It remained for Sir Alexander Blackie William Kennedy (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, became professor of engineering at the University College in London in 1874, and eventually served as president 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 exclusively 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 Machinery, was published in 1886 ("partly through pressure 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 publication was unknown to me until some years after I had given it in my lectures."[86] In fact, the law had been published by Siegfried Heinrich Aronhold (1819-1884) in his "Outline of Kinematic Geometry," which appeared in 1872 alongside Reuleaux's series in the journal that Reuleaux edited. Apparently Reuleaux did not perceive its particular significance at that time.[87]
[ [86] Alexander B. W. Kennedy, The Mechanics of Machinery, ed. 3, London, 1898, pp. vii, x.
[ [87] Siegfried Heinrich Aronhold, "Outline of Kinematic Geometry," Verein zur Beförderung des Gewerbefleisses in Preussen, 1872, vol. 51, pp. 129-155. Kennedy's theorem is on pp. 137-138.
Figure 32.—Robert Henry Smith (1852-1916), originator of velocity and acceleration polygons for kinematic analysis. Photo courtesy the Librarian, Birmingham Reference Library, England.
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 acceleration diagrams of linkages.[88] 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.
[ [88] Robert H. Smith, "A New Graphic Analysis of the Kinematics of Mechanisms," Transactions of the Royal Society of Edinburgh, 1882-1885, vol. 32, pp. 507-517, and pl. 82. Smith used this paper as the basis for a chapter in his Graphics or the Art of Calculating by Drawing Lines, London, 1889, pp. 144-162. In a footnote of his paper, Smith credited Fleeming Jenkin (1833-1885) with suggesting the term "image." After discarding as "practically useless" Kennedy's graphical differentiation, Smith complained that he had "failed to find any practical use" for Reuleaux's "method of centroids, more properly called axoids." Such statements were not calculated to encourage Kennedy and Reuleaux to advertise Smith's fame; however, I found no indication that either one took offense at the criticism. Smith's velocity and acceleration diagrams were included (apparently embalmed, so far as American engineers were concerned) in Encyclopaedia Britannica, ed. 11, 1910, vol. 17, pp. 1008-1009.