PAPER 27 (continued 2)
Reading edition
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.
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