Figure 46. — Coupler-point path-generating ma- 

 chine for four-bar linlcage. This device, built 

 by Professor Willis as a teaching aid for demon- 

 strating 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. pi. 3). 



Analysis of the Four Bar Linkage (1951), the four-bar 

 crank-and-rocker mechanism was exhaustively ana- 

 lyzed mechanically and the results were presented 

 graphically. This work was faintly praised by a Dutch 

 scholar, O. Bottema, who observed that the "com- 

 plicated analytical theory of the three-bar [sic] curve 

 has undoubtedly kept the engineer from using it" 

 and who went on to say that "we fully understand 

 the publication of an atlas by Hrones and Nelson 

 containing thousands of trajectories which must be 

 very useful in many design problems." '^^ Neverthe- 

 less, the authors furnished designers with a tool that 

 could be readily, almost instantly, understood (fig. 

 45), and the atlas has enjoyed wide circulation.'-' 

 The idea of a geometrical approach to synthesis has 

 been exploited by others in more recent publica- 

 tions,''^ and it is likely that many more variations 

 on this theme will appear. 



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,'-^ 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 lead- 

 ers in the field, "we are really talking about a hope for 

 the future rather than a great reality of the present."'-* 

 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 



given curve, has also been reviewed elsewhere,'"' 

 and I can add nothing of value. 



'When, after World War II, some of the possibilities 

 of kinematic synthesis were recognized in the United 

 States, a few perceptive teachers fanned the tinder 

 into an open flame. 



The first publication of note in this country on the 

 synthesis of linkages was a practical one, but in con- 

 ception and undertaking it was a bold enterprise. 

 In a book by John A. Hrones and G. L. Nelson, 



'^' A. E. Richard de Jonge, "Are the Russians Ahead in 

 Mechanism Analysis?" Machine Design, September 1951, vol. 23, 

 pp. 127, 200-208; O. Bottema, "Recent Work on Kinematics," 

 Applied Mechanics Reviews, April 1953, vol. 6, pp. 169-170. 



'^- Bottema, op. cil. (footnote 121). 



'-^ In 1851 Robert Willis had designed a coupler-point path- 

 generating machine (fig. 46) that could have been used to 

 produce a work similar to that of Hrones and Nelson. 



i2< R. S. Hartenberg and J. Denavit, "Systematic Mechanism 

 Design," Macliine Design, September 1954, vol. 26, pp. 167-175, 

 and October 1954, vol. 26, pp. 257-265; A. S. Hall, A. R. 

 Holowenko, and H. G. Laughlin, "Four-Bar Lever Crank 

 Mechanism," Design News, September 15, 1957, vol. 12, pp. 

 130-139, October 1, 1957, vol. 12, pp. 145-154, and October 

 15, 1957, vol. 12, pp. 132-141. For a nomographic approach, 

 with particular application to computers, see Antonin Svoboda, 

 Computing Mechanisms and Linkages, New York, 1948. 



'2' Transactions of the American Society of Mechanical Engineers, 

 1954, vol. 76, pp. 483-492. See also Transactions of the American 

 Society of Mechanical Engineers, 1955, vol. 77, pp. 853-861, and 

 1956, vol. 78, pp. 779-787. 



126 R. S. Hartenberg and J. Denavit, "Kinematic Synthesis," 

 Machine Design, September 6, 1956, vol. 28, pp. 101-105. 



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