Acting upon Ampere's clear exposition of the 

 province of kinematics and excluding, as Ampere had 

 done, the consideration of forces, an Englishman, 

 Robert Willis, made the next giant stride forward in 

 the analysis of mechanisms. Willis was 37 years old 

 in 1837 when he was appointed professor of natural 

 and experimental philosophy at Cambridge. In the 

 same year Professor Willis — a man of prodigious 

 energy and industry and an authority on archeology 

 and architectural history as well as mechanisms — 

 read his important paper "On the Teeth of Wheels" 

 before the Institution of Civil Engineers ''" and 

 commenced at Cambridge his lectures on kinematics 

 of mechanisins that culminated in his 1841 book 

 Principles of Mechanism.''^ 



It seemed clear to Willis that the problem of devising 

 a mechanism for a given purpose ought to be attacked 

 systematically, perhaps mathem.atically, in order to 

 determine "all the forms and arrangements that are 

 applicable to the desired purpose," from which the 

 designer might select the simplest or most suitable 

 combination. "At present," he wrote, "questions of 

 this kind can only be solved by that species of intui- 

 tion which long familiarity with a subject usually 

 confers upon experienced persons, but which they are 

 totally unable to communicate to others." 



In analyzing the process by which a machine was 

 designed, Willis observed: "When the mind of a 

 mechanician is occupied with the contrivance of 

 a machine he must wait until, in the midst of his 

 meditations, some happy combination presents itself 

 to his mind which may answer his purpose." He 

 ventured the opinion that at this stage of the design 

 process "the motions of the machine are the principal 

 subject of contemplation, rather than the forces 

 applied to it, or the work it has to do." Therefore 



™ Robert Willis, "On the Teeth of Wheels," Transactions of 

 the Institution of Civil Engineers of London, 1838, vol. 2, pp. 

 89-112. 



" Willis, op. cit. (footnote 21). Through the kindness of its 

 owner (Mr. Warren G. Ogden of North Andover, Massachu- 

 setts), I have had access to Willis' own copy of his 1841 edition 

 of Principles of Mechanism. The book is interleaved, and it 

 contains notes made by Willis from time to time until at least 

 1870, when the second edition was issued. Corrections, 

 emendations, notations of some of his sources (for example, 

 the De Voglie linkage mentioned in footnote 35 above), 

 notes to himself to "examine the general case" and "examine 

 the modern forms" of straight-line devices are interspersed 

 with references to authors that had borrowed from his work 

 without acknowledgment. Of one author Willis writes an 

 indignant "He ignores my work." 



he was prepared to adopt without reservation Am- 

 pere's view of kinematics, and, if possible, to make 

 the science useful to engineers by stating principles 

 that could be applied without having to fit the 

 problem at hand into the framework of the systems 

 of classification and description that had gone before. 

 He appraised the "celebrated system" of Lanz and 

 Betancourt as "a merely popular arrangement, not- 

 withstanding the apparently scientific simplicity of 

 the scheme." He rejected this scheme because "no 

 attempt is made to subject the motions to calcu- 

 lation, or to reduce these laws to general formulas, 

 for which indeed the system is totally unfitted." 



Borgnis had done a better job, Willis thought, in 

 actually describing machinery, with his "orders" 

 based upon the functions of machine elements or 

 mechanisms within the machine, but again there 

 was no means suggested by which the kinematics of 

 mechanisms could be systematically investigated. 



Although Willis commenced his treatise with yet 

 another "synoptical table of the elementary combi- 

 nations of pure mechanism," his view shifted quickly 

 from description to analysis. He was consistent in 

 his pursuit of analytical methods for "pure mech- 

 anism," eschewing any excursions into the realm 

 of forces and absolute velocities. He grasped the 

 important concept of relative displacements of 

 machine elements, and based his treatment upon 

 "the proportions and relations between the velocities 

 and directions of the pieces, and not upon their 

 actual and separate motions."''^ 



That he did not sticceed in developing the "for- 

 mulas" that would enable the student to determine 

 "all the forms and arrangements that are applicable 

 to the desired purpose" — that he did not present 

 a rational approach to synthesis — is not to be won- 

 dered at. Well over a century later we still are 

 nibbling at the fringes of the problem. Willis did, 

 nonetheless, give the thoughtful reader a glimpse 

 of the most powerful tool for kinematic synthesis 

 that has yet been devised; namely, kinematic analysis, 

 in which the argument is confined to the relative 

 displacements of points on links of a mechanism, 

 and through which the designer may grasp the nature 

 of the means at his disposal for the solution of any 

 particular problem. 



As remarked by Reuleaux a generation later, there 

 was much in Professor Willis's book that was wrong, 



'- Ibid., pp. iv, x-xii, xxi, 15. 



212 



BULLETIN 228: CONTRIBUTIONS FROM THE MUSEUM OF HISTORY AND TECHNOLOGY 



