Kinematics of Mechanisms from the Time of Watt

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]

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.

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]

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.

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).

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).

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]

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.

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.

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]

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.

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]

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.

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]

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]

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]

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.

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.

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).

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.

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.

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 a 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

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