Chapter 6

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.]

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.

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