Kinematics of Mechanisms from the Time of Watt Part 7

The author of the contentious article that appeared in _Mechanical Engineering_ in 1942 under the t.i.tle "What is Wrong with Kinematics and Mechanisms?" made several p.r.o.nouncements that were questioned by various readers, but his remarks on the meagerness of the college courses of kinematics and the "curious fact" that the textbooks "are all strangely similar in their incompleteness" went unchallenged and were, in fact, quite timely.[115]

[Footnote 115: De Jonge, _op. cit._ (footnote 78).]

It appears that in the early 1940's the general cla.s.sroom treatment of accelerations was at a level well below the existing knowledge of the subject, for in a series of articles by two teachers at Purdue attention was called to the serious consequences of errors in acceleration a.n.a.lysis occasioned by omitting the Coriolis component.[116] These authors were reversing a trend that had been given impetus by an article written in 1920 by one of their predecessors, Henry N. Bonis. The earlier article, appearing in a practical-and-proud-of-it technical magazine, demonstrated how the acceleration of a point on a flywheel governor might be determined "without the use of the fict.i.tious acceleration of Coriolis." The author's a.n.a.lysis was right enough, and he closed his article with the unimpeachable statement that "it is better psychologically for the student and practically for the engineer to understand the fundamentals thoroughly than to use a complex formula that may be misapplied." However, many readers undoubtedly read only the lead paragraph, sagely nodded their heads when they reached the word "fict.i.tious," which confirmed their half-formed conviction that anything as abstruse as the Coriolis component could have no bearing upon a practical problem, and turned the page to the "practical kinks"

section.[117]

[Footnote 116: A. S. Hall and E. S. Ault, "How Acceleration a.n.a.lysis Can Be Improved," _Machine Design_, February 1943, vol. 15, pp. 100-102, 162, 164; and March 1943, vol. 15, pp. 90-92, 168, 170. See also A. S.

Hall, "Teaching Coriolis' Law," _Journal of Engineering Education_, June 1948, vol. 38, pp. 757-765.]

[Footnote 117: Henry N. Bonis, "The Law of Coriolis," _American Machinist_, November 18, 1920, vol. 53, pp. 928-930. See also "Acceleration Determinations," _American Machinist_, November 25 and December 2, 1920, vol. 53, pp. 977-981 and 1027-1029.]

Less than 20 years ago one might have read in _Mechanical Engineering_ that "Practical machinery does not originate in mathematical formulas nor in beautiful vector diagrams." While this remark was in a letter evoked by an article, and was not a reflection of editorial policy, it was nevertheless representative of an element in the American tradition of engineering. The unconscious arrogance that is displayed in this statement of the "practical" designer's creed is giving way to recognition of the value of scholarly work. Lest the scholar develop arrogance of another sort, however, it is well to hear the author of the statement out. "A drafting machine is a useful tool," he wrote. "It is not a subst.i.tute for a draftsman."[118]

[Footnote 118: _Mechanical Engineering_, October 1942, vol. 64, p. 746.]

The scholarly interest in a subject is fairly represented by the papers that are published in the transactions of professional societies and, more recently, by original papers that appear in specialized magazines.

From 1900 to 1930 there were few papers on mechanisms, and most of those that did appear were concerned with descriptions of new "mechanical motions." In the 1930's the number of papers reported in _Engineering Index_ increased sharply, but only because the editors had begun to include foreign-language listings.

There has been in Germany a thread of continuity in the kinematics of mechanisms since the time of Reuleaux. While most of the work has had to do with a.n.a.lysis, the teasing question of synthesis that Reuleaux raised in his work has never been ignored. The developments in Germany and elsewhere have been ably reviewed by others,[119] and it is only to be noted here that two of the German papers, published in 1939 in _Maschinenbau_, appear to have been the sparks for the conflagration that still is increasing in extent and intensity. According to summaries in _Engineering Index_, R. Kraus, writing on the synthesis of the double-crank mechanism, drew fire from the Russian Z. S. Bloch, who, in 1940, discussed critically Kraus's articles and proceeded to give the outline of the "correct a.n.a.lysis of the problem" and a general numerical solution for the synthesis of "any four-bar linkage."[120] Russian work in mechanisms, dating back to Chebyshev and following the "Chebyshev theory of synthesis" in which algebraic methods are used to determine paths of minimum deviation from a given curve, has also been reviewed elsewhere,[121] and I can add nothing of value.

[Footnote 119: Grodzinski, Bottema, De Jonge, and Hartenberg and Denavit. For complete t.i.tles see list of selected references.]

[Footnote 120: My source, as noted, is _Engineering Index_. Kraus's articles are reported in 1939 and Bloch's in 1940, both under the section heading "Mechanisms."]

[Footnote 121: A. E. Richard de Jonge, "Are the Russians Ahead in Mechanism a.n.a.lysis?" _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.]

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 conception and undertaking it was a bold enterprise. In a book by John A. Hrones and G. L. Nelson, _a.n.a.lysis of the Four Bar Linkage_ (1951), the four-bar crank-and-rocker mechanism was exhaustively a.n.a.lyzed mechanically and the results were presented graphically. This work was faintly praised by a Dutch scholar, O. Bottema, who observed that the "complicated a.n.a.lytical 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.]

[Ill.u.s.tration: 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, _a.n.a.lysis of the Four Bar Linkage_ (New York, 1951, p. 635).]

[Ill.u.s.tration: 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 a.n.a.lytical theory" of linkages was stimulated by publication of Ferdinand Freudenstein's "a.n.a.lytical 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.

[Footnote 125: _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.]

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 leaders in the field, "we are really talking about a hope for the future rather than a great reality of the present."[126] 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 difficult to see how important new ideas can fail to be produced.

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

_Machine Design_, September 6, 1956, vol. 28, pp. 101-105.]

An annual Conference on Mechanisms, sponsored by Purdue University and _Machine Design_, was inaugurated in 1953 and has met with a lively response. Among other manifestations of current interest in mechanisms, the contributions of Americans to international conferences on mechanisms reflects the growing recognition of the value of scholarly investigation of the kind that can scarcely hope to yield immediately tangible results.

While we look to the future, one may ask how a lengthy view of the past can be justified. It seems to me that there is inherent in the almost feverish activity of the present the danger of becoming so preoccupied with operational theory that the goals may become clouded and the synthesis (let us put it less elegantly: the design) of mechanisms may never quite come into focus. If one knows nothing of the past, I wonder how he can with any confidence decide in what direction he must turn in order to face the future.