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. 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.

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. 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."

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." 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.

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. 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.

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."

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, 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." 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, 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." Nevertheless, the authors furnished designers with a tool that could be readily, almost instantly, understood (fig. 45), and the atlas has enjoyed wide circulation. The idea of a geometrical approach to synthesis has been exploited by others in more recent publications, 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, 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." 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.