The first publication of note in this country on the synthesis of linkages was a practical one, but in conception and undertaking it was a bold enterprise. In a book by John A. Hrones and G. L. Nelson, _Analysis of the Four Bar Linkage_ (1951), the four-bar crank-and-rocker mechanism was exhaustively analyzed mechanically and the results were presented graphically. This work was faintly praised by a Dutch scholar, O. Bottema, who observed that the "complicated 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."[122] Nevertheless, the authors furnished designers with a tool that could be readily, almost instantly, understood (fig. 45), and the atlas has enjoyed wide circulation.[123] The idea of a geometrical approach to synthesis has been exploited by others in more recent publications,[124] and it is likely that many more variations on this theme will appear. [Footnote 122: Bottema, _op. cit._ (footnote 121).] [Footnote 123: 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.] [Footnote 124: R. S. Hartenberg and J. Denavit, "Systematic Mechanism Design," _Machine 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.] [Illustration: Figure 45.--Paths of 11 points on the coupler (horizontal) link are plotted through one cycle. Dashes indicate equal time intervals. From John A. Hrones and G. L. Nelson, _Analysis of the Four Bar Linkage_ (New York, 1951, p. 635).] [Illustration: Figure 46.--Coupler-point path-generating machine for four-bar linkage. This device, built by Professor Willis as a teaching aid for demonstrating 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, pl. 3).] 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,[125] and an increasing interest in the problem is indicated by the extensive literature that has appeared in the last five years.