nism. He devoted 40 pages to showing, with obvious 

 delight, the kinematic identity of one design after an- 

 other of rotary steam engines, demolishing for all time 

 the fond hopes of ingenious but ill-informed inventors 

 who think that improvements and advances in mecha- 

 nism design consist in contortion and complexity. 



The chapter on synthesis was likewise fresh, but it 

 consisted of a discussion, not a system; and Reuleaux 

 stressed the idea that I have mentioned above in con- 

 nection with Willis' book, that synthesis will be suc- 

 cessful in proportion to the designer's understanding 

 and appreciation of analysis. Reuleaux tried to put 

 the designer on the right track by showing him clearly 

 "the essential simplicity of the means with which we 

 have to work" and by demonstrating to him "that the 

 many things which have to be done can be done with 

 but few means, and that the principles underlying 

 them all lie clearly before us."'^ 



It remained for Sir Alexander Blackie William Ken- 

 nedy (1847-1928) and Robert Henry Smith (1852- 

 1916) to add to Reuleaux's work the elements that 

 would give kinematic analysis essentially its modern 

 shape. 



Kennedy, the translator of Reuleaux's book, be- 

 came professor of engineering at the University Col- 

 lege in London in 1874, and eventually served as presi- 

 dent both of the Institution of Mechanical Engineers 

 and of the Institution of Civil Engineers. Smith, who 

 had taught in the Imperial University of Japan, was 

 professor of engineering at Mason College, now a part 

 of Birmingham University, in England. 



While Reuleaux had used instant centers almost ex- 

 clusively for the construction of centrodes (paths of 

 successive positions of an instant center). Professor 

 Kennedy recognized that instant centers might be 

 used in velocity analysis. His book. Mechanics of Ma- 

 chinery, was published in 1886 ("partly through pres- 

 sure of work and partly through ill-health, this book 

 appears only now"). In it he developed the law of 

 three centers, now known as Kennedy's theorem. He 

 noted that his law of three centers "was first given, I 

 believe, by Aronhold, although its previous publica- 

 tion was unknown to me until some years after I had 

 given it in my lectures." ^^ In fact, the law had been 

 published by Siegfried Heinrich Aronhold (1819- 

 1884) in his "Oudine of Kinematic Geometry," which 

 appeared in 1872 alongside Reuleaux's series in the 



Figure 32. — Robert Henry Smith (1852-1916), 

 originator of velocity and acceleration polygons 

 for kinematic analysis. Photo courtesy the 

 Librarian, Birmingham Reference Library, 

 England. 



journal that Reuleaux edited. Apparently Reuleaux 

 did not preceive its particular significance at that 

 time.'" 



Kennedy, after locating instant centers, determined 

 velocities by calculation and accelerations by graphical 

 differentiation of velocities, and he noted in his 

 preface that he had been unable, for a variety of 

 reasons, to make use in his book of Smith's recent 

 work. Professor Kennedy at least was aware of 

 Smith's surprisingly advanced ideas, which seem to 

 have been generally ignored by Americans and 

 Englishmen alike. 



Professor Smith, in a paper before the Royal 

 Society of Edinburgh in 1885, stated clearly the 

 ideas and methods for construction of velocity and 

 acceleratioia diagrams of linkages.** For the first 

 time, velocity and acceleration "images" of links 

 (fig. 33) were presented. It is unfortunate that 

 Smith's ideas were permitted to languish for so long 

 a time. 



By 1885 nearly all the tools for modern kinematic 



*5 Reuleaux, op. cit. (footnote 68), p. 582. 

 ^ Alexander B. W. Kennedy, The Mechanics of Machinery, ed. 

 3, London, 1898, pp. vii, x. 



^' Siegfried Heinrich Aronhold, "Outline of Kinematic Geoni- 

 etry," Verein zur Bejorderung des Gewerbefleisses in Preussen, 1872, 

 vol. 51, pp. 129-155. Kennedy's theorem is on pp. 137-138. 



" Robert H. Smith, "A New Graphic Analysis of the Kine- 

 matics of Mechanisms," Transactions of the Royal Society of Edin- 

 burgh, 1882-1885, vol. 32, pp. 507-517, and pi. 82. Smith used 



PAPER 27: KINEMATICS FROM THE TIME OF WATT 



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