along. A straight line could be drawn along a 

 straight edge; but how was one to determine whether 

 the straight edge was straight? He did not weaken 

 his argument by suggesting the obvious possibility of 

 using a piece of string. Kempe had collaborated \vith 

 Sylvester in pursuing the latter's first thoughts on the 

 subject, and one result, that to my mind exemplifies 

 the general direction of their thinking, was the 

 Sylvester-Kempe "parallel motion" (fig. 26). 



Enthusiastic as Kempe was, however, he injected 

 an apologetic note in his lecture. "That these 

 results are valuable cannot I think be doubted," he 

 said, "though it may well be that their great beauty 

 has led some to attribute to them an importance 

 which they do not really possess. . . ." He went on 

 to say that 50 years earlier, before the great improve- 

 ments in the production of true plane surfaces, the 

 straight-line mechanisms would have been more 

 important than in 1876, but he added that "linkages 

 have not at present, I think, been sufficiently put 

 before the mechanician to enable us to say what 

 value should really be set upon them." ^* 



It was during this same summer of 1876, at the 

 Loan Exhibition of Scientific Apparatus in the South 

 Kensington Museum, that the work of Franz Reu- 

 leaux, which was to have an important and lasting 

 influence on kinematics everywhere, was first intro- 

 duced to English engineers. Some 300 beautifully 

 constructed teaching aids, known as the Berlin kine- 

 matic models, were loaned to the exhibition by the 

 Royal Industrial School in Berlin, of which Reuleaux 

 was the director. These models were used by Prof. 

 Alexander B. W. Kennedy of University College, 

 London, to help explain Reuleaux's new and revolu- 

 tionarv theory of machines. ^^ 



^* Ibid., pp. 6—7. I have not pursued the matter of cognate 

 linkages (the Watt and Evans hnkages are cognates) because 

 the Roberts-Chebyshev theorem escaped my earUer search, as 

 it had apparently escaped most others until 1958. See R. S. 

 Hartenberg and J. Denavit, "The Fecund Four-Bar," Trans- 

 actions of the Fifth Confersjice on Mechanisms, Cleveland, Penton 

 Publishing Company, 1958, pp. 194-206, reprinted in Machine 

 Design, April 16, 1959, vol. 31, pp. 149-152. See also A. E. R. 

 de Jonge, "The Correlation of Hinged Four-Bar Straight-Line 

 Motion Devices by Means of the Roberts Theorem and a New 

 Proof of the Latter," Annals of the New York Academy of Sciences, 

 March 18, 1960, vol. 84, art. 3, pp. 75-145 (published 

 separately). 



'^ Alexander B. W. Kennedy, "The Berlin Kinematic 

 Models," Engineering, September 15, 1876, vol. 22, pp. 239-240. 



Scholars and Machines 



When, in 1829, Andre-Marie Ampere (1775-1836) 

 was called upon to prepare a course in theoretical and 

 experimental physics for the College de France, he 

 first set about determining the limits of the field of 

 physics. This exercise suggested to his wide-ranging 

 intellect not only the definition of physics but the 

 classification of all human knowledge. He prepared 

 his scheme of classification, tried it out on his physics 

 students, found it incomplete, returned to his study, 

 and produced finally a two-volume work wherein the 

 province of kinematics was first marked out for all to 

 see and consider. ^^ Only a few lines could be devoted 

 to so specialized a branch as kinematics, but Ampere 

 managed to capture the central idea of the subject. 



Cinematique (from the Greek word for movement) 

 was, according to Ampere, the science "in which 

 movements are considered in themselves [independent 

 of the forces which produce them], as we observe them 

 in solid bodies all about us, and especially in the 

 assemblages called machines." ^'' Kinematics, as the 

 study soon came to be known in English,"* was one 

 of the two branches of elementary mechanics, the 

 other being statics. 



In his definition of kinematics, Arnpere stated what 

 the faculty of mathematics at the Ecole Polytech- 

 nique, in Paris, had been groping toward since the 

 school's opening some 40 years earlier. The study of 

 mechanisms as an intellectual discipline most cer- 

 tainly had its origin on the left bank of the Seine, in 

 this school spawned, as suggested by one French 

 historian, =^ by the great Encyclopedic of Diderot and 

 d'Alembert. 



Because the Ecole Polytechnique had such a far- 

 reaching influence upon the point of view from which 

 mechanisms were contemplated by scholars for nearly 

 a century after the time of Watt, and by compilers of 

 dictionaries of mechanical movements for an even 



^* Andre-Marie Ampere, Essai sur la philosophic des sciences, 

 une exposition analytique d'une classification naturelle de toutes les 

 connaissances humaines, 2 vols., Paris, 1838 (for origin of the 

 project, see vol. 1, pp. v, xv). 



^' Ibid., vol. 1, pp. 51-52. 



5' Willis {op. cit. footnote 21) adopted the word "kinematics," 

 and this Anglicization subsequently became the standard term 

 for this branch of mechanics. 



5' G. Pinet, Histoire de P Ecole Polytechnique, Paris, 1887, pp. 

 viii-ix. In their forthcoming book on kinematic synthesis, 

 R. S. Hartenberg and J. Denavit will trace the germinal ideas 

 of Jacob Leupold and Leonhard Euler of the 18th century. 



PAPER 27: KINEMATICS FROM THE TIME OF WATT 



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