Kinematics of Mechanisms from the Time of Watt Part 5

Nevertheless, no earlier author had seen the problem of kinematic a.n.a.lysis so clearly or had introduced so much that was fresh, new, and of lasting value.

Reuleaux was first to state the concept of the pair; by his concept of the expansion of pairs he was able to show similarities in mechanisms that had no apparent relation. He was first to recognize that the fixed link of a mechanism was kinematically the same as the movable links.

This led him to the important notion of inversion of linkages, fixing successively the various links and thus changing the function of the mechanism. He devoted 40 pages to showing, with obvious delight, the kinematic ident.i.ty of one design after another of rotary steam engines, demolis.h.i.+ng for all time the fond hopes of ingenious but ill-informed inventors who think that improvements and advances in mechanism 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 connection with Willis' book, that synthesis will be successful in proportion to the designer's understanding and appreciation of a.n.a.lysis. 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."[85]

[Footnote 85: Reuleaux, _op. cit._ (footnote 68), p. 582.]

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 a.n.a.lysis 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 Inst.i.tution of Mechanical Engineers and of the Inst.i.tution of Civil Engineers. Smith, who had taught in the Imperial University of j.a.pan, 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 a.n.a.lysis. 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]

[Footnote 86: Alexander B. W. Kennedy, _The Mechanics of Machinery_, ed.

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

[Footnote 87: Siegfried Heinrich Aronhold, "Outline of Kinematic Geometry," _Verein zur Beforderung des Gewerbefleisses in Preussen_, 1872, vol. 51, pp. 129-155. Kennedy's theorem is on pp. 137-138.]

[Ill.u.s.tration: Figure 32.--Robert Henry Smith (1852-1916), originator of velocity and acceleration polygons for kinematic a.n.a.lysis. 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.

[Footnote 88: Robert H. Smith, "A New Graphic a.n.a.lysis 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.]

[Ill.u.s.tration: Figure 33.--Smith's velocity image (the two figures at top), and his velocity, mechanism, and acceleration diagrams, 1885. The image of link BACD is shown as figure _bacd_. The lines _pa_, _pb_, _pc_, and _pd_ are velocity vectors. This novel, original, and powerful a.n.a.lytical method was not generally adopted in English or American schools until nearly 50 years after its inception. From _Transactions of the Royal Society of Edinburgh_ (1882-1885, vol. 32, pl. 82).]

By 1885 nearly all the tools for modern kinematic a.n.a.lysis had been forged. Before discussing subsequent developments in a.n.a.lysis and synthesis, however, it will be profitable to inquire what the mechanician--designer and builder of machines--was doing while all of this intellectual effort was being expended.

Mechanicians and Mechanisms

While the inductive process of recognizing and stating true principles of the kinematics of mechanisms was proceeding through three generations of French, English, and finally German scholars, the actual design of mechanisms went ahead with scant regard for what the scholars were doing and saying.

After the demonstration by Boulton and Watt that large mechanisms could be wrought with sufficient precision to be useful, the English tool builders Maudslay, Roberts, Clement, Nasmyth, and Whitworth developed machine tools of increasing size and truth. The design of other machinery kept pace with--sometimes just behind, sometimes just ahead of--the capacity and capability of machine tools. In general, there was an increasing sophistication of mechanisms that could only be accounted for by an increase of information with which the individual designer could start.

Reuleaux pointed out in 1875 that the "almost feverish progress made in the regions of technical work" was "not a consequence of any increased capacity for intellectual action in the race, but only the perfecting and extending of the tools with which the intellect works." These tools, he said, "have increased in number just like those in the modern mechanical workshop--the men who work them remain the same." Reuleaux went on to say that the theory and practice of machine-kinematics had "carried on a separate existence side by side." The reason for this failure to apply theory to practice, and vice versa, must be sought in the defects of the theory, he thought, because "the mechanisms themselves have been quietly developed in practical machine-design, by invention and improvement, regardless of whether or not they were accorded any direct and proper theoretical recognition." He pointed out that the theories had thus far "furnished no new mechanisms."[89]

[Footnote 89: Reuleaux, _op. cit._ (footnote 68), p. 8.]

It is reasonable, therefore, to ask what was responsible for the appearance of new mechanisms, and then to see what sort of mechanisms had their origins in this period.

It is immediately evident to a designer that the progress in mechanisms came about through the spread of knowledge of what had already been done; but designers of the last century had neither the leisure nor means to be constantly visiting other workshops, near and far, to observe and study the latest developments. In the 1800's, as now, word must in the main be spread by the printed page.

Hachette's chart (fig. 28) had set the pattern for display of mechanical contrivances in practical journals and in the large number of mechanical dictionaries that were compiled to meet an apparent demand for such information. It is a little surprising, however, to find how persistent were some of Hachette's ideas that could only have come from the uppermost superficial layer of his cranium. See, for example, his "anch.o.r.ed ferryboat" (fig. 34). This device, employed by Hachette to show conversion of continuous rectilinear motion into alternating circular motion, appeared in one publication after another throughout the 19th century. As late as 1903 the ferryboat was still anch.o.r.ed in Hisc.o.x's _Mechanical Movements_, although the tide had changed (fig.

35).[90]

[Footnote 90: Gardner D. Hisc.o.x, ed., _Mechanical Movements_, ed. 10, New York, 1903, p. 151. The ferryboat did not appear in the 1917 edition.]

[Ill.u.s.tration: Figure 34.--Hachette's ferryboat of 1808, a "machine" for converting continuous rectilinear motion into alternating circular motion. From Phillipe Louis Lanz and Augustin de Betancourt, _Essai sur la composition des machines_ (Paris, 1808, pl. 2).]

[Ill.u.s.tration: Figure 35.--Ferryboat from Gardner D. Hisc.o.x, ed., _Mechanical Movements_ (ed. 10, New York, 1903, p. 151).]

During the upsurge of the Lyceum--or working-man's inst.i.tute--movement in the 1820's, Jacob Bigelow, Rumford professor of applied science at Harvard University, gave his popular lectures on the "Elements of Technology" before capacity audiences in Boston. In preparing his lecture on the elements of machinery, Bigelow used as his authorities Hachette, Lanz and Betancourt, and Olinthus Gregory's mechanical dictionary, an English work in which Hachette's cla.s.sification scheme was copied and his chart reproduced.[91]

[Footnote 91: Jacob Bigelow, _Elements of Technology_, ed. 2, Boston, 1831, pp. 231-256; Olinthus Gregory, _A Treatise of Mechanics_, 3 vols., ed. 3, London, 1815.]

A translation of the work of Lanz and Betancourt[92] under the t.i.tle _a.n.a.lytical Essay on the Construction of Machines_, was published about 1820 at London by Rudolph Ackermann (for whom the Ackermann steering linkage was named), and their synoptic chart was reprinted again in 1822 in Durham.[93] In the United States, _Appleton's Dictionary of Machines_[94] (1851) adopted the same system and used the same figures.

Apparently the wood engraver traced directly onto his block the figures from one of the reprints of Lanz and Betancourt's chart because the figures are in every case exact mirror images of the originals.

[Footnote 92: Rudolph Ackermann, _a.n.a.lytical Essay on the Construction of Machines_, London, about 1820, a translation of Lanz and Betancourt, _op. cit._ (footnote 64).]

[Footnote 93: Thomas Fenwick, _Essays on Practical Mechanics_, ed. 3, Durham, England, 1822.]

[Footnote 94: _Appleton's Dictionary of Machines, Mechanics, Engine-Work, and Engineering_, 2 vols., New York, 1851 ("Motion").]

In the _Dictionary of Engineering_[95] (London, 1873), the figures were redrawn and dozens of mechanisms were added to the repertory of mechanical motions; the result was a fair catalog of sound ideas. The ferryboat still tugged at its anchor cable, however.[96] _Knight's American Mechanical Dictionary_,[97] a cla.s.sic of detailed pictorial information compiled by a U.S. patent examiner, contained well over 10,000 finely detailed figures of various kinds of mechanical contrivances. Knight did not have a separate section on mechanisms, but there was little need for one of the Hachette variety, because his whole dictionary was a huge and fascinating compendium of ideas to be filed away in the synthetic mind. One reason for the popularity and usefulness of the various pictorial works was the peculiar ability of a wood or steel engraving to convey precise mechanical information, an advantage not possessed by modern halftone processes.

[Footnote 95: E. F. and N. Spon, _Dictionary of Engineering_, London 1873, pp. 2421-2452.]

[Footnote 96: _Ibid._, p. 2447.]

[Footnote 97: Edward H. Knight, _Knight's American Mechanical Dictionary_, 3 vols., New York 1874-1876.]

[Ill.u.s.tration: Figure 36.--Typical mechanisms from E. F. and N. Spon, _Dictionary of Engineering_ (London, 1873, pp. 2426, 2478).]

Many patent journals and other mechanical periodicals concerned with mechanics were available in English from the beginning of the 19th century, but few of them found their way into the hands of American mechanicians until after 1820. Oliver Evans (1755-1819) had much to say about "the difficulties inventive mechanics labored under for want of published records of what had preceded them, and for works of reference to help the beginner."[98] In 1817 the _North American Review_ also remarked upon the scarcity of engineering books in America.[99]

[Footnote 98: George Escol Sellers in _American Machinist_, July 12, 1884, vol. 7, p. 3.]

[Footnote 99: _North-American Review and Miscellaneous Journal_, 1819, new ser., vol. 8, pp. 13-15, 25.]

The _Scientific American_, which appeared in 1845 as a patent journal edited by the patent promoter Rufus Porter, carried almost from its beginning a column or so ent.i.tled "Mechanical Movements," in which one or two mechanisms--borrowed from an English work that had borrowed from a French work--were ill.u.s.trated and explained. The _American Artisan_ began a similar series in 1864, and in 1868 it published a compilation of the series as _Five Hundred and Seven Mechanical Movements_, "embracing all those which are most important in dynamics, hydraulics, hydrostatics, pneumatics, steam engines ... and miscellaneous machinery."[100] This collection went through many editions; it was last revived in 1943 under the t.i.tle _A Manual of Mechanical Movements_.

This 1943 edition included photographs of kinematic models.[101]

[Footnote 100: Henry T. Brown, ed., _Five Hundred and Seven Mechanical Movements_, New York, 1868.]

[Footnote 101: Will M. Clark, _A Manual of Mechanical Movements_, Garden City, New York, 1943.]

Many readers are already well acquainted with the three volumes of _Ingenious Mechanisms for Designers and Inventors_,[102] a work that resulted from a contest, announced by _Machinery_ (vol. 33, p. 405) in 1927, in which seven prizes were offered for the seven best articles on unpublished ingenious mechanisms.

[Footnote 102: _Ingenious Mechanisms for Designers and Inventors_ (vols.

1 and 2 edited by F. D. Jones, vol. 3 edited by H. L. Horton), New York, Industrial Press, 1930-1951.]