a><a href="#Footnote_103_104" class="fnanchor">[103]</a></p>
+
+<div class="footnote"><p><a name="Footnote_103_104" id="Footnote_103_104"></a><a href="#FNanchor_103_104"><span class="label">
+	[103]</span></a> U.S. Patent 2295, October 11, 1841.</p></div>
+
+<p class="center">
+<img alt="Figure 37" src="images/fig-37.jpg" width="500" height="390" /></p>
+<p>Figure 37.&#8212;Johnson's &quot;converting motion,&quot; 1841. The linkage causes the
+flywheel to make two revolutions for each double-stroke of the engine piston rod
+B. From U.S. Patent 2295, October 11, 1841.</p>
+
+<p>An Englishman who a few years earlier had invented a &quot;new Motion&quot; had claimed
+that his device would supersede the &quot;ordinary crank in steam engines,&quot; the beam,
+parallel motion, and &quot;external flywheel,&quot; reduce friction, neutralize &quot;all extra
+contending power,&quot; and leave nothing for the piston to do &quot;but the work intended
+to be done.&quot;</p>
+
+<p>A correspondent of the <em>Repertory of Patent Inventions</em> made short work of
+this device: &quot;There is hardly one assertion that can be supported by proof,&quot; he
+wrote, &quot;and most of them are palpable misstatements.&quot; The writer attacked &quot;the
+'beetle impetus wheel,' which he [the inventor] thinks us all so beetle-headed,
+as not to perceive to be a flywheel,&quot; and concluded with the statement: &quot;In
+short the whole production evinces gross ignorance either of machinery, if the
+patentee really believed what he asserted, or of mankind, if he did not.&quot;<a name="FNanchor_104_105" id="FNanchor_104_105"></a><a href="#Footnote_104_105" class="fnanchor">[104]</a></p>
+
+<div class="footnote"><p><a name="Footnote_104_105" id="Footnote_104_105"></a><a href="#FNanchor_104_105"><span class="label">
+	[104]</span></a>  <em>Repertory of Patent Inventions</em>, ser. 3, October 1828,
+	vol. 7, pp. 196-200, and December 1828, vol. 7, pp. 357-361.</p></div>
+
+<p>Although many of the mechanisms for which patents were taken out were
+designed by persons who would make no use of the principles involved even if
+such principles could at that time have been clearly stated, it is a regrettable
+fact that worthless mechanisms often got as much space as sound ones in patent
+journals, and objections such as the one above were infrequent. The slanted
+information thus conveyed to the young mechanician, who was just accumulating
+his first kinematic repertory, was at times sadly misleading.</p>
+
+<p>From even this sketchy outline of the literature on the subject, it should be
+fairly evident that there has been available to the mechanician an enormous
+quantity of information about mechanical linkages and other devices. Whatever
+one may think of the quality of the literature, it has undoubtedly had influence
+not only in supplying designers with information but in forming a tradition of
+how one ought to supply the background that will enable the mind to assemble and
+synthesize the necessary mechanism for a given purpose.<a name="FNanchor_105_106" id="FNanchor_105_106"></a><a href="#Footnote_105_106" class="fnanchor">[105]</a></p>
+
+<div class="footnote"><p><a name="Footnote_105_106" id="Footnote_105_106"></a><a href="#FNanchor_105_106"><span class="label">
+	[105]</span></a> Some additional catalogs of &quot;mechanical movements&quot; are
+	listed in the selected references at the end of this paper.</p></div>
+
+<p>Some of the mechanisms that have been given names&#8212;such as the Watt
+straight-line linkage and the Geneva stop&#8212;have appeared in textbook after
+textbook. Their only excuse for being seems to be that the authors must include
+them or risk censure by colleagues. Such mechanisms are more interesting to a
+reader, certainly, when he has some idea of what the name has to do with the
+mechanism, and who originated it. One such mechanism is the drag link.</p>
+
+<p>After I had learned of the drag link (as most American engineering students
+do), I wondered for awhile, and eventually despaired of making any sense out of
+the term. What, I wanted to know, was being dragged? Recently, in Nicholson's
+<em>Operative Mechanic and British Machinist</em> (1826), I ran across the sketch
+reproduced here as figure 38. This figure, explained Mr. Nicholson (in vol. 1,
+p. 32) &quot;represents the coupling link used by Messrs. Boulton and Watt in their
+portable steam engines. <strong>A</strong>, a strong iron pin, projecting from one of the arms of
+the fly-wheel <strong>B</strong>; <strong>D</strong>, a crank connected with the shaft
+<strong>C</strong>; and <strong>E</strong>, a link to couple
+the pin <strong>A</strong> and the crank <strong>D</strong> together, so the motion may be communicated to the
+shaft <strong>C</strong>.&quot; So the drag link was actually a link of a coupling. Nothing could be
+more logical. A drag link mechanism now makes sense to me.</p>
+
+<p class="center">
+<img alt="Figure 38" src="images/fig-38.jpg" width="500" height="330" /></p>
+<p>Figure 38.&#8212;Drag link coupling used on Boulton and Watt
+portable engines. The link E drags one shaft when the other turns. From John
+Nicholson, <em>The Operative Mechanic, and British Machinist</em> (Philadelphia,
+1826, vol. I, pl. 5).</p>
+
+<p>Directly related to the drag link coupling were the patents of John Oldham
+(1779-1840), an Irish engineer who is remembered mainly for the coupling that
+bears his name (fig. 39). His three patents, which were for various forms of
+steamboat feathering paddle wheels, involved linkages kinematically similar to
+the drag link coupling, although it is quite unlikely that Oldham recognized the
+similarity. However, for his well-known coupling, which employs an inversion of
+the elliptical trammel mechanism, I have found no evidence of a patent. Probably
+it was part of the machinery that he designed for the Bank of Ireland's printing
+house, of which Oldham was manager for many years. &quot;Mr. Oldham and his beautiful
+system&quot; were brought to the Bank of England in 1836, where Oldham remained until
+his death in 1840.<a name="FNanchor_106_107" id="FNanchor_106_107"></a><a href="#Footnote_106_107" class="fnanchor">[106]</a></p>
+
+<div class="footnote"><p><a name="Footnote_106_107" id="Footnote_106_107"></a><a href="#FNanchor_106_107"><span class="label">
+	[106]</span></a> Oldham's paddle-wheel patents were British Patents 4169
+	(October 10, 1817), 4429 (January 15, 1820), and 5445 (February 1, 1827).
+	Robert Willis (<em>op. cit.</em>  footnote 21, p. 167) noticed the existence of the
+	coupling. Drawings or descriptions of the banknote machinery apparently have
+	not been published though they probably still exist in the banks' archives.
+	The quotation is from Frederick G. Hall, <em>The Bank of Ireland 1783-1946</em>,
+	Dublin, 1949. John Francis in his <em>History of the Bank of England</em> (London,
+	1848, vol. 2, p. 232) wrote: &quot;The new machinery for printing the notes,
+	which was introduced by Mr. Oldham ... is well worthy of a visit, but would
+	be uninteresting to delineate.&quot;</p></div>
+
+<p class="center">
+<img alt="Figure 39" src="images/fig-39.jpg" width="500" height="384" /></p>
+<p>Figure 39.&#8212;<em>Top</em>, Original Oldham coupling built before 1840,
+using a cross (instead of a center disk), as sketched by Robert Willis in
+personal copy of his <em>Principles of Mechanism</em> (London, 1841, p. 167).
+<em>Bottom</em>,
+Oldham coupling as illustrated in Alexander B. W. Kennedy, <em>Kinematics of
+Machinery</em>, a translation of Franz Reuleaux' <em>Theoretische Kinematik</em>
+(London, 1876, pp. 315-316).</p>
+
+<p>The Geneva stop mechanism (fig. 40) was properly described by Willis as a
+device to permit less than a full revolution of the star wheel and thus to
+prevent overwinding of a watch spring. It was called Geneva stop because it was
+used in Geneva watches. The Geneva wheel mechanism, which permits full rotation
+of the star wheel and which is frequently used for intermittent drives, was
+improperly called a Geneva stop in a recent textbook probably because the
+logical origin of the term had been lost.</p>
+
+<p class="center">
+<img alt="Figure 40" src="images/fig-40.jpg" width="387" height="600" /></p>
+<p>Figure 40.&#8212;Geneva stop mechanism first used in Geneva watches
+to prevent overwinding. The starwheel B had one convex surface (<em>g-f</em>, dotted)
+so the wheel could be turned less than a full revolution. After Robert Willis,
+<em>Principles of Mechanism</em> (London, 1841, p. 266).</p>
+
+<p>The name for the Scotch yoke seems to be of fairly recent origin, the linkage
+being called by a Scotsman in 1869 a &quot;crank and slot-headed sliding rod&quot; (fig.
+41). I suppose that it is now known as a Scotch yoke because, in America at
+least, a &quot;Scotch&quot; was a slotted bar that was slipped under a collar on a string
+of well-drilling tools to support them while a section was being added (fig.
+42).</p>
+
+<p class="center">
+<img alt="Figure 41" src="images/fig-41.jpg" width="500" height="358" /></p>
+<p>Figure 41.&#8212;Scotch yoke, described as a &quot;crank and slot-headed
+sliding rod.&quot; From W. J. M. Rankine, <em>A Manual of Machinery and Millwork</em>
+(ed. 6, London, 1887, p. 169).</p>
+
+<p class="center">
+<img alt="Figure 42" src="images/fig-42.jpg" width="500" height="571" /></p>
+<p>Figure 42.&#8212;A &quot;Scotch&quot; supporting the top member of a string of
+well-drilling tools while a section is being added, 1876. From Edward H. Knight,
+<em>Knight's American Mechanical Dictionary</em> (New York, 1876, p. 2057).</p>
+
+<p>It was surprising to me to find that the Ackermann steering linkage, used
+today on most automobiles, was patented in 1818 when Detroit was still a
+frontier town.<a name="FNanchor_107_108" id="FNanchor_107_108"></a><a href="#Footnote_107_108" class="fnanchor">[107]</a>
+Furthermore, the man who took out the patent described himself as Rudolph
+Ackermann, publisher and printseller. I thought I had the necessary clue to the
+linkage's origin when I noticed that the first English translation of the Lanz
+and Bétancourt treatise was published by Ackermann, but the connection finally
+proved to be more logical, if less direct. Ackermann (1764-1834), son of a
+Bavarian coach builder, had spent a number of years designing coaches for
+English gentlemen in London, where he made his home. One of his more notable
+commissions was for the design of Admiral Nelson's funeral car in 1805. The
+Ackermann steering linkage was not actually Ackermann's invention, although he
+took out the British patent in his name and promoted the introduction of the
+running gear of which the linkage was a part (fig. 43). The actual inventor was
+Ackermann's friend George Lankensperger of Munich, coachmaker to the King of
+Bavaria. The advantage of being able to turn a carriage around in a limited area
+without danger of oversetting was immediately obvious, and while there was
+considerable opposition by English coachmakers to an innovation for which a
+premium had to be paid, the invention soon &quot;made its way from its own intrinsic
+merit,&quot; as Ackermann predicted it would.<a name="FNanchor_108_109" id="FNanchor_108_109"></a><a href="#Footnote_108_109" class="fnanchor">[108]</a></p>
+
+<div class="footnote"><p><a name="Footnote_107_108" id="Footnote_107_108"></a><a href="#FNanchor_107_108"><span class="label">
+	[107]</span></a>  British Patent 4212, January 27, 1818.</p></div>
+
+<div class="footnote"><p><a name="Footnote_108_109" id="Footnote_108_109"></a><a href="#FNanchor_108_109"><span class="label">
+	[108]</span></a>  Rudolph Ackermann, <em>Observations on Ackermann's Patent
+	Moveable Axles</em>, London, 1819. It was interesting to me to note an abstract
+	of W. A. Wolfe's paper &quot;Analytical Design of an Ackermann Steering Linkage&quot;
+	in <em>Mechanical Engineering</em>, September 1958, vol. 80, p. 92.</p></div>
+
+<p class="center">
+<img alt="Figure 43" src="images/fig-43.jpg" width="500" height="251" /></p>
+<p>Figure 43.&#8212;Ackermann steering linkage of 1818, currently used
+in automobiles. This linkage was invented by George Lankensperger, coachmaker to
+the King of Bavaria. From <em>Dinglers Polytechnisches Journal</em> (1820, vol.
+1, pl. 7).</p>
+
+<p>The Whitworth quick-return mechanism (fig. 44) was first applied to a
+slotter, or vertical shaper, in 1849, and was exhibited in 1851 at the Great
+Exhibition in London.<a name="FNanchor_109_110" id="FNanchor_109_110"></a><a href="#Footnote_109_110" class="fnanchor">[109]</a>
+Willis' comments on the mechanism are reproduced in figure 44. I hope that Sir
+Joseph Whitworth (1803-1887) will be remembered for sounder mechanical
+contrivances than this.</p>
+
+<div class="footnote"><p><a name="Footnote_109_110" id="Footnote_109_110"></a><a href="#FNanchor_109_110"><span class="label">
+	[109]</span></a>  The quick-return mechanism (British Patent 12907, December
+	19, 1849) was perhaps first publicly described in Charles Tomlinson, ed.,
+	<em>Cyclopaedia of Useful Arts and Manufactures</em>, London, 1854, vol. 1, p. cxliv.</p></div>
+
+<p class="center">
+<img alt="Figure 44" src="images/fig-44.jpg" width="245" height="600" /></p>
+<p>Figure 44.&#8212;Quick-return mechanism. <em>Top</em>, Early representation
+of the quick-return mechanism patented by Whitworth in 1849, from William
+Johnson, ed., <em>The Imperial Cyclopaedia of machinery</em> (Glasgow, about 1855, pl.
+88). <em>Middle</em>, Sketch by Robert Willis from his copy of <em>Principles of
+Mechanism</em> (London, 1841, p. 264), which &quot;shews Whitworth dissected into a
+simpler form&quot;; it is as obscure as most subsequent attempts have been to explain
+this mechanism without a schematic diagram. <em>Bottom</em>, Linkage that is kinematically equivalent to Whitworth's, from Robert Willis,
+<em>Principles of Mechanism</em> (London, 1841, p. 264).</p>
+
+
+<h3><a name="Mechanisms_in_America_1875-1955">Mechanisms in America, 1875-1955</a></h3>
+
+<p>Engineering colleges in the United States were occupied until the late 1940's
+with extending, refining, and sharpening the tools of analysis that had been
+suggested by Willis, Rankine, Reuleaux, Kennedy, and Smith. The actual practice
+of kinematic synthesis went on apace, but designers often declined such help as
+the analytical methods might give them and there was little exchange of ideas
+between scholars and practitioners.</p>
+
+<p>The capability and precision of machine tools were greatly enhanced during
+this period, although, with the exception of the centerless grinder, no
+significant new types of tools appeared. The machines that were made with
+machine tools increased in complexity and, with the introduction of ideas that
+made mass production of complex mechanical products economically feasible, there
+was an accelerating increase in quantity. The adoption of standards for all
+sorts of component parts also had an important bearing upon the ability of a
+designer economically to produce mechanisms that operated very nearly as he
+hoped they would.</p>
+
+<p>The study of kinematics has been considered for nearly 80 years as a
+necessary part of the mechanical engineer's training, as the dozens of textbooks
+that have been published over the years make amply clear. Until recently,
+however, one would look in vain for original work in America in the analysis or
+rational synthesis of mechanisms.</p>
+
+<p>One of the very earliest American textbooks of kinematics was the 1883 work
+of Charles W. MacCord (1836-1915), who had been appointed professor of
+mechanical drawing at Stevens Institute of Technology in Hoboken after serving
+John Ericsson, designer of the <em>Monitor</em>, as chief draftsman during the Civil
+War.<a name="FNanchor_110_111" id="FNanchor_110_111"></a><a href="#Footnote_110_111" class="fnanchor">[110]</a>
+Based upon the findings of Willis and Rankine, MacCord's <em>Kinematics</em> came too
+early to be influenced by Kennedy's improvements upon Reuleaux's work.</p>
+
+<div class="footnote"><p><a name="Footnote_110_111" id="Footnote_110_111"></a><a href="#FNanchor_110_111"><span class="label">
+	[110]</span></a>  A biographical notice and a bibliography of MacCord appears
+	in <em>Morton Memorial: A History of the Stevens Institute of Technology</em>,
+	Hoboken, 1905, pp. 219-222.</p></div>
+
+<p>When the faculty at Washington University in St. Louis introduced in 1885 a
+curriculum in &quot;dynamic engineering,&quot; reflecting a dissatisfaction with the
+traditional branches of engineering, kinematics was a senior subject and was
+taught from Rankine's <em>Machinery and Millwork</em>.<a name="FNanchor_111_112" id="FNanchor_111_112"></a><a href="#Footnote_111_112" class="fnanchor">[111]</a></p>
+
+<div class="footnote"><p><a name="Footnote_111_112" id="Footnote_111_112"></a><a href="#FNanchor_111_112"><span class="label">
+	[111]</span></a>  <em>Transactions of the American Society of Mechanical
+	Engineers</em>, 1885-1886, vol. 7, p. 757.</p></div>
+
+<p>At Massachusetts Institute of Technology, Peter Schwamb, professor of machine
+design, put together in 1885 a set of printed notes on the kinematics of
+mechanisms, based on Reuleaux's and Rankine's works. Out of these notes grew one
+of the most durable of American textbooks, first published in 1904.<a name="FNanchor_112_113" id="FNanchor_112_113"></a><a href="#Footnote_112_113" class="fnanchor">[112]</a>
+In the first edition of this work, acceleration was mentioned only once in
+passing (on p. 4). Velocities in linkages were determined by orthogonal
+components transferred from link to link. Instant centers were used only to
+determine velocities of various points on the same link. Angular velocity ratios
+were frequently noted. In the third edition, published in 1921, linear and
+angular accelerations were defined, but no acceleration analyses were made.
+Velocity analyses were altered without essential change. The fourth edition
+(1930) was essentially unchanged from the previous one. Treatment of velocity
+analysis was improved in the fifth edition (1938) and acceleration analysis was
+added. A sixth edition, further revised by Prof. V. L. Doughtie of the
+University of Texas, appeared in 1947.</p>
+
+<div class="footnote"><p><a name="Footnote_112_113" id="Footnote_112_113"></a><a href="#FNanchor_112_113"><span class="label">
+	[112]</span></a>  Peter Schwamb and Allyne L. Merrill, <em>Elements of
+	Mechanism</em>, New York, 1904. In addition to the work of Reuleaux and Rankine,
+	the authors acknowledged their use of the publications of Charles MacCord,
+	Stillman W. Robinson, Thomas W. Goodeve, and William C. Unwin. For complete
+	titles see the list of selected references.</p></div>
+
+<p>Before 1900, several other books on mechanisms had been published, and all
+followed one or another of the patterns of their predecessors. Professors Woods
+and Stahl, at the Universities of Illinois and Purdue, respectively, who
+published their <em>Elementary Mechanism</em> in 1885, said in their preface what has
+been said by many other American authors and what should have been said by many
+more. &quot;We make little claim to originality of the subject-matter,&quot; wrote Woods
+and Stahl, &quot;free use having been made of all available matter on the subject....
+Our claim to consideration is based almost entirely on the manner in which the
+subject has been presented.&quot; Not content with this disclaimer, they continued:
+&quot;There is, in fact, very little room for such originality, the ground having
+been almost completely covered by previous writers.&quot;<a name="FNanchor_113_114" id="FNanchor_113_114"></a><a href="#Footnote_113_114" class="fnanchor">[113]</a></p>
+
+<div class="footnote"><p><a name="Footnote_113_114" id="Footnote_113_114"></a><a href="#FNanchor_113_114"><span class="label">
+	[113]</span></a>  Arthur T. Woods and Albert W. Stahl, <em>Elementary
+	Mechanism</em>, New York, 1885.</p></div>
+
+<p>The similarity and aridity of kinematics textbooks in this country from
+around 1910 are most striking. The generation of textbook writers following
+MacCord, Woods and Stahl, Barr of Cornell, Robinson of Ohio State, and Schwamb
+and Merrill managed to squeeze out any remaining juice in the subject, and the
+dessication and sterilization of textbooks was nearly complete when my
+generation used them in the 1930's. Kinematics was then, in more than one
+school, very nearly as it was characterized by an observer in 1942&#8212;&quot;on an
+intellectual par with mechanical drafting.&quot;<a name="FNanchor_114_115" id="FNanchor_114_115"></a><a href="#Footnote_114_115" class="fnanchor">[114]</a>
+I can recall my own naïve belief that a textbook contained all that was known of
+the subject; and I was not disabused of my belief by my own textbook or by my
+teacher. I think I detect in several recent books a fresh, less final, and less
+tidy treatment of the kinematics of mechanisms, but I would yet recommend that
+anyone who thinks of writing a textbook take time to review, carefully and at
+first hand, not only the desk copies of books that he has accumulated but a
+score or more of earlier works, covering the last century at least. Such a study
+should result in a better appreciation of what constitutes a contribution to
+knowledge and what constitutes merely the ringing of another change.</p>
+
+<div class="footnote"><p><a name="Footnote_114_115" id="Footnote_114_115"></a><a href="#FNanchor_114_115"><span class="label">
+	[114]</span></a>  <em>Mechanical Engineering</em>, October 1942, vol. 64, p. 745.</p></div>
+
+<p>The author of the contentious article that appeared in <em>Mechanical
+Engineering</em> in 1942 under the title &quot;What is Wrong with Kinematics and
+Mechanisms?&quot; made several pronouncements that were questioned by various
+readers, but his remarks on the meagerness of the college courses of kinematics
+and the &quot;curious fact&quot; that the textbooks &quot;are all strangely similar in their
+incompleteness&quot; went unchallenged and were, in fact, quite timely.<a name="FNanchor_115_116" id="FNanchor_115_116"></a><a href="#Footnote_115_116" class="fnanchor">[115]</a></p>
+
+<div class="footnote"><p><a name="Footnote_115_116" id="Footnote_115_116"></a><a href="#FNanchor_115_116"><span class="label">
+	[115]</span></a> De Jonge, <em>op. cit.</em> (footnote 78).</p></div>
+
+<p>It appears that in the early 1940's the general classroom treatment of
+accelerations was at a level well below the existing knowledge of the subject,
+for in a series of articles by two teachers at Purdue attention was called to
+the serious consequences of errors in acceleration analysis occasioned by
+omitting the Coriolis component.<a name="FNanchor_116_117" id="FNanchor_116_117"></a><a href="#Footnote_116_117" class="fnanchor">[116]</a>
+These authors were reversing a trend that had been given impetus by an article
+written in 1920 by one of their predecessors, Henry N. Bonis. The earlier
+article, appearing in a practical-and-proud-of-it technical magazine,
+demonstrated how the acceleration of a point on a flywheel governor might be
+determined &quot;without the use of the fictitious acceleration of Coriolis.&quot; The
+author's analysis was right enough, and he closed his article with the
+unimpeachable statement that &quot;it is better psychologically for the student and
+practically for the engineer to understand the fundamentals thoroughly than to
+use a complex formula that may be misapplied.&quot; However, many readers undoubtedly
+read only the lead paragraph, sagely nodded their heads when they reached the
+word &quot;fictitious,&quot; which confirmed their half-formed conviction that anything as
+abstruse as the Coriolis component could have no bearing upon a practical
+problem, and turned the page to the &quot;practical kinks&quot; section.<a name="FNanchor_117_118" id="FNanchor_117_118"></a><a href="#Footnote_117_118" class="fnanchor">[117]</a></p>
+
+<div class="footnote"><p><a name="Footnote_116_117" id="Footnote_116_117"></a><a href="#FNanchor_116_117"><span class="label">
+	[116]</span></a>  A. S. Hall and E. S. Ault, &quot;How Acceleration Analysis Can
+	Be Improved,&quot; <em>Machine Design</em>, February 1943, vol. 15, pp. 100-102, 162,
+	164; and March 1943, vol. 15, pp. 90-92, 168, 170. See also A. S. Hall,
+	&quot;Teaching Coriolis' Law,&quot; <em>Journal of Engineering Education,</em> June 1948,
+	vol. 38, pp. 757-765.</p></div>
+
+<div class="footnote"><p><a name="Footnote_117_118" id="Footnote_117_118"></a><a href="#FNanchor_117_118"><span class="label">
+	[117]</span></a>  Henry N. Bonis, &quot;The Law of Coriolis,&quot; <em>
+	American Machinist</em>, November 18, 1920, vol. 53, pp. 928-930. See also &quot;Acceleration
+	Determinations,&quot; <em>American Machinist</em>, November 25 and December 2, 1920,
+	vol. 53, pp. 977-981 and 1027-1029.</p></div>
+
+<p>Less than 20 years ago one might have read in <em>Mechanical Engineering</em> that
+&quot;Practical machinery does not originate in mathematical formulas nor in
+beautiful vector diagrams.&quot; While this remark was in a letter evoked by an
+article, and was not a reflection of editorial policy, it was nevertheless
+representative of an element in the American tradition of engineering. The
+unconscious arrogance that is displayed in this statement of the &quot;practical&quot;
+designer's creed is giving way to recognition of the value of scholarly work.
+Lest the scholar develop arrogance of another sort, however, it is well to hear
+the author of the statement out. &quot;A drafting machine is a useful tool,&quot; he
+wrote. &quot;It is not a substitute for a draftsman.&quot;<a name="FNanchor_118_119" id="FNanchor_118_119"></a><a href="#Footnote_118_119" class="fnanchor">[118]</a></p>
+
+<div class="footnote"><p><a name="Footnote_118_119" id="Footnote_118_119"></a><a href="#FNanchor_118_119"><span class="label">
+	[118]</span></a>  <em>Mechanical Engineering</em>, October 1942, vol. 64, p. 746.</p></div>
+
+<p>The scholarly interest in a subject is fairly represented by the papers that
+are published in the transactions of professional societies and, more recently,
+by original papers that appear in specialized magazines. From 1900 to 1930 there
+were few papers on mechanisms, and most of those that did appear were concerned
+with descriptions of new &quot;mechanical motions.&quot; In the 1930's the number of
+papers reported in <em>Engineering Index</em> increased sharply, but only because the
+editors had begun to include foreign-language listings.</p>
+
+<p>There has been in Germany a thread of continuity in the kinematics of
+mechanisms since the time of Reuleaux. While most of the work has had to do with
+analysis, the teasing question of synthesis that Reuleaux raised in his work has
+never been ignored. The developments in Germany and elsewhere have been ably
+reviewed by others,<a name="FNanchor_119_120" id="FNanchor_119_120"></a><a href="#Footnote_119_120" class="fnanchor">[119]</a>
+and it is only to be noted here that two of the German papers, published in 1939
+in <em>Maschinenbau</em>, appear to have been the sparks for the conflagration that
+still is increasing in extent and intensity. According to summaries in <em>
+Engineering Index</em>, R. Kraus, writing on the synthesis of the double-crank
+mechanism, drew fire from the Russian Z. S. Bloch, who, in 1940, discussed
+critically Kraus's articles and proceeded to give the outline of the &quot;correct
+analysis of the problem&quot; and a general numerical solution for the synthesis of
+&quot;any four-bar linkage.&quot;<a name="FNanchor_120_121" id="FNanchor_120_121"></a><a href="#Footnote_120_121" class="fnanchor">[120]</a>
+Russian work in mechanisms, dating back to Chebyshev and following the
+&quot;Chebyshev theory of synthesis&quot; in which algebraic methods are used to determine
+paths of minimum deviation from a given curve, has also been reviewed elsewhere,<a name="FNanchor_121_122" id="FNanchor_121_122"></a><a href="#Footnote_121_122" class="fnanchor">[121]</a>
+and I can add nothing of value.</p>
+
+<div class="footnote"><p><a name="Footnote_119_120" id="Footnote_119_120"></a><a href="#FNanchor_119_120"><span class="label">
+	[119]</span></a> Grodzinski, Bottema, De Jonge, and Hartenberg and Denavit.
+	For complete titles see list of selected references.</p></div>
+
+<div class="footnote"><p><a name="Footnote_120_121" id="Footnote_120_121"></a><a href="#FNanchor_120_121"><span class="label">
+	[120]</span></a>  My source, as noted, is <em>Engineering Index</em>. Kraus's
+	articles are reported in 1939 and Bloch's in 1940, both under the section
+	heading &quot;Mechanisms.&quot;</p></div>
+
+<div class="footnote"><p><a name="Footnote_121_122" id="Footnote_121_122"></a><a href="#FNanchor_121_122"><span class="label">
+	[121]</span></a>  A. E. Richard de Jonge, &quot;Are the Russians Ahead in
+	Mechanism Analysis?&quot; <em>Machine Design</em>, September 1951, vol. 23, pp. 127,
+	200-208; O. Bottema, &quot;Recent Work on Kinematics,&quot; <em>Applied
+	Mechanics Reviews</em>, April 1953, vol. 6, pp. 169-170.</p></div>
+
+<p>When, after World War II, some of the possibilities of kinematic synthesis
+were recognized in the United States, a few perceptive teachers fanned the
+tinder into an open flame.</p>
+
+<p>The first publication of note in this country on the synthesis of linkages
+was a practical one, but in conception and undertaking it was a bold enterprise.
+In a book by John A. Hrones and G. L. Nelson, <em>Analysis of the Four Bar
+Linkage</em>
+(1951), the four-bar crank-and-rocker mechanism was exhaustively analyzed
+mechanically and the results were presented graphically. This work was faintly
+praised by a Dutch scholar, O. Bottema, who observed that the &quot;complicated
+analytical theory of the three-bar [sic] curve has undoubtedly kept the engineer
+from using it&quot; and who went on to say that &quot;we fully understand the publication
+of an atlas by Hrones and Nelson containing thousands of trajectories which must
+be very useful in many design problems.&quot;<a name="FNanchor_122_123" id="FNanchor_122_123"></a><a href="#Footnote_122_123" class="fnanchor">[122]</a>
+Nevertheless, the authors furnished designers with a tool that could be readily,
+almost instantly, understood (fig. 45), and the atlas has enjoyed wide
+circulation.<a name="FNanchor_123_124" id="FNanchor_123_124"></a><a href="#Footnote_123_124" class="fnanchor">[123]</a>
+The idea of a geometrical approach to synthesis has been exploited by others in
+more recent publications,<a name="FNanchor_124_125" id="FNanchor_124_125"></a><a href="#Footnote_124_125" class="fnanchor">[124]</a>
+and it is likely that many more variations on this theme will appear.</p>
+
+<div class="footnote"><p><a name="Footnote_122_123" id="Footnote_122_123"></a><a href="#FNanchor_122_123"><span class="label">
+	[122]</span></a> Bottema, <em>op. cit.</em> (footnote 121).</p></div>
+
+<div class="footnote"><p><a name="Footnote_123_124" id="Footnote_123_124"></a><a href="#FNanchor_123_124"><span class="label">
+	[123]</span></a> In 1851 Robert Willis had designed a coupler-point
+	path-generating machine (fig. 46) that could have been used to produce a
+	work similar to that of Hrones and Nelson.</p></div>
+
+<div class="footnote"><p><a name="Footnote_124_125" id="Footnote_124_125"></a><a href="#FNanchor_124_125"><span class="label">
+	[124]</span></a>  R. S. Hartenberg and J. Denavit, &quot;Systematic Mechanism
+	Design,&quot; <em>Machine Design</em>, September 1954, vol. 26, pp. 167-175, and October
+	1954, vol. 26, pp. 257-265; A. S. Hall, A. R. Holowenko, and H. G. Laughlin,
+	&quot;Four-Bar Lever Crank Mechanism,&quot; <em>Design News</em>, September 15, 1957, vol.
+	12, pp. 130-139, October 1, 1957, vol. 12, pp. 145-154, and October 15,
+	1957, vol. 12, pp. 132-141. For a nomographic approach, with particular
+	application to computers, see Antonin Svoboda, <em>Computing Mechanisms and
+	Linkages</em>, New York, 1948.</p></div>
+
+<p class="center">
+<img alt="Figure 45" src="images/fig-45.jpg" width="500" height="329" /></p>
+<p>Figure 45.&#8212;Paths of 11 points on the coupler (horizontal) link
+are plotted through one cycle. Dashes indicate equal time intervals. From John
+A. Hrones and G. L. Nelson, <em>Analysis of the Four Bar Linkage</em> (New York,
+1951, p. 635).</p>
+
+<p class="center">
+<img alt="Figure 46" src="images/fig-46.jpg" width="462" height="600" /></p>
+<p>Figure 46.&#8212;Coupler-point path-generating machine for four-bar
+linkage. This device, built by Professor Willis as a teaching aid for
+demonstrating straight-line linkages, could have been adapted to produce a plate
+like the one shown in figure 45. From Robert Willis, <em>A System of Apparatus
+for the Use of Lecturers and Experimenters</em> ... (London 1851, pl. 3).</p>
+
+<p>Pursuit of solutions to the &quot;complicated analytical theory&quot; of linkages was
+stimulated by publication of Ferdinand Freudenstein's &quot;Analytical Approach to
+the Design of Four-Link Mechanisms&quot; in 1954,<a name="FNanchor_125_126" id="FNanchor_125_126"></a><a href="#Footnote_125_126" class="fnanchor">[125]</a>
+and an increasing interest in the problem is indicated by the extensive
+literature that has appeared in the last five years.</p>
+
+<div class="footnote"><p><a name="Footnote_125_126" id="Footnote_125_126"></a><a href="#FNanchor_125_126"><span class="label">
+	[125]</span></a>  <em>Transactions of the American Society of Mechanical
+	Engineers</em>, 1954, vol. 76, pp. 483-492. See also <em>Transactions of the
+	American Society of Mechanical Engineers</em>, 1955, vol. 77, pp. 853-861, and
+	1956, vol. 78, pp. 779-787.</p></div>
+
+<p>The proper role of rational methods in the synthesis of mechanisms is not yet
+clear. &quot;While we may talk about kinematic synthesis,&quot; wrote two of today's
+leaders in the field, &quot;we are really talking about a hope for the future rather
+than a great reality of the present.&quot;<a name="FNanchor_126_127" id="FNanchor_126_127"></a><a href="#Footnote_126_127" class="fnanchor">[126]</a>
+When the mental equipment and the enthusiasm of scholars who are devoting their
+time to the problems of kinematic synthesis are considered, however, it is
+difficult to see how important new ideas can fail to be produced.</p>
+
+<div class="footnote"><p><a name="Footnote_126_127" id="Footnote_126_127"></a><a href="#FNanchor_126_127"><span class="label">
+	[126]</span></a>  R. S. Hartenberg and J. Denavit, &quot;Kinematic Synthesis,&quot;
+	<em>Machine Design</em>, September 6, 1956, vol. 28, pp. 101-105.</p></div>
+
+<p>An annual Conference on Mechanisms, sponsored by Purdue University and
+<em>Machine Design</em>, was inaugurated in 1953 and has met with a lively response.
+Among other manifestations of current interest in mechanisms, the contributions
+of Americans to international conferences on mechanisms reflects the growing
+recognition of the value of scholarly investigation of the kind that can
+scarcely hope to yield immediately tangible results.</p>
+
+<p>While we look to the future, one may ask how a lengthy view of the past can
+be justified. It seems to me that there is inherent in the almost feverish
+activity of the present the danger of becoming so preoccupied with operational
+theory that the goals may become clouded and the synthesis (let us put it less
+elegantly: the design) of mechanisms may never quite come into focus. If one
+knows nothing of the past, I wonder how he can with any confidence decide in
+what direction he must turn in order to face the future.</p>
+
+
+<p>Acknowledgment</p>
+
+<p>I am grateful to Professors Richard S. Hartenberg and Allen S. Hall, Jr., for
+reading the manuscript, making helpful comments, and suggesting material that I
+had not found. The errors, however, are mine. </p>
+<h3><a name="Additional_References">Additional References</a></h3>
+
+<p>The following list of additional reference material on kinematics may be of
+help to readers who desire to do independent research. The material is listed
+according to the section headings in the text of the present article.</p>
+
+
+<h4>TO DRAW A STRAIGHT LINE</h4>
+
+<p>KEMPE, A. B. <em>How to Draw a Straight Line.</em> London, 1877.</p>
+
+<p>Contains a useful bibliography. Reprinted in <em>Squaring the Circle and
+Other Monographs</em>, New York, Chelsea Publishing Company, 1953.</p>
+
+<p>Much attention has been given to straight-line mechanisms since the time of
+Kempe; at least a half dozen articles have appeared in the United States since
+1950, but I did not investigate the literature published after 1877.</p>
+
+
+<h4>SCHOLARS AND MACHINES</h4>
+
+<p>BECK, THEODOR. <em>Beiträge zur Geschichte des Maschinenbaues.</em> Berlin, 1899.</p>
+
+<p>Reviews of early works, such as those by Leonardo a Vinci, Biringuccio,
+Besson, Zonca, etc.</p>
+
+<p>BORGNIS, GIUSEPPE ANTONIO. <em>Traité complet de mécanique appliquée aux arts</em>.
+Paris, 1818-1821, 9 vols.</p>
+
+<p>Contains several hundred finely detailed plates of machines.</p>
+
+<p>LABOULAYE, CHARLES. <em>Traité de cinématique ou théorie des mécanismes</em>. Paris,
+1861 (ed. 2).</p>
+
+<p>This work was quoted frequently by Laboulaye's contemporaries.</p>
+
+<p>ROYAL SOCIETY OF LONDON. <em>Catalogue of Scientific Papers, 1800-1900,
+Author Index.</em> London, 1867-1902, and Cambridge, 1914-1925.</p>
+
+<p>----. <em>Catalogue of Scientific Papers, 1800-1900, Subject Index.</em> London,
+1909, vol. 2.</p>
+
+<p>This subject index was started in 1908, and by 1914 three volumes (the third
+in two parts) had been published; however, this subject index was never
+completed. Volume 2, titled <em>Mechanics</em>, has some 200 entries under &quot;Linkages.&quot;
+It is interesting to note that both of the Royal Society's monumental catalogs
+grew out of a suggestion made by Joseph Henry at a British Association meeting
+in Glasgow in 1855.</p>
+
+<p>WEISBACH, JULIUS. <em>The Mechanics of the Machinery of Transmission</em>, vol. 3,
+pt. 1, sec. 2 of <em>Mechanics of Engineering and Machinery</em>, translated by J. F.
+Klein. New York, 1890 (ed. 2).</p>
+
+
+<h4>MECHANISMS AND MECHANICIANS</h4>
+
+<p>BARBER, THOMAS W. <em>Engineer's Sketch-Book.</em> London, 1890 (ed. 2).</p>
+
+<p>HERKIMER, HERBERT. <em>Engineer's Illustrated Thesaurus.</em> New York, 1952.</p>
+
+<p>PERIODICALS. <em>Artizan</em>, from 1843; <em>Practical Mechanic and
+Engineer's Magazine</em>, from 1841; <em>Repertory of Arts and Manufactures</em>, from 1794;
+<em>Newton's London Journal of Arts and Science</em>, from 1820. (The preceding periodicals have
+many plates of patent specification drawings.) <em>The Engineer</em>, November 10,
+1933, vol. 156, p. 463, and <em>Engineering</em>, November 10, 1933, vol. 136, p. 525.
+(Recent English views questioning the utility of kinematics.)</p>
+
+<p>TATE, THOMAS. <em>Elements of Mechanism.</em> London, 1851.</p>
+
+<p>Contains figures from Lanz and Bétancourt (1808).</p>
+
+<p>WYLSON, JAMES. <em>Mechanical Inventor's Guide.</em> London, 1859.</p>
+
+<p>Contains figures from Henry Adcock, <em>Adcock's Engineers' Pocket-Book, 1858</em>.</p>
+
+
+<h4>MECHANISMS IN AMERICA, 1875-1955</h4>
+
+<p>ALBERT, CALVIN D., AND ROGERS, F. D. <em>Kinematics of Machinery.</em> New York,
+1931.</p>
+
+<p>Contains a bibliography that includes works not mentioned in the present
+paper.</p>
+
+<p>BARR, JOHN H. <em>Kinematics of Machinery.</em> New York, 1899.</p>
+
+<p>An early textbook. The author taught at Cornell University.</p>
+
+<p>BEGGS, JOSEPH S. <em>Mechanism.</em> New York, 1955.</p>
+
+<p>Contains an extensive and useful bibliography.</p>
+
+<p>BOTTEMA, O. &quot;Recent Work on Kinematics,&quot; <em>Applied Mechanics
+Reviews</em>, April
+1953, vol. 6, pp. 169-170.</p>
+
+
+<h4>CONFERENCE ON MECHANISMS.</h4>
+
+<p>This conference was sponsored by Purdue University and <em>Machine Design</em>.
+Transactions of the first two conferences appeared as special sections in
+<em>Machine Design</em>, December 1953, vol. 25, pp. 173-220, December 1954, vol. 26,
+pp. 187-236, and in collected reprints. Papers of the third and fourth
+conferences (May 1956 and October 1957) appeared in <em>Machine Design</em> over
+several months following each conference and in collected reprints. Papers of
+the fifth conference (October 1958) were collected and preprinted for conference
+participants; subsequently, all papers appeared in <em>Machine Design</em>. Collected
+reprints and preprints are available (May 1960) from Penton Publishing Company,
+Cleveland, Ohio.</p>
+
+<p>DE JONGE, A. E. RICHARD. &quot;Kinematic Synthesis of Mechanisms,&quot; <em>
+Mechanical Engineering</em>, July 1940, vol. 62, pp. 537-542.</p>
+
+<p>----. &quot;A Brief Account of Modern Kinematics,&quot; <em>Transactions of
+the American Society of Mechanical Engineers</em>, 1943, vol. 65, pp. 663-683.</p>
+
+<p>GOODEVE, THOMAS M. <em>The Elements of Mechanism.</em> London, 1903.</p>
+
+<p>An early textbook.</p>
+
+<p>GRODZINSKI, PAUL, AND MCEWEN, EWEN. &quot;Link Mechanisms in Modern Kinematics,&quot;
+<em>Journal and Proceedings of the Institution of Mechanical Engineers</em>, 1954, vol.
+168, pp. 877-896.</p>
+
+<p>This article evoked interesting discussion. It is unfortunate that
+Grodzinski's periodical, <em>Mechanism, An International Bibliography</em>, which was
+published in London in 1956-1957 and which terminated shortly after his death,
+has not been revived. Grodzinski's incisive views and informative essays are
+valuable and interesting.</p>
+
+<p>HARTENBERG, R. S. &quot;Complex Numbers and Four-Bar Linkages,&quot; <em>
+Machine Design</em>,
+March 20, 1958, vol. 30, pp. 156-163.</p>
+
+<p>This is an excellent primer. The author explains complex numbers in his usual
+lucid fashion.</p>
+
+<p>HARTENBERG, R. S., AND DENAVIT, J. &quot;Kinematic Synthesis,&quot; <em>
+Machine Design</em>,
+September 6, 1956, vol. 28, pp. 101-105.</p>
+
+<p>MACCORD, CHARLES. <em>Kinematics.</em> New York, 1883.</p>
+
+<p>An early textbook.</p>
+
+<p>ROBINSON, STILLMAN W. <em>Principles of Mechanism.</em> New York, 1896.</p>
+
+<p>An early textbook. The author taught at Ohio State University.</p>
+
+<p>UNWIN, WILLIAM C. <em>The Elements of Machine Design.</em> New York, 1882 (ed. 4).</p>
+
+<p>An early textbook. The author taught at Royal Indian Engineering College, in
+England.</p>
+<p>&nbsp;</p>
+<p>&nbsp;</p>
+
+
+<p>GOVERNMENT PRINTING OFFICE: 1962</p>
+
+<p>For sale by the Superintendent of Documents, U.S. Government Printing Office
+Washington 25, D. C.&#8212;Price 40 cents</p>
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
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+of Watt, by Eugene S. Ferguson
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+The Project Gutenberg EBook of Kinematics of Mechanisms from the Time of
+Watt, by Eugene S. Ferguson
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Kinematics of Mechanisms from the Time of Watt
+
+Author: Eugene S. Ferguson
+
+Release Date: October 31, 2008 [EBook #27106]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK KINEMATICS OF MECHANISMS ***
+
+
+
+
+Produced by Chris Curnow, Viv, Joseph Cooper and the Online
+Distributed Proofreading Team at http://www.pgdp.net
+
+
+
+
+
+[Transcriber's notes:
+
+1) Peaucillier is a printers error and has been changed to Peaucellier.
+
+2) The 4 characters at the end of the word 'Pafnuti[)i]' denote a letter
+'i' with a breve accent.]
+
+
+CONTRIBUTIONS FROM
+
+THE MUSEUM OF HISTORY AND TECHNOLOGY
+
+PAPER 27
+
+
+
+KINEMATICS OF MECHANISMS FROM THE TIME OF WATT
+
+_Eugene S. Ferguson_
+
+
+JAMES WATT, KINEMATIC SYNTHESIST      187
+
+TO DRAW A STRAIGHT LINE               199
+
+SCHOLARS AND MACHINES                 209
+
+MECHANICIANS AND MECHANISMS           216
+
+MECHANISMS IN AMERICA, 1875-1955      223
+
+ADDITIONAL REFERENCES                 229
+
+
+
+
+KINEMATICS OF MECHANISMS FROM THE TIME OF WATT
+
+
+_In an inventive tour de force that seldom, if ever, has been equalled
+for its brilliance and far-reaching consequences, James Watt radically
+altered the steam engine not only by adding a separate condenser but by
+creating a whole new family of linkages. His approach was largely
+empirical, as we use the word today._
+
+_This study suggests that, despite the glamor of today's sophisticated
+methods of calculation, a highly developed intuitive sense, reinforced
+by a knowledge of the past, is still indispensable to the design of
+successful mechanisms._
+
+THE AUTHOR: _Eugene S. Ferguson, formerly curator of mechanical and
+civil engineering in the United States National Museum, Smithsonian
+Institution, is now professor of mechanical engineering at Iowa State
+University of Science and Technology._
+
+In engineering schools today, a student is introduced to the kinematics
+of mechanisms by means of a course of kinematic analysis, which is
+concerned with principles underlying the motions occurring in
+mechanisms. These principles are demonstrated by a study of mechanisms
+already in existence, such as the linkage of a retractable landing gear,
+computing mechanisms, mechanisms used in an automobile, and the like. A
+systematic, if not rigorous, approach to the design of gears and cams
+also is usually presented in such a course. Until recently, however, no
+serious attempt was made to apply the principles developed in kinematic
+analysis to the more complex problem of kinematic synthesis of linkages.
+By kinematic synthesis is meant the designing of a linkage to produce a
+given series of motions for a particular purpose.
+
+That a rational--numerical or geometrical--approach to kinematic
+synthesis is possible is a relatively recent idea, not yet fully
+accepted; but it is this idea that is responsible for the intense
+scholarly interest in the kinematics of mechanisms that has occurred in
+this country within the last 10 years.
+
+This scholarly activity has resulted in the rediscovery of many earlier
+works on the subject, and nearly all the scholars now working in this
+field have acknowledged in one way or another their debt to those who
+arrived on the scene at an earlier time than they. There have been
+occasional reviews of the sequence and nature of developments, but the
+emphasis naturally has been upon the recent past. It seems to me that
+there is something to be gained in looking beyond our own generation, or
+even beyond the time of Franz Reuleaux (1829-1905), who is generally
+credited with originating many of our modern concepts of mechanism
+analysis and design, and to inquire into the ideas that made possible
+Reuleaux's contributions.
+
+     _Take to Kinematics. It will repay you. It is more fecund than
+     geometry; it adds a fourth dimension to space._
+
+     --Chebyshev to Sylvester, 1873
+
+While no pretense of completeness is made, I have tried in this paper to
+trace the high points in the development of kinematic analysis and
+synthesis, both in academic circles and in the workshop, noting where
+possible the influence of one upon the other. If I have devoted more
+space to particular people and episodes than is warranted by their
+contributions to the modern treatment of the subject, it is because I
+have found that the history of kinematics of mechanisms, like the
+history of any other branch of engineering, is more interesting and more
+plausible if it is recognized that its evolutionary development is the
+result of human activity. This history was wrought by people like us, no
+less intelligent and no less subject than we are to environment, to a
+subjective way of looking at things, and to a heritage of ideas and
+beliefs.
+
+I have selected the period from the time of Watt because modern
+mechanisms originated with him, and I have emphasized the first century
+of the period because by 1885 many of the ideas of modern kinematics of
+mechanisms were well developed. Linkages are discussed, to the virtual
+exclusion of gears and cams, because much of the scholarly work in
+kinematic synthesis is presently directed toward the design of linkages
+and because linkages provide a convenient thread for a narrative that
+would have become unnecessarily complex if detailed treatment of gears
+and cams had been included. I have brought the narrative down to the
+present by tracing kinematics as taught in American engineering
+schools, closing with brief mention of the scholarly activity in
+kinematics in this country since 1950. An annotated list of additional
+references is appended as an encouragement to further work in the
+history of the subject.
+
+
+James Watt, Kinematic Synthesist
+
+James Watt (1736-1819), improver of the steam engine, was a highly
+gifted designer of mechanisms, although his background included no
+formal study of mechanisms. Indeed, the study of mechanisms, without
+immediate regard to the machines in which they were used, was not
+introduced until after Watt's important work had been completed, while
+the actual design of mechanisms had been going on for several centuries
+before the time of Watt.
+
+Mechanisms that employed screws, cams, and gears were certainly in use
+by the beginning of the Christian era. While I am not aware of
+unequivocal evidence of the existence of four-bar linkages before the
+16th century, their widespread application by that time indicates that
+they probably originated much earlier. A tantalizing 13th-century sketch
+of an up-and-down sawmill (fig. 1) suggests, but does not prove, that
+the four-bar linkage was then in use. Leonardo da Vinci (1452-1519)
+delineated, if he did not build, a crank and slider mechanism, also for
+a sawmill (fig. 2). In the 16th century may be found the conversion of
+rotary to reciprocating motion (strictly speaking, an oscillation
+through a small arc of a large circle) and vice versa by use of linkages
+of rigid members (figs. 3 and 4), although the conversion of rotary to
+reciprocating motion was at that time more frequently accomplished by
+cams and intermittent gearing. Nevertheless, the idea of linkages was a
+firmly established part of the repertory of the machine builder before
+1600. In fact one might have wondered in 1588, when Agostino Ramelli
+published his book on machines,[1] whether linkages had not indeed
+reached their ultimate stage of development. To illustrate my point, I
+have selected the plate of Ramelli that most appeals to me (fig. 5),
+although the book exhibits more than 200 other machines of comparable
+complexity and ingenuity.
+
+[Footnote 1: Agostino Ramelli, _Le Diverse et Artificiose Machine_,
+Paris, 1588.]
+
+[Illustration: Figure 1.--Up-and-down sawmill of the 13th century. The
+guide mechanism at lower left, attached to the saw blade, appears to be
+a 4-bar linkage. After Robert Willis, trans. and ed., _Facsimile of the
+Sketch-Book of Wilars de Honecort_ (London, 1859, pl. 43).]
+
+[Illustration: Figure 2.--Slider-crank mechanism of Leonardo da Vinci
+(1452-1519), redrawn from his manuscript notebooks. A frame saw is
+depicted at the lower end of the guides. From Theodor Beck, _Beitraege
+zur Geschichte des Maschinenbaues_ (Berlin, 1899, p. 323).]
+
+[Illustration: Figure 3.--Blowing engine by Vanuccio Biringuccio, about
+1540, showing conversion of motion of the waterwheel shaft from rotation
+to oscillation. From Theodor Beck, _Beitraege zur Geschichte des
+Maschinenbaues_ (Berlin, 1899, p. 120).]
+
+[Illustration: Figure 4.--Grain mill, 1588, showing conversion of motion
+of the operating bars from oscillation to rotation. Note the
+fly-weights, predecessors of the flywheel. From Agostino Ramelli, _Le
+Diverse et Artificiose Machine_ (Paris, 1588, pl. opposite p. 199).]
+
+[Illustration: Figure 5.--Machine for raising water. Such a machine was
+built in Spain during the 16th century and was operated for some 80
+years. From Agostino Ramelli, _Le Diverse et Artificiose Machine_
+(Paris, 1588, p. 199).]
+
+There was a vast difference, both in conception and execution, between
+the linkages of Ramelli and those of James Watt some 200 years later.
+Watt was responsible for initiating profound changes in mechanical
+technology, but it should be recognized that the mechanic arts had,
+through centuries of slow development, reached the stage where his
+genius could flourish. The knowledge and ability to provide the
+materials and tools necessary for Watt's researches were at hand, and
+through the optimism and patient encouragement of his partner, Matthew
+Boulton, they were placed at his disposal.
+
+Watt's genius was nowhere more evident than in his synthesis of
+linkages. An essential ingredient in the success of Watt's linkages,
+however, was his partner's appreciation of the entirely new order of
+refinement that they called for. Matthew Boulton, who had been a
+successful manufacturer of buttons and metal novelties long before his
+partnership with Watt was formed, had recognized at once the need for
+care in the building of Watt's steam engine. On February 7, 1769, he had
+written Watt:[2] "I presumed that your engine would require money,
+very accurate workmanship and extensive correspondence to make it turn
+out to the best advantage and that the best means of keeping up the
+reputation and doing the invention justice would be to keep the
+executive part of it out of the hands of the multitude of empirical
+engineers, who from ignorance, want of experience and want of necessary
+convenience, would be very liable to produce bad and inaccurate
+workmanship; all of which deficiencies would affect the reputation of
+the invention." Boulton expected to build the engines in his shop "with
+as great a difference of accuracy as there is between the blacksmith and
+the mathematical instrument maker." The Soho Works of Boulton and Watt,
+in Birmingham, England, solved for Watt the problem of producing "in
+great" (that is, in sizes large enough to be useful in steam engines)
+the mechanisms that he devised.[3]
+
+[Footnote 2: Henry W. Dickinson, _James Watt, Craftsman & Engineer_,
+Cambridge, Cambridge University Press, 1936, pp. 52-53.]
+
+[Footnote 3: James P. Muirhead, _The Origin and Progress of the
+Mechanical Inventions of James Watt_, London, 1854, vol. 1, pp. 56, 64.
+This work, in three volumes, contains letters, other documents, and
+plates of patent specification drawings.]
+
+The contributions of Boulton and Watt to practical mechanics "in great"
+cannot be overestimated. There were in the 18th century instrument
+makers and makers of timekeepers who had produced astonishingly
+accurate work, but such work comprised relatively small items, all being
+within the scope of a bench lathe, hand tools, and superb handwork. The
+rapid advancement of machine tools, which greatly expanded the scope of
+the machine-building art, began during the Boulton and Watt partnership
+(1775-1800).
+
+In April 1775 the skirmish at Concord between American colonists and
+British redcoats marked the beginning of a war that was to determine for
+the future the course of political events in the Western Hemisphere.
+
+Another event of April 1775 occurring in Birmingham now appears to have
+been one that marked the beginning of a new era of technological
+advance. It was near the end of this month that Boulton, at the Soho
+Works, wrote to his partner and commented upon receiving the cast iron
+steam engine cylinder that had been finished in John Wilkinson's boring
+mill:
+
+     ... it seems tolerably true, but is an inch thick and weighs about
+     10 cwt. Its diameter is about as much above 18 inches as the tin
+     one was under, and therefore it is become necessary to add a brass
+     hoop to the piston, which is made almost two inches broad.[4]
+
+[Footnote 4: _Ibid._, vol. 2, p. 84.]
+
+This cylinder indeed marked the turning point in the discouragingly long
+development of the Watt steam engine, which for 10 years had occupied
+nearly all of Watt's thoughts and all the time he could spare from the
+requirements of earning a living. Although there were many trials ahead
+for the firm of Boulton and Watt in further developing and perfecting
+the steam engine, the crucial problem of leakage of steam past the
+piston in the cylinder had now been solved by Wilkinson's new boring
+mill, which was the first large machine tool capable of boring a
+cylinder both round and straight.
+
+The boring mill is pertinent to the development of linkages "in great,"
+being the first of a new class of machine tools that over the next 50 or
+60 years came to include nearly all of the basic types of heavy
+chip-removing tools that are in use today. The development of tools was
+accelerated by the inherent accuracy required of the linkages that were
+originated by Watt. Once it had been demonstrated that a large and
+complex machine, such as the steam engine, could be built accurately
+enough so that its operation would be relatively free of trouble, many
+outstanding minds became engaged in the development of machines and
+tools. It is interesting, however, to see how Watt and others grappled
+with the solutions of problems that resulted from the advance of the
+steam engine.
+
+During the 1770's the demand for continuous, dependable power applied to
+a rotating shaft was becoming insistent, and much of Boulton's and
+Watt's effort was directed toward meeting this demand. Mills of all
+kinds used water or horses to turn "wheel-work," but, while these
+sources of power were adequate for small operations, the quantity of
+water available was often limited, and the use of enormous horse-whims
+was frequently impracticable.
+
+The only type of steam engine then in existence was the Newcomen beam
+engine, which had been introduced in 1712 by Thomas Newcomen, also an
+Englishman. This type of engine was widely used, mostly for pumping
+water out of mines but occasionally for pumping water into a reservoir
+to supply a waterwheel. It was arranged with a vertical steam cylinder
+located beneath one end of a large pivoted working beam and a vertical
+plunger-type pump beneath the other end. Heavy, flat chains were secured
+to a sector at each end of the working beam and to the engine and pump
+piston rods in such a way that the rods were always tangent to a circle
+whose center was at the beam pivot. The weight of the reciprocating pump
+parts pulled the pump end of the beam down; the atmosphere, acting on
+the open top of the piston in the steam cylinder, caused the engine end
+of the beam to be pulled down when the steam beneath the piston was
+condensed. The chains would of course transmit force from piston to beam
+only in tension.
+
+It is now obvious that a connecting rod, a crank, and a sufficiently
+heavy flywheel might have been used in a conventional Newcomen engine in
+order to supply power to a rotating shaft, but contemporary evidence
+makes it clear that this solution was by no means obvious to Watt nor to
+his contemporaries.
+
+At the time of his first engine patent, in 1769, Watt had devised a
+"steam wheel," or rotary engine, that used liquid mercury in the lower
+part of a toroidal chamber to provide a boundary for steam spaces
+successively formed by flap gates within the chamber. The practical
+difficulties of construction finally ruled out this solution to the
+problem of a rotating power source, but not until after Boulton and
+Watt had spent considerable effort and money on it.[5]
+
+[Footnote 5: Henry W. Dickinson and Rhys Jenkins, _James Watt and the
+Steam Engine_, Oxford, Clarendon Press, 1927, pp. 146-148, pls. 14, 31.
+This work presents a full and knowledgeable discussion, based on primary
+material, of the development of Watt's many contributions to mechanical
+technology. It is ably summarized in Dickinson, _op. cit._ (footnote
+2).]
+
+In 1777 a speaker before the Royal Society in London observed that in
+order to obtain rotary output from a reciprocating steam engine, a crank
+"naturally occurs in theory," but that in fact the crank is impractical
+because of the irregular rate of going of the engine and its variable
+length of stroke. He said that on the first variation of length of
+stroke the machine would be "either broken to pieces, or turned
+back."[6] John Smeaton, in the front rank of English steam engineers of
+his time, was asked in 1781 by His Majesty's Victualling-Office for his
+opinion as to whether a steam-powered grain mill ought to be driven by a
+crank or by a waterwheel supplied by a pump. Smeaton's conclusion was
+that the crank was quite unsuited to a machine in which regularity of
+operation was a factor. "I apprehend," he wrote, "that no motion
+communicated from the reciprocating beam of a fire engine can ever act
+perfectly equal and steady in producing a circular motion, like the
+regular efflux of water in turning a waterwheel." He recommended,
+incidentally, that a Boulton and Watt steam engine be used to pump water
+to supply the waterwheel.[7] Smeaton had thought of a flywheel, but he
+reasoned that a flywheel large enough to smooth out the halting, jerky
+operation of the steam engines that he had observed would be more of an
+encumbrance than a pump, reservoir, and waterwheel.[8]
+
+[Footnote 6: John Farey, _A Treatise on the Steam Engine_, London, 1827,
+pp. 408-409.]
+
+[Footnote 7: _Reports of the Late John Smeaton, F.R.S._, London, 1812,
+vol. 2, pp. 378-380.]
+
+[Footnote 8: Farey, _op. cit._ (footnote 6), p. 409.]
+
+The simplicity of the eventual solution of the problem was not clear to
+Watt at this time. He was not, as tradition has it, blocked merely by
+the existence of a patent for a simple crank and thus forced to invent
+some other device as a substitute.
+
+Matthew Wasbrough, of Bristol, the engineer commonly credited with the
+crank patent, made no mention of a crank in his patent specification,
+but rather intended to make use of "racks with teeth," or "one or more
+pullies, wheels, segments of wheels, to which are fastened rotchets and
+clicks or palls...." He did, however, propose to "add a fly or flys, in
+order to render the motion more regular and uniform." Unfortunately for
+us, he submitted no drawings with his patent specification.[9]
+
+[Footnote 9: British Patent 1213, March 10, 1779.]
+
+James Pickard, of Birmingham, like Boulton, a buttonmaker, in 1780
+patented a counterweighted crank device (fig. 6) that was expected to
+remove the objection to a crank, which operated with changing leverage
+and thus irregular power. In figure 6, the counterweighted wheel,
+revolving twice for each revolution of the crank (A), would allow the
+counterweight to descend while the crank passed the dead-center position
+and would be raised while the crank had maximum leverage. No mention of
+a flywheel was made in this patent.[10]
+
+[Footnote 10: British Patent 1263, August 23, 1780.]
+
+[Illustration: Figure 6.--One of the steam engine "Crank Patents" that
+hindered James Watt's progress. This patent, granted to James Pickard in
+1780, claimed only the arrangement of counterweights, not the crank. The
+crank pin to which the connecting rod was attached is at _Aa_. From
+British Patent 1263, August 23, 1780.]
+
+Wasbrough, finding that his "rotchets and clicks" did not serve,
+actually used, in 1780, a crank with a flywheel. Watt was aware of this,
+but he remained unconvinced of the superiority of the crank over other
+devices and did not immediately appreciate the regulating ability of a
+flywheel.[11] In April 1781 Watt wrote to Boulton, who was then out of
+town: "I know from experiment that the other contrivance, which you saw
+me try, performs at least as well, and has in fact many advantages over
+the crank."[12] The "other contrivance" probably was his swash wheel
+which he built and which appeared on his next important patent
+specification (fig. 7a). Also in this patent were four other devices,
+one of which was easily recognizable as a crank, and two of which were
+eccentrics (fig. 7a, b). The fourth device was the well-known
+sun-and-planet gearing (fig. 7e).[13] In spite of the similarity of the
+simple crank to the several variations devised by Watt, this patent drew
+no fire from Wasbrough or Pickard, perhaps because no reasonable person
+would contend that the crank itself was a patentable feature, or perhaps
+because the similarity was not at that time so obvious. However, Watt
+steered clear of directly discernible application of cranks because he
+preferred to avoid a suit that might overthrow his or other patents. For
+example, if the Wasbrough and Pickard patents had been voided, they
+would have become public property; and Watt feared that they might
+"get into the hands of men more ingenious," who would give Boulton and
+Watt more competition than Wasbrough and Pickard.[14]
+
+[Footnote 11: Dickinson and Jenkins, _op. cit._ (footnote 5), pp. 150,
+154.]
+
+[Footnote 12: _Ibid._, p. 154.]
+
+[Footnote 13: William Murdock, at this time a Boulton and Watt erector,
+may have suggested this arrangement. _Ibid._, p. 56.]
+
+[Footnote 14: Muirhead, _op. cit._ (footnote 3), vol. 3, note on p. 39.]
+
+[Illustration: Figure 7.--James Watt's five alternative devices for the
+conversion of reciprocating motion to rotary motion in a steam engine.
+(British Patent 1306, October 25, 1781). From James P. Muirhead, _The
+Origin and Progress of the Mechanical Inventions of James Watt_ (London,
+1854, vol. 3, pls. 3-5, 7).]
+
+[Illustration: (a) "Inclined wheel." The vertical shaft at _D_ is
+rotated by action of wheels _H_ and _J_ on cam, or swash plate, _ABC_.
+Boulton and Watt tried this device but discarded it.]
+
+[Illustration: (b) Counterweighted crank wheel.]
+
+[Illustration: (c) "Eccentric wheel" with external yoke hung from
+working beam. The wheel pivots at _C_.]
+
+[Illustration: (d) "Eccentric wheel" with internal driving wheel hung
+from working beam. Wheel _B_ is pivoted at center of shaft _A_.]
+
+[Illustration: (e) Sun-and-planet gearing. This is the idea actually
+employed in Boulton and Watt engines. As the optional link _JK_ held the
+gearwheel centers always equidistant, the annular guide _G_ was not
+used.]
+
+The sun-and-planet arrangement, with gears of equal size, was adopted by
+Watt for nearly all the rotative engines that he built during the term
+of the "crank patents." This arrangement had the advantage of turning
+the flywheel through two revolutions during a single cycle of operation
+of the piston, thus requiring a flywheel only one-fourth the size of the
+flywheel needed if a simple crank were used. The optional link (JK of
+fig. 7e) was used in the engines as built.
+
+From the first, the rotative engines were made double-acting--that is,
+work was done by steam alternately in each end of the cylinder. The
+double-acting engine, unlike the single-acting pumping engine, required
+a piston rod that would push as well as pull. It was in the solution of
+this problem that Watt's originality and sure judgment were most clearly
+demonstrated.
+
+A rack and sector arrangement (fig. 8) was used on some engines. The
+first one, according to Watt, "has broke out several teeth of the rack,
+but works steady."[15] A little later he told a correspondent that his
+double-acting engine "acts so powerfully that it has broken all its
+tackling repeatedly. We have now tamed it, however."[16]
+
+[Footnote 15: James Watt, March 31, 1783, quoted in Dickinson and
+Jenkins, _op. cit._ (footnote 5), p. 140.]
+
+[Footnote 16: Watt to De Luc, April 26, 1783, quoted in Muirhead, _op.
+cit._ (footnote 3), vol. 2, p. 174.]
+
+[Illustration: Figure 8.--Watt engine of 1782 (British Patent 1321,
+March 12, 1782) showing the rack and sector used to guide the upper end
+of the piston rod and to transmit force from piston to working beam.
+This engine, with a 30-inch cylinder and an 8-foot stroke, was arranged
+for pumping. Pump rod _SS_ is hung from sector of the working beam. From
+James P. Muirhead, _The Origin and Progress of the Mechanical Inventions
+of James Watt_ (London, 1854, vol. 3, pl. 15).]
+
+It was about a year later that the straight-line linkage[17] was thought
+out. "I have started a new hare," Watt wrote to his partner. "I have
+got a glimpse of a method of causing the piston-rod to move up and down
+perpendicularly, by only fixing it to a piece of iron upon the beam,
+without chains, or perpendicular guides, or untowardly frictions,
+arch-heads, or other pieces of clumsiness.... I have only tried it in a
+slight model yet, so cannot build upon it, though I think it a very
+probable thing to succeed, and one of the most ingenious simple pieces
+of mechanism I have contrived...."[18]
+
+[Footnote 17: Watt's was a four-bar linkage. All four-bar straight-line
+linkages that have no sliding pairs trace only an approximately straight
+line. The exact straight-line linkage in a single plane was not known
+until 1864 (see p. 204). In 1853 Pierre-Frederic Sarrus (1798-1861), a
+French professor of mathematics at Strasbourg, devised an accordion-like
+spatial linkage that traced a true straight line. Described but not
+illustrated (Academie des Sciences, Paris, _Comptes rendus_, 1853, vol.
+36, pp. 1036-1038, 1125), the mechanism was forgotten and twice
+reinvented; finally, the original invention was rediscovered by an
+English writer in 1905. For chronology, see Florian Cajori, _A History
+of Mathematics_, ed. 2, New York, 1919, p. 301.]
+
+[Footnote 18: Muirhead, _op. cit._ (footnote 3), vol. 2, pp. 191-192.]
+
+Watt's marvelously simple straight-line linkage was incorporated into a
+large beam engine almost immediately, and the usually pessimistic and
+reserved inventor was close to a state of elation when he told Boulton
+that the "new central perpendicular motion answers beyond expectation,
+and does not make the shadow of a noise."[19] This linkage, which was
+included in an extensive patent of 1784, and two alternative devices are
+illustrated here (fig. 9). One of the alternatives is a guided crosshead
+(fig. 9, top right).
+
+[Footnote 19: _Ibid._, p. 202.]
+
+[Illustration: Figure 9.--Watt's mechanisms for guiding the upper end of
+the piston rod of a double-acting engine (British Patent 1432, April 28,
+1784). _Top left_, straight-line linkage; _top right_, crosshead and
+guide arrangement; _lower left_, piston rod _A_ is guided by sectors _D_
+and _E_, suspended by flexible cords. From James P. Muirhead, _The
+Origin and Progress of the Mechanical Inventions of James Watt_ (London,
+1854, vol. 3, pls. 21, 22).]
+
+Brilliant as was the conception of this linkage, it was followed up by a
+synthesis that is very little short of incredible. In order to make the
+linkage attached to the beam of his engines more compact, Watt had
+plumbed his experience for ideas; his experience had yielded up the work
+done much earlier on a drafting machine that made use of a
+pantograph.[20] Watt combined his straight-line linkage with a
+pantograph, one link becoming a member of the pantograph.
+
+[Footnote 20: "It has only one fault," he had told a friend on December
+24, 1773, after describing the drafting machine to him, "which is, that
+it will not do, because it describes conic sections instead of straight
+lines." _Ibid._, p. 71.]
+
+The length of each oscillating link of the straight-line linkage was
+thus reduced to one-fourth instead of one-half the beam length, and the
+entire mechanism could be constructed so that it would not extend
+beyond the end of the working beam. This arrangement soon came to be
+known as Watt's "parallel motion" (fig. 10).[21] Years later Watt told
+his son: "Though I am not over anxious after fame, yet I am more proud
+of the parallel motion than of any other mechanical invention I have
+ever made."[22]
+
+[Footnote 21: Throughout the 19th century the term "parallel motion" was
+used indiscriminately to refer to any straight-line linkage. I have not
+discovered the origin of the term. Watt did not use it in his patent
+specification, and I have not found it in his writings or elsewhere
+before 1808 (see footnote 22). _The Cyclopaedia_ (Abraham Rees, ed.,
+London, 1819, vol. 26) defined parallel motion as "a term used among
+practical mechanics to denote the rectilinear motion of a piston-rod,
+&c. in the direction of its length; and contrivances, by which such
+alternate rectilinear motions are converted into continuous rotatory
+ones, or _vice versa_...." Robert Willis in his _Principles of
+Mechanism_ (London, 1841, p. 399) described parallel motion as "a term
+somewhat awkwardly applied to a combination of jointed rods, the purpose
+of which is to cause a point to describe a straight line...." A. B.
+Kempe in _How to Draw a Straight Line_ (London, 1877, p. 49) wrote: "I
+have been more than once asked to get rid of the objectionable term
+'parallel motion.' I do not know how it came to be employed, and it
+certainly does not express what is intended. The expression, however,
+has now become crystallised, and I for one cannot undertake to find a
+solvent."]
+
+[Footnote 22: Muirhead, _op. cit._ (footnote 3), vol. 3, note on p. 89.]
+
+[Illustration: Figure 10.--Watt's "parallel motion." Engine's working
+beam is pivoted at _A_. Pivot _F_ is attached to the engine frame. From
+Dyonysius Lardner, _The Steam Engine_ (Philadelphia, 1852), pl. 5
+(American ed. 5 from London ed. 5).]
+
+The Watt four-bar linkage was employed 75 years after its inception by
+the American Charles B. Richards when, in 1861, he designed his first
+high-speed engine indicator (fig. 11). Introduced into England the
+following year, the Richards Indicator was an immediate success, and
+many thousands were sold over the next 20 or 30 years.[23]
+
+[Footnote 23: Charles T. Porter, _Engineering Reminiscences_, New York,
+1908, pp. 58-59, 90.]
+
+[Illustration: Figure 11.--Richards high-speed engine indicator of 1861,
+showing application of the Watt straight-line linkage. (_USNM 307515_;
+_Smithsonian photo 46570_).]
+
+In considering the order of synthetic ability required to design the
+straight-line linkage and to combine it with a pantograph, it should be
+kept in mind that this was the first one of a long line of such
+mechanisms.[24] Once the idea was abroad, it was only to be expected
+that many variations and alternative solutions should appear. One
+wonders, however, what direction the subsequent work would have taken
+if Watt had not so clearly pointed the way.
+
+[Footnote 24: At least one earlier straight-line linkage, an arrangement
+later ascribed to Richard Roberts, had been depicted before Watt's
+patent (Pierre Patte, _Memoirs sur les objets les plus importants de
+l'architecture_, Paris, 1769, p. 229 and pl. 11). However, this linkage
+(reproduced here in figure 18) had no detectable influence on Watt or on
+subsequent practice.]
+
+In 1827 John Farey, in his exhaustive study of the steam engine, wrote
+perhaps the best contemporary view of Watt's work. Farey as a young man
+had several times talked with the aging Watt, and he had reflected upon
+the nature of the intellect that had caused Watt to be recognized as a
+genius, even within his own lifetime. In attempting to explain Watt's
+genius, Farey set down some observations that are pertinent not only to
+kinematic synthesis but to the currently fashionable term "creativity."
+
+In Farey's opinion Watt's inventive faculty was far superior to that of
+any of his contemporaries; but his many and various ideas would have
+been of little use if he had not possessed a very high order of
+judgment, that "faculty of distinguishing between ideas; decomposing
+compound ideas into more simple elements; arranging them into classes,
+and comparing them together...."
+
+Farey was of the opinion that while a mind like Watt's could produce
+brilliant new ideas, still the "common stock of ideas which are current
+amongst communities and professions, will generally prove to be of a
+better quality than the average of those new ideas, which can be
+produced by any individual from the operation of his own mind, without
+assistance from others." Farey concluded with the observation that "the
+most useful additions to that common stock, usually proceed from the
+individuals who are well acquainted with the whole series."[25]
+
+[Footnote 25: Farey, _op. cit._ (footnote 6), pp. 651, 652.]
+
+
+To Draw a Straight Line
+
+During most of the century after James Watt had produced his parallel
+motion, the problem of devising a linkage, one point of which would
+describe a straight line, was one that tickled the fancies of
+mathematicians, of ingenious mechanics, and of gentlemanly dabblers in
+ideas. The quest for a straight-line mechanism more accurate than that
+of Watt far outlasted the pressing practical need for such a device.
+Large metal planing machines were well known by 1830, and by midcentury
+crossheads and crosshead guides were used on both sides of the Atlantic
+in engines with and without working beams.
+
+By 1819 John Farey had observed quite accurately that, in England at
+least, many other schemes had been tried and found wanting and that "no
+methods have been found so good as the original engine; and we
+accordingly find, that all the most established and experienced
+manufacturers make engines which are not altered in any great feature
+from Mr. Watt's original engine...."[26]
+
+[Footnote 26: In Rees, _op. cit._ (footnote 21), vol. 34 ("Steam
+Engine"). John Farey was the writer of this article (see Farey, _op.
+cit._, p. vi).]
+
+Two mechanisms for producing a straight line were introduced before the
+Boulton and Watt monopoly ended in 1800. Perhaps the first was by Edmund
+Cartwright (1743-1823), who is said to have had the original idea for a
+power loom. This geared device (fig. 12), was characterized
+patronizingly by a contemporary American editor as possessing "as much
+merit as can possibly be attributed to a gentleman engaged in the
+pursuit of mechanical studies for his own amusement."[27] Only a few
+small engines were made under the patent.[28]
+
+[Footnote 27: _Emporium of Arts and Sciences_, December 1813, new ser.,
+vol. 2, no. 1, p. 81.]
+
+[Footnote 28: Farey, _op. cit._ (footnote 6), p. 666.]
+
+[Illustration: Figure 12.--Cartwright's geared straight-line mechanism
+of about 1800. From Abraham Rees, _The Cyclopaedia_ (London, 1819,
+"Steam Engine," pl. 5).]
+
+The properties of a hypocycloid were recognized by James White, an
+English engineer, in his geared design which employed a pivot located on
+the pitch circle of a spur gear revolving inside an internal gear. The
+diameter of the pitch circle of the spur gear was one-half that of the
+internal gear, with the result that the pivot, to which the piston rod
+was connected, traced out a diameter of the large pitch circle (fig.
+13). White in 1801 received from Napoleon Bonaparte a medal for this
+invention when it was exhibited at an industrial exposition in
+Paris.[29] Some steam engines employing White's mechanism were built,
+but without conspicuous commercial success. White himself rather agreed
+that while his invention was "allowed to possess curious properties, and
+to be a _pretty_ thing, opinions do not all concur in declaring it,
+essentially and generally, a _good_ thing."[30]
+
+[Footnote 29: H. W. Dickinson, "James White and His 'New Century of
+Inventions,'" _Transactions of the Newcomen Society_, 1949-1951, vol.
+27, pp. 175-179.]
+
+[Footnote 30: James White, _A New Century of Inventions_, Manchester,
+1822, pp. 30-31, 338. A hypocycloidal engine used in Stourbridge,
+England, is in the Henry Ford Museum.]
+
+[Illustration: Figure 13.--James White's hypocycloidal straight-line
+mechanism, about 1800. The fly-weights (at the ends of the diagonal arm)
+functioned as a flywheel. From James White, _A New Century of
+Inventions_ (Manchester, 1822, pl. 7).]
+
+The first of the non-Watt four-bar linkages appeared shortly after 1800.
+The origin of the grasshopper beam motion is somewhat obscure, although
+it came to be associated with the name of Oliver Evans, the American
+pioneer in the employment of high-pressure steam. A similar idea,
+employing an isosceles linkage, was patented in 1803 by William
+Freemantle, an English watchmaker (fig. 14).[31] This is the linkage
+that was attributed much later to John Scott Russell (1808-1882), the
+prominent naval architect.[32] An inconclusive hint that Evans had
+devised his straight-line linkage by 1805 appeared in a plate
+illustrating his _Abortion of the Young Steam Engineer's Guide_
+(Philadelphia, 1805), and it was certainly used on his Columbian engine
+(fig. 15), which was built before 1813. The Freemantle linkage, in
+modified form, appeared in Rees's _Cyclopaedia_ of 1819 (fig. 16), but
+it is doubtful whether even this would have been readily recognized as
+identical with the Evans linkage, because the connecting rod was at the
+opposite end of the working beam from the piston rod, in accordance with
+established usage, while in the Evans linkage the crank and connecting
+rod were at the same end of the beam. It is possible that Evans got his
+idea from an earlier English periodical, but concrete evidence is
+lacking.
+
+[Footnote 31: British Patent 2741, November 17, 1803.]
+
+[Footnote 32: William J. M. Rankine, _Manual of Machinery and Millwork_,
+ed. 6, London, 1887, p. 275.]
+
+[Illustration: Figure 14.--Freemantle straight-line linkage, later
+called the Scott Russell linkage. From British Patent 2741, November 17,
+1803.]
+
+[Illustration: Figure 15.--Oliver Evans' "Columbian" engine, 1813,
+showing the Evans, or "grasshopper," straight-line linkage. From
+_Emporium of Arts and Sciences_ (new ser., vol. 2, no. 3, April 1814,
+pl. opposite p. 380).]
+
+[Illustration: Figure 16.--Modified Freemantle linkage, 1819, which is
+kinematically the same as the Evans linkage. Pivots _D_ and _E_ are
+attached to engine frame. From Abraham Rees, _The Cyclopaedia_ (London,
+1819, "Parallel Motions," pl. 3).]
+
+If the idea did in fact originate with Evans, it is strange that he did
+not mention it in his patent claims, or in the descriptions that he
+published of his engines.[33] The practical advantage of the Evans
+linkage, utilizing as it could a much lighter working beam than the Watt
+or Freemantle engines, would not escape Oliver Evans, and he was not a
+man of excessive modesty where his own inventions were concerned.
+
+[Footnote 33: Greville and Dorothy Bathe, _Oliver Evans_, Philadelphia,
+1935, pp. 88, 196, and _passim_.]
+
+Another four-bar straight-line linkage that became well known was
+attributed to Richard Roberts of Manchester (1789-1864), who around 1820
+had built one of the first metal planing machines, which machines helped
+make the quest for straight-line linkages largely academic. I have not
+discovered what occasioned the introduction of the Roberts linkage, but
+it dated from before 1841. Although Roberts patented many complex
+textile machines, an inspection of all of his patent drawings has failed
+to provide proof that he was the inventor of the Roberts linkage.[34]
+The fact that the same linkage is shown in an engraving of 1769 (fig.
+18) further confuses the issue.[35]
+
+[Footnote 34: Robert Willis (_op. cit._ [Footnote 21] p. 411) credited
+Richard Roberts with the linkage. Roberts' 15 British patent drawings
+exhibit complex applications of cams, levers, guided rods, cords, and so
+forth, but no straight-line mechanism. In his patent no. 6258 of April
+13, 1832, for a steam engine and locomotive carriage, Roberts used
+Watt's "parallel motion" on a beam driven by a vertical cylinder.]
+
+[Footnote 35: This engraving appeared as plate 11 in Pierre Patte's 1769
+work (_op. cit._ footnote 24). Patte stated that the machine depicted in
+his plate 11 was invented by M. de Voglie and was actually used in
+1756.]
+
+[Illustration: Figure 17.--Straight-line linkage (before 1841)
+attributed to Richard Roberts by Robert Willis. From A. B. Kempe, _How
+to Draw a Straight Line_ (London, 1877, p. 10).]
+
+[Illustration: Figure 18.--Machine for sawing off pilings under water,
+about 1760, designed by De Voglie. The Roberts linkage operates the bar
+(_Q_ in detailed sketch) at the rear of the machine below the operators.
+The significance of the linkage apparently was not generally recognized.
+A similar machine depicted in Diderot's _Encyclopedie_, published
+several years later, did not employ the straight-line linkage. From
+Pierre Patte, _Memoirs sur les objets plus importants de l'architecture_
+(Paris, 1769, pl. 11).]
+
+The appearance in 1864 of Peaucellier's exact straight-line linkage went
+nearly unnoticed. A decade later, when news of its invention crossed
+the Channel to England, this linkage excited a flurry of interest, and
+variations of it occupied mathematical minds for several years. For at
+least 10 years before and 20 years after the final solution of the
+problem, Professor Chebyshev,[36] a noted mathematician of the
+University of St. Petersburg, was interested in the matter. Judging by
+his published works and his reputation abroad, Chebyshev's interest
+amounted to an obsession.
+
+[Footnote 36: This is the Library of Congress spelling]
+
+Pafnuti[)i] L'vovich Chebyshev was born in 1821, near Moscow, and
+entered the University of Moscow in 1837. In 1853, after visiting France
+and England and observing carefully the progress of applied mechanics in
+those countries, he read his first paper on approximate straight-line
+linkages, and over the next 30 years he attacked the problem with new
+vigor at least a dozen times. He found that the two principal
+straight-line linkages then in use were Watt's and Evans'. Chebyshev
+noted the departure of these linkages from a straight line and
+calculated the deviation as of the fifth degree, or about 0.0008 inch
+per inch of beam length. He proposed a modification of the Watt linkage
+to refine its accuracy but found that he would have to more than double
+the length of the working beam. Chebyshev concluded ruefully that his
+modification would "present great practical difficulties."[37]
+
+[Footnote 37: _Oeuvres de P. L. Tchebychef_, 2 vols., St. Petersburg,
+1899-1907, vol. 1, p. 538; vol. 2, pp. 57, 85.]
+
+At length an idea occurred to Chebyshev that would enable him to
+approach if not quite attain a true straight line. If one mechanism was
+good, he reasoned, two would be better, _et cetera, ad infinitum_. The
+idea was simply to combine, or compound, four-link approximate linkages,
+arranging them in such a way that the errors would be successively
+reduced. Contemplating first a combination of the Watt and Evans
+linkages (fig. 19), Chebyshev recognized that if point D of the Watt
+linkage followed nearly a straight line, point A of the Evans linkage
+would depart even less from a straight line. He calculated the deviation
+in this case as of the 11th degree. He then replaced Watt's linkage by
+one that is usually called the Chebyshev straight-line mechanism (fig.
+20), with the result that precision was increased to the 13th
+degree.[38] The steam engine that he displayed at the Vienna Exhibition
+in 1873 employed this linkage--the Chebyshev mechanism compounded with
+the Evans, or approximate isosceles, linkage. An English visitor to the
+exhibition commented that "the motion is of little or no practical use,
+for we can scarcely imagine circumstances under which it would be more
+advantageous to use such a complicated system of levers, with so many
+joints to be lubricated and so many pins to wear, than a solid guide of
+some kind; but at the same time the arrangement is very ingenious and in
+this respect reflects great credit on its designer."[39]
+
+[Footnote 38: _Ibid._, vol. 2, pp. 93, 94.]
+
+[Footnote 39: _Engineering_, October 3, 1873, vol. 16, p. 284.]
+
+[Illustration: Figure 19.--Pafnuti[)i] L'vovich Chebyshev (1821-1894),
+Russian mathematician active in analysis and synthesis of straight-line
+mechanisms. From _Ouvres de P. L. Tchebychef_ (St. Petersburg, 1907,
+vol. 2, frontispiece).]
+
+[Illustration: Figure 20.--Chebyshev's combination (about 1867) of
+Watt's and Evans' linkages to reduce errors inherent in each. Points
+_C_, _C'_, and _C"_ are fixed; _A_ is the tracing point. From _Oeuvres
+de P. L. Tchebychef_ (St. Petersburg, 1907, vol. 2, p. 93).]
+
+[Illustration: Figure 21.--_Top_: Chebyshev straight-line linkage, 1867;
+from A. B. Kempe, _How to Draw a Straight Line_ (London, 1877, p. 11).
+_Bottom_: Chebyshev-Evans combination, 1867; from _Oeuvres de P. L.
+Tchebychef_ (St. Petersburg, 1907, vol. 2, p. 94). Points _C_, _C'_, and
+_C"_ are fixed. _A_ is the tracing point.]
+
+There is a persistent rumor that Professor Chebyshev sought to
+demonstrate the impossibility of constructing any linkage, regardless of
+the number of links, that would generate a straight line; but I have
+found only a dubious statement in the _Grande Encyclopedie_[40] of the
+late 19th century and a report of a conversation with the Russian by an
+Englishman, James Sylvester, to the effect that Chebyshev had "succeeded
+in proving the nonexistence of a five-bar link-work capable of producing
+a perfect parallel motion...."[41] Regardless of what tradition may have
+to say about what Chebyshev said, it is of course well known that
+Captain Peaucellier was the man who finally synthesized the exact
+straight-line mechanism that bears his name.
+
+[Footnote 40: _La Grande Encyclopedie_, Paris, 1886 ("Peaucellier").]
+
+[Footnote 41: James Sylvester, "Recent Discoveries in Mechanical
+Conversion of Motion," _Notices of the Proceedings of the Royal
+Institution of Great Britain_, 1873-1875, vol. 7, p. 181. The fixed link
+was not counted by Sylvester; in modern parlance this would be a
+six-link mechanism.]
+
+[Illustration: Figure 22.--Peaucellier exact straight-line linkage,
+1873. From A. B. Kempe, _How to Draw a Straight Line_ (London, 1877, p.
+12).]
+
+[Illustration: Figure 23.--Model of the Peaucellier "Compas Compose,"
+deposited in Conservatoire National des Arts et Metiers, Paris, 1875.
+Photo courtesy of the Conservatoire.] [Illustration: Figure 24.--James
+Joseph Sylvester (1814-1897), mathematician and lecturer on
+straight-line linkages. From _Proceedings of the Royal Society of
+London_ (1898, vol. 63, opposite p. 161).]
+
+Charles-Nicolas Peaucellier, a graduate of the Ecole Polytechnique and a
+captain in the French corps of engineers, was 32 years old in 1864 when
+he wrote a short letter to the editor of _Nouvelles Annales de
+mathematiques_ (ser. 2, vol. 3, pp. 414-415) in Paris. He called
+attention to what he termed "compound compasses," a class of linkages
+that included Watt's parallel motion, the pantograph, and the polar
+planimeter. He proposed to design linkages to describe a straight line,
+a circle of any radius no matter how large, and conic sections, and he
+indicated in his letter that he had arrived at a solution.
+
+This letter stirred no pens in reply, and during the next 10 years the
+problem merely led to the filling of a few academic pages by Peaucellier
+and Amedee Mannheim (1831-1906), also a graduate of Ecole Polytechnique,
+a professor of mathematics, and the designer of the Mannheim slide rule.
+Finally, in 1873, Captain Peaucellier gave his solution to the readers
+of the _Nouvelles Annales_. His reasoning, which has a distinct flavor
+of discovery by hindsight, was that since a linkage generates a curve
+that can be expressed algebraically, it must follow that any algebraic
+curve can be generated by a suitable linkage--it was only necessary to
+find the suitable linkage. He then gave a neat geometric proof,
+suggested by Mannheim, for his straight-line "compound compass."[42]
+
+[Footnote 42: Charles-Nicholas Peaucellier, "Note sur une question de
+geometrie de compas," _Nouvelles Annales de mathematiques_, 1873, ser.
+2, vol. 12, pp. 71-78. A sketch of Mannheim's work is in Florian Cajori,
+_A History of the Logarithmic Slide Rule_, New York, about 1910,
+reprinted in _String Figures and Other Monographs_, New York, Chelsea
+Publishing Company, 1960.]
+
+On a Friday evening in January 1874 Albemarle Street in London was
+filled with carriages, each maneuvering to unload its charge of
+gentlemen and their ladies at the door of the venerable hall of the
+Royal Institution. Amidst a "mighty rustling of silks," the elegant
+crowd made its way to the auditorium for one of the famous weekly
+lectures. The speaker on this occasion was James Joseph Sylvester, a
+small intense man with an enormous head, sometime professor of
+mathematics at the University of Virginia, in America, and more recently
+at the Royal Military Academy in Woolwich. He spoke from the same
+rostrum that had been occupied by Davy, Faraday, Tyndall, Maxwell, and
+many other notable scientists. Professor Sylvester's subject was "Recent
+Discoveries in Mechanical Conversion of Motion."[43]
+
+[Footnote 43: Sylvester, _op. cit._ (footnote 41), pp. 179-198. It
+appears from a comment in this lecture that Sylvester was responsible
+for the word "linkage." According to Sylvester, a linkage consists of an
+even number of links, a "link-work" of an odd number. Since the fixed
+member was not considered as a link by Sylvester, this distinction
+became utterly confusing when Reuleaux's work was published in 1876.
+Although "link" was used by Watt in a patent specification, it is not
+probable that he ever used the term "link-work"--at any rate, my search
+for his use of it has been fruitless. "Link work" is used by Willis
+(_op. cit._ footnote 21), but the term most likely did not originate
+with him. I have not found the word "linkage" used earlier than
+Sylvester.]
+
+Remarking upon the popular appeal of most of the lectures, a
+contemporary observer noted that while many listeners might prefer to
+hear Professor Tyndall expound on the acoustic opacity of the
+atmosphere, "those of a higher and drier turn of mind experience
+ineffable delight when Professor Sylvester holds forth on the conversion
+of circular into parallel motion."[44]
+
+[Footnote 44: Bernard H. Becker, _Scientific London_, London, 1874, pp.
+45, 50, 51.]
+
+Sylvester's aim was to bring the Peaucellier linkage to the notice of
+the English-speaking world, as it had been brought to his attention by
+Chebyshev--during a recent visit of the Russian to England--and to give
+his listeners some insight into the vastness of the field that he saw
+opened by the discovery of the French soldier.[45]
+
+[Footnote 45: Sylvester, _op. cit._ (footnote 41), p. 183; _Nature_,
+November 13, 1873, vol. 9, p. 33.]
+
+"The perfect parallel motion of Peaucellier looks so simple," he
+observed, "and moves so easily that people who see it at work almost
+universally express astonishment that it waited so long to be
+discovered." But that was not his reaction at all. The more one reflects
+upon the problem, Sylvester continued, he "wonders the more that it was
+ever found out, and can see no reason why it should have been
+discovered for a hundred years to come. Viewed _a priori_ there was
+nothing to lead up to it. It bears not the remotest analogy (except in
+the fact of a double centring) to Watt's parallel motion or any of its
+progeny."[46]
+
+[Footnote 46: Sylvester, _op. cit._ (footnote 41), p. 181.]
+
+It must be pointed out, parenthetically at least, that James Watt had
+not only had to solve the problem as best he could, but that he had no
+inkling, so far as experience was concerned, that a solvable problem
+existed.
+
+Sylvester interrupted his panegyric long enough to enumerate some of the
+practical results of the Peaucellier linkage. He said that Mr. Penrose,
+the eminent architect and surveyor to St. Paul's Cathedral, had "put up
+a house-pump worked by a negative Peaucellier cell, to the great
+wonderment of the plumber employed, who could hardly believe his senses
+when he saw the sling attached to the piston-rod moving in a true
+vertical line, instead of wobbling as usual from side to side."
+Sylvester could see no reason "why the perfect parallel motion should
+not be employed with equal advantage in the construction of ordinary
+water-closets." The linkage was to be employed by "a gentleman of
+fortune" in a marine engine for his yacht, and there was talk of using
+it to guide a piston rod "in certain machinery connected with some new
+apparatus for the ventilation and filtration of the air of the Houses of
+Parliament." In due course, Mr. Prim, "engineer to the Houses," was
+pleased to show his adaptation of the Peaucellier linkage to his new
+blowing engines, which proved to be exceptionally quiet in their
+operation (fig. 25).[47] A bit on the ludicrous side, also, was
+Sylvester's 78-bar linkage that traced a straight line along the line
+connecting the two fixed centers of the linkage.[48]
+
+[Footnote 47: _Ibid._, pp. 182, 183, 188, 193.]
+
+[Footnote 48: Kempe, _op. cit._ (footnote 21), p. 17.]
+
+[Illustration: Figure 25.--Mr. Prim's blowing engine used for
+ventilating the House of Commons, 1877. The crosshead of the
+reciprocating air pump is guided by a Peaucellier linkage shown at the
+center. The slate-lined air cylinders had rubber-flap inlet and exhaust
+valves and a piston whose periphery was formed by two rows of brush
+bristles. Prim's machine was driven by a steam engine. Photograph by
+Science Museum, London.]
+
+Before dismissing with a smile the quaint ideas of our Victorian
+forbears, however, it is well to ask, 88 years later, whether some
+rather elaborate work reported recently on the synthesis of
+straight-line mechanisms is more to the point, when the principal
+objective appears to be the moving of an indicator on a "pleasing,
+expanded" (i.e., squashed flat) radio dial.[49]
+
+[Footnote 49: _Machine Design_, December 1954, vol. 26, p. 210.]
+
+But Professor Sylvester was more interested, really, in the mathematical
+possibilities of the Peaucellier linkage, as no doubt our modern
+investigators are. Through a compounding of Peaucellier mechanisms, he
+had already devised square-root and cube-root extractors, an angle
+trisector, and a quadratic-binomial root extractor, and he could see no
+limits to the computing abilities of linkages as yet undiscovered.[50]
+
+[Footnote 50: Sylvester, _op. cit._ (footnote 41), p. 191.]
+
+Sylvester recalled fondly, in a footnote to his lecture, his experience
+with a little mechanical model of the Peaucellier linkage at an earlier
+dinner meeting of the Philosophical Club of the Royal Society. The
+Peaucellier model had been greeted by the members with lively
+expressions of admiration "when it was brought in with the dessert, to
+be seen by them after dinner, as is the laudable custom among members of
+that eminent body in making known to each other the latest scientific
+novelties." And Sylvester would never forget the reaction of his
+brilliant friend Sir William Thomson (later Lord Kelvin) upon being
+handed the same model in the Athenaeum Club. After Sir William had
+operated it for a time, Sylvester reached for the model, but he was
+rebuffed by the exclamation "No! I have not had nearly enough of it--it
+is the most beautiful thing I have ever seen in my life."[51]
+
+[Footnote 51: _Ibid._, p. 183.]
+
+The aftermath of Professor Sylvester's performance at the Royal
+Institution was considerable excitement amongst a limited company of
+interested mathematicians. Many alternatives to the Peaucellier
+straight-line linkage were suggested by several writers of papers for
+learned journals.[52]
+
+[Footnote 52: For a summary of developments and references, see Kempe,
+_op. cit._ (footnote 21), pp. 49-51. Two of Hart's six-link exact
+straight-line linkages referred to by Kempe are illustrated in Henry M.
+Cundy and A. P. Rollett, _Mathematical Models_, Oxford, Oxford
+University Press, 1952, pp. 204-205. Peaucellier's linkage was of eight
+links.]
+
+In the summer of 1876, after Sylvester had departed from England to take
+up his post as professor of mathematics in the new Johns Hopkins
+University in Baltimore, Alfred Bray Kempe, a young barrister who
+pursued mathematics as a hobby, delivered at London's South Kensington
+Museum a lecture with the provocative title "How to Draw a Straight
+Line."[53]
+
+[Footnote 53: Kempe, _op. cit._ (footnote 21), p. 26.]
+
+In order to justify the Peaucellier linkage, Kempe belabored the point
+that a perfect circle could be generated by means of a pivoted bar and a
+pencil, while the generation of a straight line was most difficult if
+not impossible until Captain Peaucellier came along. A straight line
+could be drawn along a straight edge; but how was one to determine
+whether the straight edge was straight? He did not weaken his argument
+by suggesting the obvious possibility of using a piece of string. Kempe
+had collaborated with Sylvester in pursuing the latter's first thoughts
+on the subject, and one result, that to my mind exemplifies the general
+direction of their thinking, was the Sylvester-Kempe "parallel motion"
+(fig. 26).
+
+[Illustration: Figure 26.--Sylvester-Kempe translating linkage, 1877.
+The upper and lower plates remain parallel and equidistant. From A. B.
+Kempe, _How to Draw a Straight Line_ (London, 1877, p. 37).]
+
+[Illustration: Figure 27.--Gaspard Monge (1746-1818), professor of
+mathematics at the Ecole Polytechnique from 1794 and founder of the
+academic discipline of machine kinematics, From _Livre du Centenaire,
+1794-1894, Ecole Polytechnique_ (Paris, 1895, vol. 1, frontispiece).]
+
+Enthusiastic as Kempe was, however, he injected an apologetic note in
+his lecture. "That these results are valuable cannot I think be
+doubted," he said, "though it may well be that their great beauty has
+led some to attribute to them an importance which they do not really
+possess...." He went on to say that 50 years earlier, before the great
+improvements in the production of true plane surfaces, the straight-line
+mechanisms would have been more important than in 1876, but he added
+that "linkages have not at present, I think, been sufficiently put
+before the mechanician to enable us to say what value should really be
+set upon them."[54]
+
+[Footnote 54: _Ibid._, pp. 6-7. I have not pursued the matter of cognate
+linkages (the Watt and Evans linkages are cognates) because the
+Roberts-Chebyshev theorem escaped my earlier search, as it had
+apparently escaped most others until 1958. See R. S. Hartenberg and J.
+Denavit, "The Fecund Four-Bar," _Transactions of the Fifth Conference on
+Mechanisms_, Cleveland, Penton Publishing Company, 1958, pp. 194-206,
+reprinted in _Machine Design_, April 16, 1959, vol. 31, pp. 149-152. See
+also A. E. R. de Jonge, "The Correlation of Hinged Four-Bar
+Straight-Line Motion Devices by Means of the Roberts Theorem and a New
+Proof of the Latter," _Annals of the New York Academy of Sciences_,
+March 18, 1960, vol. 84, art. 3, pp. 75-145 (published separately).]
+
+It was during this same summer of 1876, at the Loan Exhibition of
+Scientific Apparatus in the South Kensington Museum, that the work of
+Franz Reuleaux, which was to have an important and lasting influence on
+kinematics everywhere, was first introduced to English engineers. Some
+300 beautifully constructed teaching aids, known as the Berlin kinematic
+models, were loaned to the exhibition by the Royal Industrial School in
+Berlin, of which Reuleaux was the director. These models were used by
+Prof. Alexander B. W. Kennedy of University College, London, to help
+explain Reuleaux's new and revolutionary theory of machines.[55]
+
+[Footnote 55: Alexander B. W. Kennedy, "The Berlin Kinematic Models,"
+_Engineering_, September 15, 1876, vol. 22, pp. 239-240.]
+
+
+Scholars and Machines
+
+When, in 1829, Andre-Marie Ampere (1775-1836) was called upon to prepare
+a course in theoretical and experimental physics for the College de
+France, he first set about determining the limits of the field of
+physics. This exercise suggested to his wide-ranging intellect not only
+the definition of physics but the classification of all human knowledge.
+He prepared his scheme of classification, tried it out on his physics
+students, found it incomplete, returned to his study, and produced
+finally a two-volume work wherein the province of kinematics was first
+marked out for all to see and consider.[56] Only a few lines could be
+devoted to so specialized a branch as kinematics, but Ampere managed to
+capture the central idea of the subject.
+
+[Footnote 56: Andre-Marie Ampere, _Essai sur la philosophie des
+sciences, une exposition analytique d'une classification naturelle de
+toutes les connaissances humaines_, 2 vols., Paris, 1838 (for origin of
+the project, see vol. 1, pp. v, xv).]
+
+Cinematique (from the Greek word for movement) was, according to Ampere,
+the science "in which movements are considered in themselves
+[independent of the forces which produce them], as we observe them in
+solid bodies all about us, and especially in the assemblages called
+machines."[57] Kinematics, as the study soon came to be known in
+English,[58] was one of the two branches of elementary mechanics, the
+other being statics.
+
+[Footnote 57: _Ibid._, vol. 1, pp. 51-52.]
+
+[Footnote 58: Willis (_op. cit._ footnote 21) adopted the word
+"kinematics," and this Anglicization subsequently became the standard
+term for this branch of mechanics.]
+
+In his definition of kinematics, Ampere stated what the faculty of
+mathematics at the Ecole Polytechnique, in Paris, had been groping
+toward since the school's opening some 40 years earlier. The study of
+mechanisms as an intellectual discipline most certainly had its origin
+on the left bank of the Seine, in this school spawned, as suggested by
+one French historian,[59] by the great _Encyclopedie_ of Diderot and
+d'Alembert.
+
+[Footnote 59: G. Pinet, _Histoire de l'Ecole Polytechnique_, Paris,
+1887, pp. viii-ix. In their forthcoming book on kinematic synthesis, R.
+S. Hartenberg and J. Denavit will trace the germinal ideas of Jacob
+Leupold and Leonhard Euler of the 18th century.]
+
+Because the Ecole Polytechnique had such a far-reaching influence upon
+the point of view from which mechanisms were contemplated by scholars
+for nearly a century after the time of Watt, and by compilers of
+dictionaries of mechanical movements for an even longer time, it is
+well to look for a moment at the early work that was done there. If one
+is interested in origins, it might be profitable for him to investigate
+the military school in the ancient town of Mezieres, about 150 miles
+northeast of Paris. It was here that Lazare Carnot, one of the principal
+founders of the Ecole Polytechnique, in 1783 published his essay on
+machines,[60] which was concerned, among other things, with showing the
+impossibility of "perpetual motion"; and it was from Mezieres that
+Gaspard Monge and Jean Hachette[61] came to Paris to work out the system
+of mechanism classification that has come to be associated with the
+names of Lanz and Betancourt.
+
+[Footnote 60: Lazare N. M. Carnot, _Essai sur les machines en general_,
+Mezieres, 1783 (later published as _Principes fondamentaux de
+l'equilibre et du mouvement_, Paris, 1803).]
+
+[Footnote 61: Biographical notices of Monge and Hachette appear in
+_Encyclopaedia Britannica_, ed. 11. See also _L'Ecole Polytechnique,
+Livre du Centenaire_, Paris, 1895, vol. 1, p. 11ff.]
+
+Gaspard Monge (1746-1818), who while a draftsman at Mezieres originated
+the methods of descriptive geometry, came to the Ecole Polytechnique as
+professor of mathematics upon its founding in 1794, the second year of
+the French Republic. According to Jean Nicolas Pierre Hachette
+(1769-1834), who was junior to Monge in the department of descriptive
+geometry, Monge planned to give a two-months' course devoted to the
+elements of machines. Having barely gotten his department under way,
+however, Monge became involved in Napoleon's ambitious scientific
+mission to Egypt and, taking leave of his family and his students,
+embarked for the distant shores.
+
+"Being left in charge," wrote Hachette, "I prepared the course of which
+Monge had given only the first idea, and I pursued the study of machines
+in order to analyze and classify them, and to relate geometrical and
+mechanical principles to their construction." Changes of curriculum
+delayed introduction of the course until 1806, and not until 1811 was
+his textbook ready, but the outline of his ideas was presented to his
+classes in chart form (fig. 28). This chart was the first of the widely
+popular synoptical tables of mechanical movements.[62]
+
+[Footnote 62: Jean N. P. Hachette, _Traite elementaire des machines_,
+Paris, 1811, p. v.]
+
+[Illustration: Figure 28.--Hachette's synoptic chart of elementary
+mechanisms, 1808. This was the first of many charts of mechanical
+movements that enjoyed wide popularity for over 100 years.
+
+From Jean N. P. Hachette, _Traite Elementaire des Machines_ (Paris,
+1811, pl. 1).]
+
+Hachette classified all mechanisms by considering the conversion of one
+motion into another. His elementary motions were continuous circular,
+alternating circular, continuous rectilinear, and alternating
+rectilinear. Combining one motion with another--for example, a treadle
+and crank converted alternating circular to continuous circular
+motion--he devised a system that supplied a frame of reference for the
+study of mechanisms. In the U.S. Military Academy at West Point,
+Hachette's treatise, in the original French, was used as a textbook in
+1824, and perhaps earlier.[63]
+
+[Footnote 63: This work was among the books sent back by Sylvanus Thayer
+when he visited France in 1816 to observe the education of the French
+army cadets. Thayer's visit resulted in his adopting the philosophy of
+the Ecole Polytechnique in his reorganization of the U.S. Military
+Academy and, incidentally, in his inclusion of Hachette's course in the
+Academy's curriculum (U.S. Congress, _American State Papers_,
+Washington, 1832-1861, Class v, Military Affairs, vol. 2, p. 661: Sidney
+Forman, _West Point_, New York, 1950, pp. 36-60). There is a collection
+of miscellaneous papers (indexed under Sylvanus Thayer and William
+McRee, U.S. National Archives, RG 77, Office, Chief of Engineers, Boxes
+1 and 6) pertaining to the U.S. Military Academy of this period, but I
+found no mention of kinematics in this collection.]
+
+Lanz and Betancourt, scholars from Spain at the Ecole Polytechnique,
+plugged some of the gaps in Hachette's system by adding continuous and
+alternating curvilinear motion, which doubled the number of combinations
+to be treated, but the advance of their work over that of Hachette was
+one of degree rather than of kind.[64]
+
+[Footnote 64: Phillipe Louis Lanz and Augustin de Betancourt, _Essai sur
+la composition des machines_, Paris, 1808. Hachette's chart and an
+outline of his elementary course on machines is bound with the Princeton
+University Library copy of the Lanz and Betancourt work. This copy
+probably represents the first textbook of kinematics. Betancourt was
+born in 1760 in Teneriffe, attended the military school in Madrid, and
+became inspector-general of Spanish roads and canals. He was in England
+before 1789, learning how to build Watt engines, and he introduced the
+engines to Paris in 1790 (see Farey, _op. cit._, p. 655). He entered
+Russian service in 1808 and died in St. Petersburg in 1826 J. C.
+Poggendorff, _Biographisches-literarisches Handwoerterbuch fuer Mathematik
+..._, Leipzig, 1863, vol. 1.]
+
+[Illustration: Figure 29.--Robert Willis (1800-1875), Jacksonian
+Professor, Cambridge University, and author of _Principles of
+Mechanism_, one of the landmark books in the development of kinematics
+of mechanisms. Photo courtesy Gonville and Caius College, Cambridge
+University.]
+
+Giuseppe Antonio Borgnis, an Italian "engineer and member of many
+academies" and professor of mechanics at the University of Pavia in
+Italy, in his monumental, nine-volume _Traite complet de mechanique
+appliquee aux arts_, caused a bifurcation of the structure built upon
+Hachette's foundation of classification when he introduced six orders of
+machine elements and subdivided these into classes and species. His six
+orders were _recepteurs_ (receivers of motion from the prime mover),
+_communicateurs_, _modificateurs_ (modifiers of velocity), _supports_
+(e.g., bearings), _regulateurs_ (e.g., governors), and _operateurs_,
+which produced the final effect.[65]
+
+[Footnote 65: Giuseppe Antonio Borgnis, _Theorie de la mecanique
+usuelle_ in _Traite complet de mecanique appliquee aux arts_, Paris,
+1818, vol. 1, pp. xiv-xvi.]
+
+The brilliant Gaspard-Gustave de Coriolis (1792-1843)--remembered mainly
+for a paper of a dozen pages explaining the nature of the acceleration
+that bears his name[66]--was another graduate of the Ecole Polytechnique
+who wrote on the subject of machines. His book,[67] published in 1829,
+was provoked by his recognition that the designer of machines needed
+more knowledge than his undergraduate work at the Ecole Polytechnique
+was likely to give him. Although he embraced a part of Borgnis'
+approach, adopting _recepteurs_, _communicateurs_, and _operateurs_,
+Coriolis indicated by the title of his book that he was more concerned
+with forces than with relative displacements. However, the attractively
+simple three-element scheme of Coriolis became well fixed in French
+thinking.[68]
+
+[Footnote 66: Gaspard-Gustave de Coriolis, "Memoire sur les equations du
+mouvement relatif des systemes de corps," _Journal de l'Ecole
+Polytechnique_, 1835, vol. 15, pp. 142-154.]
+
+[Footnote 67: Gaspard-Gustave de Coriolis, _De Calcul de l'effet des
+machines_, Paris, 1829. In this book Coriolis proposed the now generally
+accepted equation, work = force x distance (pp. iii, 2).]
+
+[Footnote 68: The renowned Jean Victor Poncelet lent weight to this
+scheme. (See Franz Reuleaux, _Theoretische Kinematik: Grundzuege einer
+Theorie des Maschinenwesens_, Braunschweig, 1875, translated by
+Alexander B. W. Kennedy as _The Kinematics of Machinery: Outlines of a
+Theory of Machines_, London, 1876, pp. 11, 487. I have used the Kennedy
+translation in the Reuleaux references throughout the present work.)]
+
+Michel Chasles (1793-1880), another graduate of the Ecole Polytechnique,
+contributed some incisive ideas in his papers on instant centers[69]
+published during the 1830's, but their tremendous importance in
+kinematic analysis was not recognized until much later.
+
+[Footnote 69: The instant center was probably first recognized by Jean
+Bernoulli (1667-1748) in his "De Centro Spontaneo Rotationis" (_Johannis
+Bernoulli ... Opera Omnia ..._, Lausanne, 1742, vol. 4, p. 265ff.).]
+
+[Illustration: Figure 30.--Franz Reuleaux (1829-1905). His _Theoretische
+Kinematik_, published in 1875, provided the basis for modern kinematic
+analysis. Photo courtesy Deutsches Museum, Munich.]
+
+Acting upon Ampere's clear exposition of the province of kinematics and
+excluding, as Ampere had done, the consideration of forces, an
+Englishman, Robert Willis, made the next giant stride forward in the
+analysis of mechanisms. Willis was 37 years old in 1837 when he was
+appointed professor of natural and experimental philosophy at Cambridge.
+In the same year Professor Willis--a man of prodigious energy and
+industry and an authority on archeology and architectural history as
+well as mechanisms--read his important paper "On the Teeth of Wheels"
+before the Institution of Civil Engineers[70] and commenced at Cambridge
+his lectures on kinematics of mechanisms that culminated in his 1841
+book _Principles of Mechanism_.[71]
+
+[Footnote 70: Robert Willis, "On the Teeth of Wheels," _Transactions of
+the Institution of Civil Engineers of London_, 1838, vol. 2, pp.
+89-112.]
+
+[Footnote 71: Willis, _op. cit._ (footnote 21). Through the kindness of
+its owner (Mr. Warren G. Ogden of North Andover, Massachusetts), I have
+had access to Willis' own copy of his 1841 edition of _Principles of
+Mechanism_. The book is interleaved, and it contains notes made by
+Willis from time to time until at least 1870, when the second edition
+was issued. Corrections, emendations, notations of some of his sources
+(for example, the De Voglie linkage mentioned in footnote 35 above),
+notes to himself to "examine the general case" and "examine the modern
+forms" of straight-line devices are interspersed with references to
+authors that had borrowed from his work without acknowledgment. Of one
+author Willis writes an indignant "He ignores my work."]
+
+It seemed clear to Willis that the problem of devising a mechanism for a
+given purpose ought to be attacked systematically, perhaps
+mathematically, in order to determine "all the forms and arrangements
+that are applicable to the desired purpose," from which the designer
+might select the simplest or most suitable combination. "At present," he
+wrote, "questions of this kind can only be solved by that species of
+intuition which long familiarity with a subject usually confers upon
+experienced persons, but which they are totally unable to communicate to
+others."
+
+In analyzing the process by which a machine was designed, Willis
+observed: "When the mind of a mechanician is occupied with the
+contrivance of a machine, he must wait until, in the midst of his
+meditations, some happy combination presents itself to his mind which
+may answer his purpose." He ventured the opinion that at this stage of
+the design process "the motions of the machine are the principal subject
+of contemplation, rather than the forces applied to it, or the work it
+has to do." Therefore he was prepared to adopt without reservation
+Ampere's view of kinematics, and, if possible, to make the science
+useful to engineers by stating principles that could be applied without
+having to fit the problem at hand into the framework of the systems of
+classification and description that had gone before. He appraised the
+"celebrated system" of Lanz and Betancourt as "a merely popular
+arrangement, notwithstanding the apparently scientific simplicity of the
+scheme." He rejected this scheme because "no attempt is made to subject
+the motions to calculation, or to reduce these laws to general formulas,
+for which indeed the system is totally unfitted."
+
+Borgnis had done a better job, Willis thought, in actually describing
+machinery, with his "orders" based upon the functions of machine
+elements or mechanisms within the machine, but again there was no means
+suggested by which the kinematics of mechanisms could be systematically
+investigated.
+
+Although Willis commenced his treatise with yet another "synoptical
+table of the elementary combinations of pure mechanism," his view
+shifted quickly from description to analysis. He was consistent in his
+pursuit of analytical methods for "pure mechanism," eschewing any
+excursions into the realm of forces and absolute velocities. He grasped
+the important concept of relative displacements of machine elements, and
+based his treatment upon "the proportions and relations between the
+velocities and directions of the pieces, and not upon their actual and
+separate motions."[72]
+
+[Footnote 72: _Ibid._, pp. iv, x-xii, xxi, 15.]
+
+That he did not succeed in developing the "formulas" that would enable
+the student to determine "all the forms and arrangements that are
+applicable to the desired purpose"--that he did not present a rational
+approach to synthesis--is not to be wondered at. Well over a century
+later we still are nibbling at the fringes of the problem. Willis did,
+nonetheless, give the thoughtful reader a glimpse of the most powerful
+tool for kinematic synthesis that has yet been devised; namely,
+kinematic analysis, in which the argument is confined to the relative
+displacements of points on links of a mechanism, and through which the
+designer may grasp the nature of the means at his disposal for the
+solution of any particular problem.
+
+As remarked by Reuleaux a generation later, there was much in Professor
+Willis's book that was wrong, but it was an original, thoughtful work
+that departed in spirit if not always in method from its predecessors.
+_Principles of Mechanism_ was a prominent landmark along the road to a
+rational discipline of machine-kinematics.
+
+A phenomenal engineer of the 19th century was the Scottish professor of
+civil engineering at the University of Glasgow, William John MacQuorn
+Rankine. Although he was at the University for only 17 years--he died at
+the age of 52, in 1872--he turned out during that time four thick
+manuals on such diverse subjects as civil engineering, ship-building,
+thermodynamics, and machinery and mill-work, in addition to literally
+hundreds of papers, articles, and notes for scientific journals and the
+technical press. Endowed with apparently boundless energy, he found time
+from his studies to command a battalion of rifle volunteers and to
+compose and sing comic and patriotic songs. His manuals, often used as
+textbooks, were widely circulated and went through many editions.
+Rankine's work had a profound effect upon the practice of engineering by
+setting out principles in a form that could be grasped by people who
+were dismayed by the treatment usually found in the learned journals.
+
+When Rankine's book titled _A Manual of Machinery and Millwork_ was
+published in 1869 it was accurately characterized by a reviewer as
+"dealing with the _principles_ of machinery and millworks, and as such
+it is entirely distinct from [other works on the same subject] which
+treat more of the practical applications of such principles than of the
+principles themselves."[73]
+
+[Footnote 73: _Engineering_, London, August 13, 1869, vol. 8, p. 111.]
+
+Rankine borrowed what appeared useful from Willis' _Principles of
+Mechanism_ and from other sources. His treatment of kinematics was not
+as closely reasoned as the later treatises of Reuleaux and Kennedy,
+which will be considered below. Rankine did, however, for the first time
+show the utility of instant centers in velocity analysis, although he
+made use only of the instant centers involving the fixed link of a
+linkage. Like others before him, he considered the fixed link of a
+mechanism as something quite different from the movable links, and he
+did not perceive the possibilities opened up by determining the instant
+center of two movable links.
+
+Many other books dealing with mechanisms were published during the
+middle third of the century, but none of them had a discernible
+influence upon the advance of kinematical ideas.[74] The center of
+inquiry had by the 1860's shifted from France to Germany. Only by
+scattered individuals in England, Italy, and France was there any
+impatience with the well-established, general understanding of the
+machine-building art.
+
+[Footnote 74: Several such books are referred to by Reuleaux, _op. cit._
+(footnote 68), pp. 12-16.]
+
+In Germany, on the other hand, there was a surge of industrial activity
+that attracted some very able men to the problems of how machines ought
+to be built. Among the first of these was Ferdinand Redtenbacher
+(1809-1863), professor of mechanical engineering in the polytechnic
+school in Karlsruhe, not far from Heidelberg. Redtenbacher, although he
+despaired of the possibility of finding a "true system on which to base
+the study of mechanisms," was nevertheless a factor in the development
+of such a system. He had young Franz Reuleaux in his classes for two
+years, from 1850. During that time the older man's commanding presence,
+his ability as a lecturer, and his infectious impatience with the
+existing order influenced Reuleaux to follow the scholar's trail that
+led him to eminence as an authority of the first rank.[75]
+
+[Footnote 75: See Carl Weihe, "Franz Reuleaux und die Grundlagen seiner
+Kinematik," Deutsches Museum, Munich, _Abhandlung und Berichte_, 1942,
+p. 2; Friedrich Klemm, _Technik: Eine Geschichte ihrer Probleme_,
+Freiburg and Munich, Verlag Karl Alber, 1954, translated by Dorothea W.
+Singer as _A History of Western Technology_, New York, Charles
+Scribner's Sons, 1959, p. 317.]
+
+Before he was 25 years old Franz Reuleaux published, in collaboration
+with a classmate, a textbook whose translated title would be
+_Constructive Lessons for the Machine Shop_.[76] His several years in
+the workshop, before and after coming under Redtenbacher's influence,
+gave his works a practical flavor, simple and direct. According to one
+observer, Reuleaux's book exhibited "a recognition of the claims of
+practice such as Englishmen do not generally associate with the writings
+of a German scientific professor."[77]
+
+[Footnote 76: See Weihe, _op. cit._ (footnote 75), p. 3; Hans Zopke,
+"Professor Franz Reuleaux," _Cassier's Magazine_, December 1896, vol.
+11, pp. 133-139; _Transactions of the American Society of Mechanical
+Engineers_, 1904-1905, vol. 26, pp. 813-817.]
+
+[Footnote 77: _Engineering_, London, September 8, 1876, vol. 22, p.
+197.]
+
+Reuleaux's original ideas on kinematics, which are responsible for the
+way in which we look at mechanisms today, were sufficiently formed in
+1864 for him to lecture upon them.[78] Starting in 1871, he published
+his findings serially in the publication of the Verein zur Befoerderung
+des Gewerbefleisses in Preussen (Society for the Advancement of Industry
+in Prussia), of which he was editor. In 1875 these articles were brought
+together in the book that established his fame--_Theoretische
+Kinematik...._[79]
+
+[Footnote 78: A. E. Richard de Jonge, "What is Wrong with Kinematics and
+Mechanisms?" _Mechanical Engineering_, April 1942, vol. 64, pp. 273-278
+(comments on this paper are in _Mechanical Engineering_, October 1942,
+vol. 64, pp. 744-751); Zopke, _op. cit._ (footnote 76), p. 135.]
+
+[Footnote 79: Reuleaux, _op. cit._ (footnote 68). This was not the last
+of Reuleaux's books. His trilogy on kinematics and machine design is
+discussed by De Jonge, _op. cit._ (footnote 78).]
+
+In the introduction of this book, Reuleaux wrote:
+
+     In the development of every exact science, its substance having
+     grown sufficiently to make generalization possible, there is a time
+     when a series of changes bring it into clearness. This time has
+     most certainly arrived for the science of kinematics. The number of
+     mechanisms has grown almost out of measure, and the number of ways
+     in which they are applied no less. It has become absolutely
+     impossible still to hold the thread which can lead in any way
+     through this labyrinth by the existing methods.[80]
+
+[Footnote 80: Reuleaux, _op. cit._ (footnote 68), p. 23.]
+
+Reuleaux's confidence that it would be his own work that would bring
+order out of confusion was well founded. His book had already been
+translated into Italian and was being translated into French when, only
+a year after its publication, it was presented by Prof. Alexander B. W.
+Kennedy in English translation.[81]
+
+[Footnote 81: _Ibid._, p. iii.]
+
+The book was enthusiastically reviewed by the weekly London journal
+_Engineering_,[82] and it was given lengthy notice by the rival journal,
+_The Engineer_. The editor of _The Engineer_ thought that the
+mechanician would find in it many new ideas, that he would be "taught to
+detect hitherto hidden resemblances, and that he must part--reluctantly,
+perhaps--with many of his old notions." "But," added the editor with
+considerable justice, "that he [the mechanician] would suddenly
+recognize in Professor Reuleaux's 'kinematic notation,' 'analysis,' and
+'synthesis,' the long-felt want of his professional existence we do not
+for a moment believe."[83] Indeed, the fresh and sharp ideas of Reuleaux
+were somewhat clouded by a long (600-page) presentation; and his
+kinematic notation, which required another attempt at classification,
+did not simplify the presentation of radically new ideas.[84]
+
+[Footnote 82: _Engineering_, _loc. cit._ (footnote 77).]
+
+[Footnote 83: _The Engineer_, London, March 30 and April 13, 1877, vol.
+43, pp. 211-212, 247-248.]
+
+[Footnote 84: It is perhaps significant that the first paper of the
+First Conference on Mechanisms at Purdue University was Allen S. Hall's
+"Mechanisms and Their Classification," which appeared in _Machine
+Design_, December 1953, vol. 25, pp. 174-180. The place of
+classification in kinematic synthesis is suggested in Ferdinand
+Freudenstein's "Trends in Kinematics of Mechanisms," _Applied Mechanics
+Reviews_, September 1959, vol. 12, pp. 587-590.]
+
+[Illustration: Figure 31.--Alexander Blackie William Kennedy
+(1847-1928), translator of Reuleaux' _Theoretische Kinematik_ and
+discoverer of Kennedy's "Law of Three Centers." From _Minutes of the
+Proceedings of the Institution of Civil Engineers_ (1907, vol. 167,
+frontispiece).]
+
+Nevertheless, no earlier author had seen the problem of kinematic
+analysis so clearly or had introduced so much that was fresh, new, and
+of lasting value.
+
+Reuleaux was first to state the concept of the pair; by his concept of
+the expansion of pairs he was able to show similarities in mechanisms
+that had no apparent relation. He was first to recognize that the fixed
+link of a mechanism was kinematically the same as the movable links.
+This led him to the important notion of inversion of linkages, fixing
+successively the various links and thus changing the function of the
+mechanism. He devoted 40 pages to showing, with obvious delight, the
+kinematic identity of one design after another of rotary steam engines,
+demolishing for all time the fond hopes of ingenious but ill-informed
+inventors who think that improvements and advances in mechanism design
+consist in contortion and complexity.
+
+The chapter on synthesis was likewise fresh, but it consisted of a
+discussion, not a system; and Reuleaux stressed the idea that I have
+mentioned above in connection with Willis' book, that synthesis will be
+successful in proportion to the designer's understanding and
+appreciation of analysis. Reuleaux tried to put the designer on the
+right track by showing him clearly "the essential simplicity of the
+means with which we have to work" and by demonstrating to him "that the
+many things which have to be done can be done with but few means, and
+that the principles underlying them all lie clearly before us."[85]
+
+[Footnote 85: Reuleaux, _op. cit._ (footnote 68), p. 582.]
+
+It remained for Sir Alexander Blackie William Kennedy (1847-1928) and
+Robert Henry Smith (1852-1916) to add to Reuleaux's work the elements
+that would give kinematic analysis essentially its modern shape.
+
+Kennedy, the translator of Reuleaux's book, became professor of
+engineering at the University College in London in 1874, and eventually
+served as president both of the Institution of Mechanical Engineers and
+of the Institution of Civil Engineers. Smith, who had taught in the
+Imperial University of Japan, was professor of engineering at Mason
+College, now a part of Birmingham University, in England.
+
+While Reuleaux had used instant centers almost exclusively for the
+construction of centrodes (paths of successive positions of an instant
+center), Professor Kennedy recognized that instant centers might be used
+in velocity analysis. His book, _Mechanics of Machinery_, was published
+in 1886 ("partly through pressure of work and partly through ill-health,
+this book appears only now"). In it he developed the law of three
+centers, now known as Kennedy's theorem. He noted that his law of three
+centers "was first given, I believe, by Aronhold, although its previous
+publication was unknown to me until some years after I had given it in
+my lectures."[86] In fact, the law had been published by Siegfried
+Heinrich Aronhold (1819-1884) in his "Outline of Kinematic Geometry,"
+which appeared in 1872 alongside Reuleaux's series in the journal that
+Reuleaux edited. Apparently Reuleaux did not perceive its particular
+significance at that time.[87]
+
+[Footnote 86: Alexander B. W. Kennedy, _The Mechanics of Machinery_, ed.
+3, London, 1898, pp. vii, x.]
+
+[Footnote 87: Siegfried Heinrich Aronhold, "Outline of Kinematic
+Geometry," _Verein zur Befoerderung des Gewerbefleisses in Preussen_,
+1872, vol. 51, pp. 129-155. Kennedy's theorem is on pp. 137-138.]
+
+[Illustration: Figure 32.--Robert Henry Smith (1852-1916), originator of
+velocity and acceleration polygons for kinematic analysis. Photo
+courtesy the Librarian, Birmingham Reference Library, England.]
+
+Kennedy, after locating instant centers, determined velocities by
+calculation and accelerations by graphical differentiation of
+velocities, and he noted in his preface that he had been unable, for a
+variety of reasons, to make use in his book of Smith's recent work.
+Professor Kennedy at least was aware of Smith's surprisingly advanced
+ideas, which seem to have been generally ignored by Americans and
+Englishmen alike.
+
+Professor Smith, in a paper before the Royal Society of Edinburgh in
+1885, stated clearly the ideas and methods for construction of velocity
+and acceleration diagrams of linkages.[88] For the first time, velocity
+and acceleration "images" of links (fig. 33) were presented. It is
+unfortunate that Smith's ideas were permitted to languish for so long a
+time.
+
+[Footnote 88: Robert H. Smith, "A New Graphic Analysis of the Kinematics
+of Mechanisms," _Transactions of the Royal Society of Edinburgh_,
+1882-1885, vol. 32, pp. 507-517, and pl. 82. Smith used this paper as
+the basis for a chapter in his _Graphics or the Art of Calculating by
+Drawing Lines_, London, 1889, pp. 144-162. In a footnote of his paper,
+Smith credited Fleeming Jenkin (1833-1885) with suggesting the term
+"image." After discarding as "practically useless" Kennedy's graphical
+differentiation, Smith complained that he had "failed to find any
+practical use" for Reuleaux's "method of centroids, more properly called
+axoids." Such statements were not calculated to encourage Kennedy and
+Reuleaux to advertise Smith's fame; however, I found no indication that
+either one took offense at the criticism. Smith's velocity and
+acceleration diagrams were included (apparently embalmed, so far as
+American engineers were concerned) in _Encyclopaedia Britannica_, ed.
+11, 1910, vol. 17, pp. 1008-1009.]
+
+[Illustration: Figure 33.--Smith's velocity image (the two figures at
+top), and his velocity, mechanism, and acceleration diagrams, 1885. The
+image of link BACD is shown as figure _bacd_. The lines _pa_, _pb_,
+_pc_, and _pd_ are velocity vectors. This novel, original, and powerful
+analytical method was not generally adopted in English or American
+schools until nearly 50 years after its inception. From _Transactions of
+the Royal Society of Edinburgh_ (1882-1885, vol. 32, pl. 82).]
+
+By 1885 nearly all the tools for modern kinematic analysis had been
+forged. Before discussing subsequent developments in analysis and
+synthesis, however, it will be profitable to inquire what the
+mechanician--designer and builder of machines--was doing while all of
+this intellectual effort was being expended.
+
+
+Mechanicians and Mechanisms
+
+While the inductive process of recognizing and stating true principles
+of the kinematics of mechanisms was proceeding through three generations
+of French, English, and finally German scholars, the actual design of
+mechanisms went ahead with scant regard for what the scholars were doing
+and saying.
+
+After the demonstration by Boulton and Watt that large mechanisms could
+be wrought with sufficient precision to be useful, the English tool
+builders Maudslay, Roberts, Clement, Nasmyth, and Whitworth developed
+machine tools of increasing size and truth. The design of other
+machinery kept pace with--sometimes just behind, sometimes just ahead
+of--the capacity and capability of machine tools. In general, there was
+an increasing sophistication of mechanisms that could only be accounted
+for by an increase of information with which the individual designer
+could start.
+
+Reuleaux pointed out in 1875 that the "almost feverish progress made in
+the regions of technical work" was "not a consequence of any increased
+capacity for intellectual action in the race, but only the perfecting
+and extending of the tools with which the intellect works." These tools,
+he said, "have increased in number just like those in the modern
+mechanical workshop--the men who work them remain the same." Reuleaux
+went on to say that the theory and practice of machine-kinematics had
+"carried on a separate existence side by side." The reason for this
+failure to apply theory to practice, and vice versa, must be sought in
+the defects of the theory, he thought, because "the mechanisms
+themselves have been quietly developed in practical machine-design, by
+invention and improvement, regardless of whether or not they were
+accorded any direct and proper theoretical recognition." He pointed out
+that the theories had thus far "furnished no new mechanisms."[89]
+
+[Footnote 89: Reuleaux, _op. cit._ (footnote 68), p. 8.]
+
+It is reasonable, therefore, to ask what was responsible for the
+appearance of new mechanisms, and then to see what sort of mechanisms
+had their origins in this period.
+
+It is immediately evident to a designer that the progress in mechanisms
+came about through the spread of knowledge of what had already been
+done; but designers of the last century had neither the leisure nor
+means to be constantly visiting other workshops, near and far, to
+observe and study the latest developments. In the 1800's, as now, word
+must in the main be spread by the printed page.
+
+Hachette's chart (fig. 28) had set the pattern for display of mechanical
+contrivances in practical journals and in the large number of mechanical
+dictionaries that were compiled to meet an apparent demand for such
+information. It is a little surprising, however, to find how persistent
+were some of Hachette's ideas that could only have come from the
+uppermost superficial layer of his cranium. See, for example, his
+"anchored ferryboat" (fig. 34). This device, employed by Hachette to
+show conversion of continuous rectilinear motion into alternating
+circular motion, appeared in one publication after another throughout
+the 19th century. As late as 1903 the ferryboat was still anchored in
+Hiscox's _Mechanical Movements_, although the tide had changed (fig.
+35).[90]
+
+[Footnote 90: Gardner D. Hiscox, ed., _Mechanical Movements_, ed. 10,
+New York, 1903, p. 151. The ferryboat did not appear in the 1917
+edition.]
+
+[Illustration: Figure 34.--Hachette's ferryboat of 1808, a "machine" for
+converting continuous rectilinear motion into alternating circular
+motion. From Phillipe Louis Lanz and Augustin de Betancourt, _Essai sur
+la composition des machines_ (Paris, 1808, pl. 2).]
+
+[Illustration: Figure 35.--Ferryboat from Gardner D. Hiscox, ed.,
+_Mechanical Movements_ (ed. 10, New York, 1903, p. 151).]
+
+During the upsurge of the Lyceum--or working-man's institute--movement
+in the 1820's, Jacob Bigelow, Rumford professor of applied science at
+Harvard University, gave his popular lectures on the "Elements of
+Technology" before capacity audiences in Boston. In preparing his
+lecture on the elements of machinery, Bigelow used as his authorities
+Hachette, Lanz and Betancourt, and Olinthus Gregory's mechanical
+dictionary, an English work in which Hachette's classification scheme
+was copied and his chart reproduced.[91]
+
+[Footnote 91: Jacob Bigelow, _Elements of Technology_, ed. 2, Boston,
+1831, pp. 231-256; Olinthus Gregory, _A Treatise of Mechanics_, 3 vols.,
+ed. 3, London, 1815.]
+
+A translation of the work of Lanz and Betancourt[92] under the title
+_Analytical Essay on the Construction of Machines_, was published about
+1820 at London by Rudolph Ackermann (for whom the Ackermann steering
+linkage was named), and their synoptic chart was reprinted again in 1822
+in Durham.[93] In the United States, _Appleton's Dictionary of
+Machines_[94] (1851) adopted the same system and used the same figures.
+Apparently the wood engraver traced directly onto his block the figures
+from one of the reprints of Lanz and Betancourt's chart because the
+figures are in every case exact mirror images of the originals.
+
+[Footnote 92: Rudolph Ackermann, _Analytical Essay on the Construction
+of Machines_, London, about 1820, a translation of Lanz and Betancourt,
+_op. cit._ (footnote 64).]
+
+[Footnote 93: Thomas Fenwick, _Essays on Practical Mechanics_, ed. 3,
+Durham, England, 1822.]
+
+[Footnote 94: _Appleton's Dictionary of Machines, Mechanics,
+Engine-Work, and Engineering_, 2 vols., New York, 1851 ("Motion").]
+
+In the _Dictionary of Engineering_[95] (London, 1873), the figures were
+redrawn and dozens of mechanisms were added to the repertory of
+mechanical motions; the result was a fair catalog of sound ideas. The
+ferryboat still tugged at its anchor cable, however.[96] _Knight's
+American Mechanical Dictionary_,[97] a classic of detailed pictorial
+information compiled by a U.S. patent examiner, contained well over
+10,000 finely detailed figures of various kinds of mechanical
+contrivances. Knight did not have a separate section on mechanisms, but
+there was little need for one of the Hachette variety, because his whole
+dictionary was a huge and fascinating compendium of ideas to be filed
+away in the synthetic mind. One reason for the popularity and usefulness
+of the various pictorial works was the peculiar ability of a wood or
+steel engraving to convey precise mechanical information, an advantage
+not possessed by modern halftone processes.
+
+[Footnote 95: E. F. and N. Spon, _Dictionary of Engineering_, London
+1873, pp. 2421-2452.]
+
+[Footnote 96: _Ibid._, p. 2447.]
+
+[Footnote 97: Edward H. Knight, _Knight's American Mechanical
+Dictionary_, 3 vols., New York 1874-1876.]
+
+[Illustration: Figure 36.--Typical mechanisms from E. F. and N. Spon,
+_Dictionary of Engineering_ (London, 1873, pp. 2426, 2478).]
+
+Many patent journals and other mechanical periodicals concerned with
+mechanics were available in English from the beginning of the 19th
+century, but few of them found their way into the hands of American
+mechanicians until after 1820. Oliver Evans (1755-1819) had much to say
+about "the difficulties inventive mechanics labored under for want of
+published records of what had preceded them, and for works of reference
+to help the beginner."[98] In 1817 the _North American Review_ also
+remarked upon the scarcity of engineering books in America.[99]
+
+[Footnote 98: George Escol Sellers in _American Machinist_, July 12,
+1884, vol. 7, p. 3.]
+
+[Footnote 99: _North-American Review and Miscellaneous Journal_, 1819,
+new ser., vol. 8, pp. 13-15, 25.]
+
+The _Scientific American_, which appeared in 1845 as a patent journal
+edited by the patent promoter Rufus Porter, carried almost from its
+beginning a column or so entitled "Mechanical Movements," in which one
+or two mechanisms--borrowed from an English work that had borrowed from
+a French work--were illustrated and explained. The _American Artisan_
+began a similar series in 1864, and in 1868 it published a compilation
+of the series as _Five Hundred and Seven Mechanical Movements_,
+"embracing all those which are most important in dynamics, hydraulics,
+hydrostatics, pneumatics, steam engines ... and miscellaneous
+machinery."[100] This collection went through many editions; it was last
+revived in 1943 under the title _A Manual of Mechanical Movements_.
+This 1943 edition included photographs of kinematic models.[101]
+
+[Footnote 100: Henry T. Brown, ed., _Five Hundred and Seven Mechanical
+Movements_, New York, 1868.]
+
+[Footnote 101: Will M. Clark, _A Manual of Mechanical Movements_, Garden
+City, New York, 1943.]
+
+Many readers are already well acquainted with the three volumes of
+_Ingenious Mechanisms for Designers and Inventors_,[102] a work that
+resulted from a contest, announced by _Machinery_ (vol. 33, p. 405) in
+1927, in which seven prizes were offered for the seven best articles on
+unpublished ingenious mechanisms.
+
+[Footnote 102: _Ingenious Mechanisms for Designers and Inventors_ (vols.
+1 and 2 edited by F. D. Jones, vol. 3 edited by H. L. Horton), New York,
+Industrial Press, 1930-1951.]
+
+There was an interesting class of United States patents called
+"Mechanical Movements" that comprised scores of patents issued
+throughout the middle decades of the 19th century. A sampling of these
+patents shows that while some were for devices used in particular
+machines--such as a ratchet device for a numbering machine, a locking
+index for gunmaking machinery, and a few gear trains--the great majority
+were for converting reciprocating motion to rotary motion. Even a
+cursory examination of these patents reveals an appalling absence of
+sound mechanical sense, and many of them appear to be attempts at
+"perpetual motion," in spite of an occasional disclaimer of such intent.
+
+Typical of many of these patented devices was a linkage for
+"multiplying" the motion of a flywheel, proposed in 1841 by Charles
+Johnson of Amity, Illinois (fig. 37). "It is not pretended that there is
+any actual gain of power," wrote Mr. Johnson; and probably he meant it.
+The avowed purpose of his linkage was to increase the speed of a
+flywheel and thus decrease its size.[103]
+
+[Footnote 103: U.S. Patent 2295, October 11, 1841.]
+
+[Illustration: Figure 37.--Johnson's "converting motion," 1841. The
+linkage causes the flywheel to make two revolutions for each
+double-stroke of the engine piston rod B. From U.S. Patent 2295, October
+11, 1841.]
+
+An Englishman who a few years earlier had invented a "new Motion" had
+claimed that his device would supersede the "ordinary crank in steam
+engines," the beam, parallel motion, and "external flywheel," reduce
+friction, neutralize "all extra contending power," and leave nothing for
+the piston to do "but the work intended to be done."
+
+A correspondent of the _Repertory of Patent Inventions_ made short work
+of this device: "There is hardly one assertion that can be supported by
+proof," he wrote, "and most of them are palpable misstatements." The
+writer attacked "the 'beetle impetus wheel,' which he [the inventor]
+thinks us all so beetle-headed, as not to perceive to be a flywheel,"
+and concluded with the statement: "In short the whole production evinces
+gross ignorance either of machinery, if the patentee really believed
+what he asserted, or of mankind, if he did not."[104]
+
+[Footnote 104: _Repertory of Patent Inventions_, ser. 3, October 1828,
+vol. 7, pp. 196-200, and December 1828, vol. 7, pp. 357-361.]
+
+Although many of the mechanisms for which patents were taken out were
+designed by persons who would make no use of the principles involved
+even if such principles could at that time have been clearly stated, it
+is a regrettable fact that worthless mechanisms often got as much space
+as sound ones in patent journals, and objections such as the one above
+were infrequent. The slanted information thus conveyed to the young
+mechanician, who was just accumulating his first kinematic repertory,
+was at times sadly misleading.
+
+From even this sketchy outline of the literature on the subject, it
+should be fairly evident that there has been available to the
+mechanician an enormous quantity of information about mechanical
+linkages and other devices. Whatever one may think of the quality of the
+literature, it has undoubtedly had influence not only in supplying
+designers with information but in forming a tradition of how one ought
+to supply the background that will enable the mind to assemble and
+synthesize the necessary mechanism for a given purpose.[105]
+
+[Footnote 105: Some additional catalogs of "mechanical movements" are
+listed in the selected references at the end of this paper.]
+
+Some of the mechanisms that have been given names--such as the Watt
+straight-line linkage and the Geneva stop--have appeared in textbook
+after textbook. Their only excuse for being seems to be that the authors
+must include them or risk censure by colleagues. Such mechanisms are
+more interesting to a reader, certainly, when he has some idea of what
+the name has to do with the mechanism, and who originated it. One such
+mechanism is the drag link.
+
+After I had learned of the drag link (as most American engineering
+students do), I wondered for awhile, and eventually despaired of making
+any sense out of the term. What, I wanted to know, was being dragged?
+Recently, in Nicholson's _Operative Mechanic and British Machinist_
+(1826), I ran across the sketch reproduced here as figure 38. This
+figure, explained Mr. Nicholson (in vol. 1, p. 32) "represents the
+coupling link used by Messrs. Boulton and Watt in their portable steam
+engines. A, a strong iron pin, projecting from one of the arms of the
+fly-wheel B; D, a crank connected with the shaft C; and E, a link to
+couple the pin A and the crank D together, so the motion may be
+communicated to the shaft C." So the drag link was actually a link of a
+coupling. Nothing could be more logical. A drag link mechanism now makes
+sense to me.
+
+[Illustration: Figure 38.--Drag link coupling used on Boulton and Watt
+portable engines. The link E drags one shaft when the other turns. From
+John Nicholson, _The Operative Mechanic, and British Machinist_
+(Philadelphia, 1826, vol. I, pl. 5).]
+
+Directly related to the drag link coupling were the patents of John
+Oldham (1779-1840), an Irish engineer who is remembered mainly for the
+coupling that bears his name (fig. 39). His three patents, which were
+for various forms of steamboat feathering paddle wheels, involved
+linkages kinematically similar to the drag link coupling, although it is
+quite unlikely that Oldham recognized the similarity. However, for his
+well-known coupling, which employs an inversion of the elliptical
+trammel mechanism, I have found no evidence of a patent. Probably it was
+part of the machinery that he designed for the Bank of Ireland's
+printing house, of which Oldham was manager for many years. "Mr. Oldham
+and his beautiful system" were brought to the Bank of England in 1836,
+where Oldham remained until his death in 1840.[106]
+
+[Footnote 106: Oldham's paddle-wheel patents were British Patents 4169
+(October 10, 1817), 4429 (January 15, 1820), and 5445 (February 1,
+1827). Robert Willis (_op. cit._ footnote 21, p. 167) noticed the
+existence of the coupling. Drawings or descriptions of the banknote
+machinery apparently have not been published though they probably still
+exist in the banks' archives. The quotation is from Frederick G. Hall,
+_The Bank of Ireland 1783-1946_, Dublin, 1949. John Francis in his
+_History of the Bank of England_ (London, 1848, vol. 2, p. 232) wrote:
+"The new machinery for printing the notes, which was introduced by Mr.
+Oldham ... is well worthy of a visit, but would be uninteresting to
+delineate."]
+
+[Illustration: Figure 39.--_Top_, Original Oldham coupling built before
+1840, using a cross (instead of a center disk), as sketched by Robert
+Willis in personal copy of his _Principles of Mechanism_ (London, 1841,
+p. 167). _Bottom_, Oldham coupling as illustrated in Alexander B. W.
+Kennedy, _Kinematics of Machinery_, a translation of Franz Reuleaux'
+_Theoretische Kinematik_ (London, 1876, pp. 315-316).]
+
+The Geneva stop mechanism (fig. 40) was properly described by Willis as
+a device to permit less than a full revolution of the star wheel and
+thus to prevent overwinding of a watch spring. It was called Geneva stop
+because it was used in Geneva watches. The Geneva wheel mechanism, which
+permits full rotation of the star wheel and which is frequently used
+for intermittent drives, was improperly called a Geneva stop in a
+recent textbook probably because the logical origin of the term had been
+lost.
+
+[Illustration: Figure 40.--Geneva stop mechanism first used in Geneva
+watches to prevent overwinding. The starwheel B had one convex surface
+(_g-f_, dotted) so the wheel could be turned less than a full
+revolution. After Robert Willis, _Principles of Mechanism_ (London,
+1841, p. 266).]
+
+The name for the Scotch yoke seems to be of fairly recent origin, the
+linkage being called by a Scotsman in 1869 a "crank and slot-headed
+sliding rod" (fig. 41). I suppose that it is now known as a Scotch yoke
+because, in America at least, a "Scotch" was a slotted bar that was
+slipped under a collar on a string of well-drilling tools to support
+them while a section was being added (fig. 42).
+
+[Illustration: Figure 41.--Scotch yoke, described as a "crank and
+slot-headed sliding rod." From W. J. M. Rankine, _A Manual of Machinery
+and Millwork_ (ed. 6, London, 1887, p. 169).]
+
+[Illustration: Figure 42.--A "Scotch" supporting the top member of a
+string of well-drilling tools while a section is being added, 1876. From
+Edward H. Knight, _Knight's American Mechanical Dictionary_ (New York,
+1876, p. 2057).]
+
+It was surprising to me to find that the Ackermann steering linkage,
+used today on most automobiles, was patented in 1818 when Detroit was
+still a frontier town.[107] Furthermore, the man who took out the patent
+described himself as Rudolph Ackermann, publisher and printseller. I
+thought I had the necessary clue to the linkage's origin when I noticed
+that the first English translation of the Lanz and Betancourt treatise
+was published by Ackermann, but the connection finally proved to be more
+logical, if less direct. Ackermann (1764-1834), son of a Bavarian coach
+builder, had spent a number of years designing coaches for English
+gentlemen in London, where he made his home. One of his more notable
+commissions was for the design of Admiral Nelson's funeral car in 1805.
+The Ackermann steering linkage was not actually Ackermann's invention,
+although he took out the British patent in his name and promoted the
+introduction of the running gear of which the linkage was a part (fig.
+43). The actual inventor was Ackermann's friend George Lankensperger of
+Munich, coachmaker to the King of Bavaria. The advantage of being able
+to turn a carriage around in a limited area without danger of
+oversetting was immediately obvious, and while there was considerable
+opposition by English coachmakers to an innovation for which a premium
+had to be paid, the invention soon "made its way from its own intrinsic
+merit," as Ackermann predicted it would.[108]
+
+[Footnote 107: British Patent 4212, January 27, 1818.]
+
+[Footnote 108: Rudolph Ackermann, _Observations on Ackermann's Patent
+Moveable Axles_, London, 1819. It was interesting to me to note an
+abstract of W. A. Wolfe's paper "Analytical Design of an Ackermann
+Steering Linkage" in _Mechanical Engineering_, September 1958, vol. 80,
+p. 92.]
+
+[Illustration: Figure 43.--Ackermann steering linkage of 1818, currently
+used in automobiles. This linkage was invented by George Lankensperger,
+coachmaker to the King of Bavaria. From _Dinglers Polytechnisches
+Journal_ (1820, vol. 1, pl. 7).]
+
+The Whitworth quick-return mechanism (fig. 44) was first applied to a
+slotter, or vertical shaper, in 1849, and was exhibited in 1851 at the
+Great Exhibition in London.[109] Willis' comments on the mechanism are
+reproduced in figure 44. I hope that Sir Joseph Whitworth (1803-1887)
+will be remembered for sounder mechanical contrivances than this.
+
+[Footnote 109: The quick-return mechanism (British Patent 12907,
+December 19, 1849) was perhaps first publicly described in Charles
+Tomlinson, ed., _Cyclopaedia of Useful Arts and Manufactures_, London,
+1854, vol. 1, p. cxliv.]
+
+[Illustration: Figure 44.--Quick-return mechanism. _Top_, Early
+representation of the quick-return mechanism patented by Whitworth in
+1849, from William Johnson, ed., _The Imperial Cyclopaedia of machinery_
+(Glasgow, about 1855, pl. 88). _Middle_, Sketch by Robert Willis from
+his copy of _Principles of Mechanism_ (London, 1841, p. 264), which
+"shews Whitworth dissected into a simpler form"; it is as obscure as
+most subsequent attempts have been to explain this mechanism without a
+schematic diagram. _Bottom_, Linkage that is kinematically equivalent to
+Whitworth's, from Robert Willis, _Principles of Mechanism_ (London,
+1841, p. 264).]
+
+
+Mechanisms in America, 1875-1955
+
+Engineering colleges in the United States were occupied until the late
+1940's with extending, refining, and sharpening the tools of analysis
+that had been suggested by Willis, Rankine, Reuleaux, Kennedy, and
+Smith. The actual practice of kinematic synthesis went on apace, but
+designers often declined such help as the analytical methods might give
+them and there was little exchange of ideas between scholars and
+practitioners.
+
+The capability and precision of machine tools were greatly enhanced
+during this period, although, with the exception of the centerless
+grinder, no significant new types of tools appeared. The machines that
+were made with machine tools increased in complexity and, with the
+introduction of ideas that made mass production of complex mechanical
+products economically feasible, there was an accelerating increase in
+quantity. The adoption of standards for all sorts of component parts
+also had an important bearing upon the ability of a designer
+economically to produce mechanisms that operated very nearly as he hoped
+they would.
+
+The study of kinematics has been considered for nearly 80 years as a
+necessary part of the mechanical engineer's training, as the dozens of
+textbooks that have been published over the years make amply clear.
+Until recently, however, one would look in vain for original work in
+America in the analysis or rational synthesis of mechanisms.
+
+One of the very earliest American textbooks of kinematics was the 1883
+work of Charles W. MacCord (1836-1915), who had been appointed professor
+of mechanical drawing at Stevens Institute of Technology in Hoboken
+after serving John Ericsson, designer of the _Monitor_, as chief
+draftsman during the Civil War.[110] Based upon the findings of Willis
+and Rankine, MacCord's _Kinematics_ came too early to be influenced by
+Kennedy's improvements upon Reuleaux's work.
+
+[Footnote 110: A biographical notice and a bibliography of MacCord
+appears in _Morton Memorial: A History of the Stevens Institute of
+Technology_, Hoboken, 1905, pp. 219-222.]
+
+When the faculty at Washington University in St. Louis introduced in
+1885 a curriculum in "dynamic engineering," reflecting a
+dissatisfaction with the traditional branches of engineering, kinematics
+was a senior subject and was taught from Rankine's _Machinery and
+Millwork_.[111]
+
+[Footnote 111: _Transactions of the American Society of Mechanical
+Engineers_, 1885-1886, vol. 7, p. 757.]
+
+At Massachusetts Institute of Technology, Peter Schwamb, professor of
+machine design, put together in 1885 a set of printed notes on the
+kinematics of mechanisms, based on Reuleaux's and Rankine's works. Out
+of these notes grew one of the most durable of American textbooks, first
+published in 1904.[112] In the first edition of this work, acceleration
+was mentioned only once in passing (on p. 4). Velocities in linkages
+were determined by orthogonal components transferred from link to link.
+Instant centers were used only to determine velocities of various points
+on the same link. Angular velocity ratios were frequently noted. In the
+third edition, published in 1921, linear and angular accelerations were
+defined, but no acceleration analyses were made. Velocity analyses were
+altered without essential change. The fourth edition (1930) was
+essentially unchanged from the previous one. Treatment of velocity
+analysis was improved in the fifth edition (1938) and acceleration
+analysis was added. A sixth edition, further revised by Prof. V. L.
+Doughtie of the University of Texas, appeared in 1947.
+
+[Footnote 112: Peter Schwamb and Allyne L. Merrill, _Elements of
+Mechanism_, New York, 1904. In addition to the work of Reuleaux and
+Rankine, the authors acknowledged their use of the publications of
+Charles MacCord, Stillman W. Robinson, Thomas W. Goodeve, and William C.
+Unwin. For complete titles see the list of selected references.]
+
+Before 1900, several other books on mechanisms had been published, and
+all followed one or another of the patterns of their predecessors.
+Professors Woods and Stahl, at the Universities of Illinois and Purdue,
+respectively, who published their _Elementary Mechanism_ in 1885, said
+in their preface what has been said by many other American authors and
+what should have been said by many more. "We make little claim to
+originality of the subject-matter," wrote Woods and Stahl, "free use
+having been made of all available matter on the subject.... Our claim to
+consideration is based almost entirely on the manner in which the
+subject has been presented." Not content with this disclaimer, they
+continued: "There is, in fact, very little room for such originality,
+the ground having been almost completely covered by previous
+writers."[113]
+
+[Footnote 113: Arthur T. Woods and Albert W. Stahl, _Elementary
+Mechanism_, New York, 1885.]
+
+The similarity and aridity of kinematics textbooks in this country from
+around 1910 are most striking. The generation of textbook writers
+following MacCord, Woods and Stahl, Barr of Cornell, Robinson of Ohio
+State, and Schwamb and Merrill managed to squeeze out any remaining
+juice in the subject, and the dessication and sterilization of textbooks
+was nearly complete when my generation used them in the 1930's.
+Kinematics was then, in more than one school, very nearly as it was
+characterized by an observer in 1942--"on an intellectual par with
+mechanical drafting."[114] I can recall my own naive belief that a
+textbook contained all that was known of the subject; and I was not
+disabused of my belief by my own textbook or by my teacher. I think I
+detect in several recent books a fresh, less final, and less tidy
+treatment of the kinematics of mechanisms, but I would yet recommend
+that anyone who thinks of writing a textbook take time to review,
+carefully and at first hand, not only the desk copies of books that he
+has accumulated but a score or more of earlier works, covering the last
+century at least. Such a study should result in a better appreciation of
+what constitutes a contribution to knowledge and what constitutes merely
+the ringing of another change.
+
+[Footnote 114: _Mechanical Engineering_, October 1942, vol. 64, p. 745.]
+
+The author of the contentious article that appeared in _Mechanical
+Engineering_ in 1942 under the title "What is Wrong with Kinematics and
+Mechanisms?" made several pronouncements that were questioned by various
+readers, but his remarks on the meagerness of the college courses of
+kinematics and the "curious fact" that the textbooks "are all strangely
+similar in their incompleteness" went unchallenged and were, in fact,
+quite timely.[115]
+
+[Footnote 115: De Jonge, _op. cit._ (footnote 78).]
+
+It appears that in the early 1940's the general classroom treatment of
+accelerations was at a level well below the existing knowledge of the
+subject, for in a series of articles by two teachers at Purdue attention
+was called to the serious consequences of errors in acceleration
+analysis occasioned by omitting the Coriolis component.[116] These
+authors were reversing a trend that had been given impetus by an article
+written in 1920 by one of their predecessors, Henry N. Bonis. The
+earlier article, appearing in a practical-and-proud-of-it technical
+magazine, demonstrated how the acceleration of a point on a flywheel
+governor might be determined "without the use of the fictitious
+acceleration of Coriolis." The author's analysis was right enough, and
+he closed his article with the unimpeachable statement that "it is
+better psychologically for the student and practically for the engineer
+to understand the fundamentals thoroughly than to use a complex formula
+that may be misapplied." However, many readers undoubtedly read only the
+lead paragraph, sagely nodded their heads when they reached the word
+"fictitious," which confirmed their half-formed conviction that anything
+as abstruse as the Coriolis component could have no bearing upon a
+practical problem, and turned the page to the "practical kinks"
+section.[117]
+
+[Footnote 116: A. S. Hall and E. S. Ault, "How Acceleration Analysis Can
+Be Improved," _Machine Design_, February 1943, vol. 15, pp. 100-102,
+162, 164; and March 1943, vol. 15, pp. 90-92, 168, 170. See also A. S.
+Hall, "Teaching Coriolis' Law," _Journal of Engineering Education_, June
+1948, vol. 38, pp. 757-765.]
+
+[Footnote 117: Henry N. Bonis, "The Law of Coriolis," _American
+Machinist_, November 18, 1920, vol. 53, pp. 928-930. See also
+"Acceleration Determinations," _American Machinist_, November 25 and
+December 2, 1920, vol. 53, pp. 977-981 and 1027-1029.]
+
+Less than 20 years ago one might have read in _Mechanical Engineering_
+that "Practical machinery does not originate in mathematical formulas
+nor in beautiful vector diagrams." While this remark was in a letter
+evoked by an article, and was not a reflection of editorial policy, it
+was nevertheless representative of an element in the American tradition
+of engineering. The unconscious arrogance that is displayed in this
+statement of the "practical" designer's creed is giving way to
+recognition of the value of scholarly work. Lest the scholar develop
+arrogance of another sort, however, it is well to hear the author of
+the statement out. "A drafting machine is a useful tool," he wrote. "It
+is not a substitute for a draftsman."[118]
+
+[Footnote 118: _Mechanical Engineering_, October 1942, vol. 64, p. 746.]
+
+The scholarly interest in a subject is fairly represented by the papers
+that are published in the transactions of professional societies and,
+more recently, by original papers that appear in specialized magazines.
+From 1900 to 1930 there were few papers on mechanisms, and most of those
+that did appear were concerned with descriptions of new "mechanical
+motions." In the 1930's the number of papers reported in _Engineering
+Index_ increased sharply, but only because the editors had begun to
+include foreign-language listings.
+
+There has been in Germany a thread of continuity in the kinematics of
+mechanisms since the time of Reuleaux. While most of the work has had to
+do with analysis, the teasing question of synthesis that Reuleaux raised
+in his work has never been ignored. The developments in Germany and
+elsewhere have been ably reviewed by others,[119] and it is only to be
+noted here that two of the German papers, published in 1939 in
+_Maschinenbau_, appear to have been the sparks for the conflagration
+that still is increasing in extent and intensity. According to summaries
+in _Engineering Index_, R. Kraus, writing on the synthesis of the
+double-crank mechanism, drew fire from the Russian Z. S. Bloch, who, in
+1940, discussed critically Kraus's articles and proceeded to give the
+outline of the "correct analysis of the problem" and a general numerical
+solution for the synthesis of "any four-bar linkage."[120] Russian work
+in mechanisms, dating back to Chebyshev and following the "Chebyshev
+theory of synthesis" in which algebraic methods are used to determine
+paths of minimum deviation from a given curve, has also been reviewed
+elsewhere,[121] and I can add nothing of value.
+
+[Footnote 119: Grodzinski, Bottema, De Jonge, and Hartenberg and
+Denavit. For complete titles see list of selected references.]
+
+[Footnote 120: My source, as noted, is _Engineering Index_. Kraus's
+articles are reported in 1939 and Bloch's in 1940, both under the
+section heading "Mechanisms."]
+
+[Footnote 121: A. E. Richard de Jonge, "Are the Russians Ahead in
+Mechanism Analysis?" _Machine Design_, September 1951, vol. 23, pp. 127,
+200-208; O. Bottema, "Recent Work on Kinematics," _Applied Mechanics
+Reviews_, April 1953, vol. 6, pp. 169-170.]
+
+When, after World War II, some of the possibilities of kinematic
+synthesis were recognized in the United States, a few perceptive
+teachers fanned the tinder into an open flame.
+
+The first publication of note in this country on the synthesis of
+linkages was a practical one, but in conception and undertaking it was a
+bold enterprise. In a book by John A. Hrones and G. L. Nelson,
+_Analysis of the Four Bar Linkage_ (1951), the four-bar crank-and-rocker
+mechanism was exhaustively analyzed mechanically and the results were
+presented graphically. This work was faintly praised by a Dutch scholar,
+O. Bottema, who observed that the "complicated analytical theory of the
+three-bar [sic] curve has undoubtedly kept the engineer from using it"
+and who went on to say that "we fully understand the publication of an
+atlas by Hrones and Nelson containing thousands of trajectories which
+must be very useful in many design problems."[122] Nevertheless, the
+authors furnished designers with a tool that could be readily, almost
+instantly, understood (fig. 45), and the atlas has enjoyed wide
+circulation.[123] The idea of a geometrical approach to synthesis has
+been exploited by others in more recent publications,[124] and it is
+likely that many more variations on this theme will appear.
+
+[Footnote 122: Bottema, _op. cit._ (footnote 121).]
+
+[Footnote 123: In 1851 Robert Willis had designed a coupler-point
+path-generating machine (fig. 46) that could have been used to produce a
+work similar to that of Hrones and Nelson.]
+
+[Footnote 124: R. S. Hartenberg and J. Denavit, "Systematic Mechanism
+Design," _Machine Design_, September 1954, vol. 26, pp. 167-175, and
+October 1954, vol. 26, pp. 257-265; A. S. Hall, A. R. Holowenko, and H.
+G. Laughlin, "Four-Bar Lever Crank Mechanism," _Design News_, September
+15, 1957, vol. 12, pp. 130-139, October 1, 1957, vol. 12, pp. 145-154,
+and October 15, 1957, vol. 12, pp. 132-141. For a nomographic approach,
+with particular application to computers, see Antonin Svoboda,
+_Computing Mechanisms and Linkages_, New York, 1948.]
+
+[Illustration: Figure 45.--Paths of 11 points on the coupler
+(horizontal) link are plotted through one cycle. Dashes indicate equal
+time intervals. From John A. Hrones and G. L. Nelson, _Analysis of the
+Four Bar Linkage_ (New York, 1951, p. 635).]
+
+[Illustration: Figure 46.--Coupler-point path-generating machine for
+four-bar linkage. This device, built by Professor Willis as a teaching
+aid for demonstrating straight-line linkages, could have been adapted to
+produce a plate like the one shown in figure 45. From Robert Willis, _A
+System of Apparatus for the Use of Lecturers and Experimenters_ ...
+(London 1851, pl. 3).]
+
+Pursuit of solutions to the "complicated analytical theory" of linkages
+was stimulated by publication of Ferdinand Freudenstein's "Analytical
+Approach to the Design of Four-Link Mechanisms" in 1954,[125] and an
+increasing interest in the problem is indicated by the extensive
+literature that has appeared in the last five years.
+
+[Footnote 125: _Transactions of the American Society of Mechanical
+Engineers_, 1954, vol. 76, pp. 483-492. See also _Transactions of the
+American Society of Mechanical Engineers_, 1955, vol. 77, pp. 853-861,
+and 1956, vol. 78, pp. 779-787.]
+
+The proper role of rational methods in the synthesis of mechanisms is
+not yet clear. "While we may talk about kinematic synthesis," wrote two
+of today's leaders in the field, "we are really talking about a hope for
+the future rather than a great reality of the present."[126] When the
+mental equipment and the enthusiasm of scholars who are devoting their
+time to the problems of kinematic synthesis are considered, however, it
+is difficult to see how important new ideas can fail to be produced.
+
+[Footnote 126: R. S. Hartenberg and J. Denavit, "Kinematic Synthesis,"
+_Machine Design_, September 6, 1956, vol. 28, pp. 101-105.]
+
+An annual Conference on Mechanisms, sponsored by Purdue University and
+_Machine Design_, was inaugurated in 1953 and has met with a lively
+response. Among other manifestations of current interest in mechanisms,
+the contributions of Americans to international conferences on
+mechanisms reflects the growing recognition of the value of scholarly
+investigation of the kind that can scarcely hope to yield immediately
+tangible results.
+
+While we look to the future, one may ask how a lengthy view of the past
+can be justified. It seems to me that there is inherent in the almost
+feverish activity of the present the danger of becoming so preoccupied
+with operational theory that the goals may become clouded and the
+synthesis (let us put it less elegantly: the design) of mechanisms may
+never quite come into focus. If one knows nothing of the past, I wonder
+how he can with any confidence decide in what direction he must turn in
+order to face the future.
+
+
+Acknowledgment
+
+I am grateful to Professors Richard S. Hartenberg and Allen S. Hall,
+Jr., for reading the manuscript, making helpful comments, and suggesting
+material that I had not found. The errors, however, are mine.
+
+
+Additional References
+
+The following list of additional reference material on kinematics may be
+of help to readers who desire to do independent research. The material
+is listed according to the section headings in the text of the present
+article.
+
+
+TO DRAW A STRAIGHT LINE
+
+KEMPE, A. B. _How to Draw a Straight Line._ London, 1877.
+
+Contains a useful bibliography. Reprinted in _Squaring the Circle and
+Other Monographs_, New York, Chelsea Publishing Company, 1953.
+
+Much attention has been given to straight-line mechanisms since the time
+of Kempe; at least a half dozen articles have appeared in the United
+States since 1950, but I did not investigate the literature published
+after 1877.
+
+
+SCHOLARS AND MACHINES
+
+BECK, THEODOR. _Beitraege zur Geschichte des Maschinenbaues._ Berlin,
+1899.
+
+Reviews of early works, such as those by Leonardo da Vinci, Biringuccio,
+Besson, Zonca, etc.
+
+BORGNIS, GIUSEPPE ANTONIO. _Traite complet de mecanique appliquee aux
+arts._ Paris, 1818-1821, 9 vols.
+
+Contains several hundred finely detailed plates of machines.
+
+LABOULAYE, CHARLES. _Traite de cinematique ou theorie des mecanismes._
+Paris, 1861 (ed. 2).
+
+This work was quoted frequently by Laboulaye's contemporaries.
+
+ROYAL SOCIETY OF LONDON. _Catalogue of Scientific Papers, 1800-1900,
+Author Index._ London, 1867-1902, and Cambridge, 1914-1925.
+
+----. _Catalogue of Scientific Papers, 1800-1900, Subject Index._
+London, 1909, vol. 2.
+
+This subject index was started in 1908, and by 1914 three volumes (the
+third in two parts) had been published; however, this subject index was
+never completed. Volume 2, titled _Mechanics_, has some 200 entries
+under "Linkages." It is interesting to note that both of the Royal
+Society's monumental catalogs grew out of a suggestion made by Joseph
+Henry at a British Association meeting in Glasgow in 1855.
+
+WEISBACH, JULIUS. _The Mechanics of the Machinery of Transmission_, vol.
+3, pt. 1, sec. 2 of _Mechanics of Engineering and Machinery_, translated
+by J. F. Klein. New York, 1890 (ed. 2).
+
+
+MECHANISMS AND MECHANICIANS
+
+BARBER, THOMAS W. _Engineer's Sketch-Book._ London, 1890 (ed. 2).
+
+HERKIMER, HERBERT. _Engineer's Illustrated Thesaurus._ New York, 1952.
+
+PERIODICALS. _Artizan_, from 1843; _Practical Mechanic and Engineer's
+Magazine_, from 1841; _Repertory of Arts and Manufactures_, from 1794;
+_Newton's London Journal of Arts and Science_, from 1820. (The preceding
+periodicals have many plates of patent specification drawings.) _The
+Engineer_, November 10, 1933, vol. 156, p. 463, and _Engineering_,
+November 10, 1933, vol. 136, p. 525. (Recent English views questioning
+the utility of kinematics.)
+
+TATE, THOMAS. _Elements of Mechanism._ London, 1851.
+
+Contains figures from Lanz and Betancourt (1808).
+
+WYLSON, JAMES. _Mechanical Inventor's Guide._ London, 1859.
+
+Contains figures from Henry Adcock, _Adcock's Engineers' Pocket-Book,
+1858_.
+
+
+MECHANISMS IN AMERICA, 1875-1955
+
+ALBERT, CALVIN D., AND ROGERS, F. D. _Kinematics of Machinery._ New
+York, 1931.
+
+Contains a bibliography that includes works not mentioned in the present
+paper.
+
+BARR, JOHN H. _Kinematics of Machinery._ New York, 1899.
+
+An early textbook. The author taught at Cornell University.
+
+BEGGS, JOSEPH S. _Mechanism._ New York, 1955.
+
+Contains an extensive and useful bibliography.
+
+BOTTEMA, O. "Recent Work on Kinematics," _Applied Mechanics Reviews_,
+April 1953, vol. 6, pp. 169-170.
+
+
+CONFERENCE ON MECHANISMS.
+
+This conference was sponsored by Purdue University and _Machine Design_.
+Transactions of the first two conferences appeared as special sections
+in _Machine Design_, December 1953, vol. 25, pp. 173-220, December 1954,
+vol. 26, pp. 187-236, and in collected reprints. Papers of the third and
+fourth conferences (May 1956 and October 1957) appeared in _Machine
+Design_ over several months following each conference and in collected
+reprints. Papers of the fifth conference (October 1958) were collected
+and preprinted for conference participants; subsequently, all papers
+appeared in _Machine Design_. Collected reprints and preprints are
+available (May 1960) from Penton Publishing Company, Cleveland, Ohio.
+
+DE JONGE, A. E. RICHARD. "Kinematic Synthesis of Mechanisms,"
+_Mechanical Engineering_, July 1940, vol. 62, pp. 537-542.
+
+----. "A Brief Account of Modern Kinematics," _Transactions of the
+American Society of Mechanical Engineers_, 1943, vol. 65, pp. 663-683.
+
+GOODEVE, THOMAS M. _The Elements of Mechanism._ London, 1903.
+
+An early textbook.
+
+GRODZINSKI, PAUL, AND MCEWEN, EWEN. "Link Mechanisms in Modern
+Kinematics," _Journal and Proceedings of the Institution of Mechanical
+Engineers_, 1954, vol. 168, pp. 877-896.
+
+This article evoked interesting discussion. It is unfortunate that
+Grodzinski's periodical, _Mechanism, An International Bibliography_,
+which was published in London in 1956-1957 and which terminated shortly
+after his death, has not been revived. Grodzinski's incisive views and
+informative essays are valuable and interesting.
+
+HARTENBERG, R. S. "Complex Numbers and Four-Bar Linkages," _Machine
+Design_, March 20, 1958, vol. 30, pp. 156-163.
+
+This is an excellent primer. The author explains complex numbers in his
+usual lucid fashion.
+
+HARTENBERG, R. S., AND DENAVIT, J. "Kinematic Synthesis," _Machine
+Design_, September 6, 1956, vol. 28, pp. 101-105.
+
+MACCORD, CHARLES. _Kinematics._ New York, 1883.
+
+An early textbook.
+
+ROBINSON, STILLMAN W. _Principles of Mechanism._ New York, 1896.
+
+An early textbook. The author taught at Ohio State University.
+
+UNWIN, WILLIAM C. _The Elements of Machine Design._ New York, 1882 (ed.
+4).
+
+An early textbook. The author taught at Royal Indian Engineering
+College, in England.
+
+
+GOVERNMENT PRINTING OFFICE: 1962
+
+For sale by the Superintendent of Documents, U.S. Government Printing
+Office Washington 25, D. C.--Price 40 cents
+
+
+
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