Kinematics of Mechanisms from the Time of Watt Part 1

Kinematics of Mechanisms from the Time of Watt.

by Eugene S. Ferguson.

_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 Inst.i.tution, 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 a.n.a.lysis, 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 a.n.a.lysis 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 a.n.a.lysis 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 s.p.a.ce._

--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 a.n.a.lysis 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 s.p.a.ce 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 ill.u.s.trate 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.]

[Ill.u.s.tration: 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).]

[Ill.u.s.tration: Figure 2.--Slider-crank mechanism of Leonardo da Vinci (1452-1519), redrawn from his ma.n.u.script notebooks. A frame saw is depicted at the lower end of the guides. From Theodor Beck, _Beitrage zur Geschichte des Maschinenbaues_ (Berlin, 1899, p. 323).]

[Ill.u.s.tration: Figure 3.--Blowing engine by Vanuccio Biringuccio, about 1540, showing conversion of motion of the waterwheel shaft from rotation to oscillation. From Theodor Beck, _Beitrage zur Geschichte des Maschinenbaues_ (Berlin, 1899, p. 120).]

[Ill.u.s.tration: 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).]

[Ill.u.s.tration: 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 b.u.t.tons 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 mult.i.tude 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. d.i.c.kinson, _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 doc.u.ments, 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 bra.s.s 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 cla.s.s 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 quant.i.ty 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 s.p.a.ces 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. d.i.c.kinson 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 d.i.c.kinson, _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 enc.u.mbrance 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 subst.i.tute.

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 b.u.t.tonmaker, 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 pa.s.sed 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.]