Kinematics of Mechanisms from the Time of Watt Part 4

[Ill.u.s.tration: Figure 29.--Robert Willis (1800-1875), Jacksonian Professor, Cambridge University, and author of _Principles of Mechanism_, one of the landmark books in the development of kinematics of mechanisms. Photo courtesy Gonville and Caius College, Cambridge University.]

Giuseppe Antonio Borgnis, an Italian "engineer and member of many academies" and professor of mechanics at the University of Pavia in Italy, in his monumental, nine-volume _Traite complet de mechanique appliquee aux arts_, caused a bifurcation of the structure built upon Hachette's foundation of cla.s.sification when he introduced six orders of machine elements and subdivided these into cla.s.ses and species. His six orders were _recepteurs_ (receivers of motion from the prime mover), _communicateurs_, _modificateurs_ (modifiers of velocity), _supports_ (e.g., bearings), _regulateurs_ (e.g., governors), and _operateurs_, which produced the final effect.[65]

[Footnote 65: Giuseppe Antonio Borgnis, _Theorie de la mecanique usuelle_ in _Traite complet de mecanique appliquee aux arts_, Paris, 1818, vol. 1, pp. xiv-xvi.]

The brilliant Gaspard-Gustave de Coriolis (1792-1843)--remembered mainly for a paper of a dozen pages explaining the nature of the acceleration that bears his name[66]--was another graduate of the Ecole Polytechnique who wrote on the subject of machines. His book,[67] published in 1829, was provoked by his recognition that the designer of machines needed more knowledge than his undergraduate work at the Ecole Polytechnique was likely to give him. Although he embraced a part of Borgnis'

approach, adopting _recepteurs_, _communicateurs_, and _operateurs_, Coriolis indicated by the t.i.tle of his book that he was more concerned with forces than with relative displacements. However, the attractively simple three-element scheme of Coriolis became well fixed in French thinking.[68]

[Footnote 66: Gaspard-Gustave de Coriolis, "Memoire sur les equations du mouvement relatif des systemes de corps," _Journal de l'Ecole Polytechnique_, 1835, vol. 15, pp. 142-154.]

[Footnote 67: Gaspard-Gustave de Coriolis, _De Calcul de l'effet des machines_, Paris, 1829. In this book Coriolis proposed the now generally accepted equation, work = force distance (pp. iii, 2).]

[Footnote 68: The renowned Jean Victor Poncelet lent weight to this scheme. (See Franz Reuleaux, _Theoretische Kinematik: Grundzuge einer Theorie des Maschinenwesens_, Braunschweig, 1875, translated by Alexander B. W. Kennedy as _The Kinematics of Machinery: Outlines of a Theory of Machines_, London, 1876, pp. 11, 487. I have used the Kennedy translation in the Reuleaux references throughout the present work.)]

Michel Chasles (1793-1880), another graduate of the Ecole Polytechnique, contributed some incisive ideas in his papers on instant centers[69]

published during the 1830's, but their tremendous importance in kinematic a.n.a.lysis was not recognized until much later.

[Footnote 69: The instant center was probably first recognized by Jean Bernoulli (1667-1748) in his "De Centro Spontaneo Rotationis" (_Johannis Bernoulli ... Opera Omnia ..._, Lausanne, 1742, vol. 4, p. 265ff.).]

[Ill.u.s.tration: Figure 30.--Franz Reuleaux (1829-1905). His _Theoretische Kinematik_, published in 1875, provided the basis for modern kinematic a.n.a.lysis. Photo courtesy Deutsches Museum, Munich.]

Acting upon Ampere's clear exposition of the province of kinematics and excluding, as Ampere had done, the consideration of forces, an Englishman, Robert Willis, made the next giant stride forward in the a.n.a.lysis of mechanisms. Willis was 37 years old in 1837 when he was appointed professor of natural and experimental philosophy at Cambridge.

In the same year Professor Willis--a man of prodigious energy and industry and an authority on archeology and architectural history as well as mechanisms--read his important paper "On the Teeth of Wheels"

before the Inst.i.tution of Civil Engineers[70] and commenced at Cambridge his lectures on kinematics of mechanisms that culminated in his 1841 book _Principles of Mechanism_.[71]

[Footnote 70: Robert Willis, "On the Teeth of Wheels," _Transactions of the Inst.i.tution of Civil Engineers of London_, 1838, vol. 2, pp.

89-112.]

[Footnote 71: Willis, _op. cit._ (footnote 21). Through the kindness of its owner (Mr. Warren G. Ogden of North Andover, Ma.s.sachusetts), I have had access to Willis' own copy of his 1841 edition of _Principles of Mechanism_. The book is interleaved, and it contains notes made by Willis from time to time until at least 1870, when the second edition was issued. Corrections, emendations, notations of some of his sources (for example, the De Voglie linkage mentioned in footnote 35 above), notes to himself to "examine the general case" and "examine the modern forms" of straight-line devices are interspersed with references to authors that had borrowed from his work without acknowledgment. Of one author Willis writes an indignant "He ignores my work."]

It seemed clear to Willis that the problem of devising a mechanism for a given purpose ought to be attacked systematically, perhaps mathematically, in order to determine "all the forms and arrangements that are applicable to the desired purpose," from which the designer might select the simplest or most suitable combination. "At present," he wrote, "questions of this kind can only be solved by that species of intuition which long familiarity with a subject usually confers upon experienced persons, but which they are totally unable to communicate to others."

In a.n.a.lyzing the process by which a machine was designed, Willis observed: "When the mind of a mechanician is occupied with the contrivance of a machine, he must wait until, in the midst of his meditations, some happy combination presents itself to his mind which may answer his purpose." He ventured the opinion that at this stage of the design process "the motions of the machine are the princ.i.p.al subject of contemplation, rather than the forces applied to it, or the work it has to do." Therefore he was prepared to adopt without reservation Ampere's view of kinematics, and, if possible, to make the science useful to engineers by stating principles that could be applied without having to fit the problem at hand into the framework of the systems of cla.s.sification and description that had gone before. He appraised the "celebrated system" of Lanz and Betancourt as "a merely popular arrangement, notwithstanding the apparently scientific simplicity of the scheme." He rejected this scheme because "no attempt is made to subject the motions to calculation, or to reduce these laws to general formulas, for which indeed the system is totally unfitted."

Borgnis had done a better job, Willis thought, in actually describing machinery, with his "orders" based upon the functions of machine elements or mechanisms within the machine, but again there was no means suggested by which the kinematics of mechanisms could be systematically investigated.

Although Willis commenced his treatise with yet another "synoptical table of the elementary combinations of pure mechanism," his view shifted quickly from description to a.n.a.lysis. He was consistent in his pursuit of a.n.a.lytical methods for "pure mechanism," eschewing any excursions into the realm of forces and absolute velocities. He grasped the important concept of relative displacements of machine elements, and based his treatment upon "the proportions and relations between the velocities and directions of the pieces, and not upon their actual and separate motions."[72]

[Footnote 72: _Ibid._, pp. iv, x-xii, xxi, 15.]

That he did not succeed in developing the "formulas" that would enable the student to determine "all the forms and arrangements that are applicable to the desired purpose"--that he did not present a rational approach to synthesis--is not to be wondered at. Well over a century later we still are nibbling at the fringes of the problem. Willis did, nonetheless, give the thoughtful reader a glimpse of the most powerful tool for kinematic synthesis that has yet been devised; namely, kinematic a.n.a.lysis, in which the argument is confined to the relative displacements of points on links of a mechanism, and through which the designer may grasp the nature of the means at his disposal for the solution of any particular problem.

As remarked by Reuleaux a generation later, there was much in Professor Willis's book that was wrong, but it was an original, thoughtful work that departed in spirit if not always in method from its predecessors.

_Principles of Mechanism_ was a prominent landmark along the road to a rational discipline of machine-kinematics.

A phenomenal engineer of the 19th century was the Scottish professor of civil engineering at the University of Glasgow, William John MacQuorn Rankine. Although he was at the University for only 17 years--he died at the age of 52, in 1872--he turned out during that time four thick manuals on such diverse subjects as civil engineering, ship-building, thermodynamics, and machinery and mill-work, in addition to literally hundreds of papers, articles, and notes for scientific journals and the technical press. Endowed with apparently boundless energy, he found time from his studies to command a battalion of rifle volunteers and to compose and sing comic and patriotic songs. His manuals, often used as textbooks, were widely circulated and went through many editions.

Rankine's work had a profound effect upon the practice of engineering by setting out principles in a form that could be grasped by people who were dismayed by the treatment usually found in the learned journals.

When Rankine's book t.i.tled _A Manual of Machinery and Millwork_ was published in 1869 it was accurately characterized by a reviewer as "dealing with the _principles_ of machinery and millworks, and as such it is entirely distinct from [other works on the same subject] which treat more of the practical applications of such principles than of the principles themselves."[73]

[Footnote 73: _Engineering_, London, August 13, 1869, vol. 8, p. 111.]

Rankine borrowed what appeared useful from Willis' _Principles of Mechanism_ and from other sources. His treatment of kinematics was not as closely reasoned as the later treatises of Reuleaux and Kennedy, which will be considered below. Rankine did, however, for the first time show the utility of instant centers in velocity a.n.a.lysis, although he made use only of the instant centers involving the fixed link of a linkage. Like others before him, he considered the fixed link of a mechanism as something quite different from the movable links, and he did not perceive the possibilities opened up by determining the instant center of two movable links.

Many other books dealing with mechanisms were published during the middle third of the century, but none of them had a discernible influence upon the advance of kinematical ideas.[74] The center of inquiry had by the 1860's shifted from France to Germany. Only by scattered individuals in England, Italy, and France was there any impatience with the well-established, general understanding of the machine-building art.

[Footnote 74: Several such books are referred to by Reuleaux, _op. cit._ (footnote 68), pp. 12-16.]

In Germany, on the other hand, there was a surge of industrial activity that attracted some very able men to the problems of how machines ought to be built. Among the first of these was Ferdinand Redtenbacher (1809-1863), professor of mechanical engineering in the polytechnic school in Karlsruhe, not far from Heidelberg. Redtenbacher, although he despaired of the possibility of finding a "true system on which to base the study of mechanisms," was nevertheless a factor in the development of such a system. He had young Franz Reuleaux in his cla.s.ses for two years, from 1850. During that time the older man's commanding presence, his ability as a lecturer, and his infectious impatience with the existing order influenced Reuleaux to follow the scholar's trail that led him to eminence as an authority of the first rank.[75]

[Footnote 75: See Carl Weihe, "Franz Reuleaux und die Grundlagen seiner Kinematik," Deutsches Museum, Munich, _Abhandlung und Berichte_, 1942, p. 2; Friedrich Klemm, _Technik: Eine Geschichte ihrer Probleme_, Freiburg and Munich, Verlag Karl Alber, 1954, translated by Dorothea W.

Singer as _A History of Western Technology_, New York, Charles Scribner's Sons, 1959, p. 317.]

Before he was 25 years old Franz Reuleaux published, in collaboration with a cla.s.smate, a textbook whose translated t.i.tle would be _Constructive Lessons for the Machine Shop_.[76] His several years in the workshop, before and after coming under Redtenbacher's influence, gave his works a practical flavor, simple and direct. According to one observer, Reuleaux's book exhibited "a recognition of the claims of practice such as Englishmen do not generally a.s.sociate with the writings of a German scientific professor."[77]

[Footnote 76: See Weihe, _op. cit._ (footnote 75), p. 3; Hans Zopke, "Professor Franz Reuleaux," _Ca.s.sier's Magazine_, December 1896, vol.

11, pp. 133-139; _Transactions of the American Society of Mechanical Engineers_, 1904-1905, vol. 26, pp. 813-817.]

[Footnote 77: _Engineering_, London, September 8, 1876, vol. 22, p.

197.]

Reuleaux's original ideas on kinematics, which are responsible for the way in which we look at mechanisms today, were sufficiently formed in 1864 for him to lecture upon them.[78] Starting in 1871, he published his findings serially in the publication of the Verein zur Beforderung des Gewerbefleisses in Preussen (Society for the Advancement of Industry in Prussia), of which he was editor. In 1875 these articles were brought together in the book that established his fame--_Theoretische Kinematik...._[79]

[Footnote 78: A. E. Richard de Jonge, "What is Wrong with Kinematics and Mechanisms?" _Mechanical Engineering_, April 1942, vol. 64, pp. 273-278 (comments on this paper are in _Mechanical Engineering_, October 1942, vol. 64, pp. 744-751); Zopke, _op. cit._ (footnote 76), p. 135.]

[Footnote 79: Reuleaux, _op. cit._ (footnote 68). This was not the last of Reuleaux's books. His trilogy on kinematics and machine design is discussed by De Jonge, _op. cit._ (footnote 78).]

In the introduction of this book, Reuleaux wrote:

In the development of every exact science, its substance having grown sufficiently to make generalization possible, there is a time when a series of changes bring it into clearness. This time has most certainly arrived for the science of kinematics. The number of mechanisms has grown almost out of measure, and the number of ways in which they are applied no less. It has become absolutely impossible still to hold the thread which can lead in any way through this labyrinth by the existing methods.[80]

[Footnote 80: Reuleaux, _op. cit._ (footnote 68), p. 23.]

Reuleaux's confidence that it would be his own work that would bring order out of confusion was well founded. His book had already been translated into Italian and was being translated into French when, only a year after its publication, it was presented by Prof. Alexander B. W.

Kennedy in English translation.[81]

[Footnote 81: _Ibid._, p. iii.]

The book was enthusiastically reviewed by the weekly London journal _Engineering_,[82] and it was given lengthy notice by the rival journal, _The Engineer_. The editor of _The Engineer_ thought that the mechanician would find in it many new ideas, that he would be "taught to detect hitherto hidden resemblances, and that he must part--reluctantly, perhaps--with many of his old notions." "But," added the editor with considerable justice, "that he [the mechanician] would suddenly recognize in Professor Reuleaux's 'kinematic notation,' 'a.n.a.lysis,' and 'synthesis,' the long-felt want of his professional existence we do not for a moment believe."[83] Indeed, the fresh and sharp ideas of Reuleaux were somewhat clouded by a long (600-page) presentation; and his kinematic notation, which required another attempt at cla.s.sification, did not simplify the presentation of radically new ideas.[84]

[Footnote 82: _Engineering_, _loc. cit._ (footnote 77).]

[Footnote 83: _The Engineer_, London, March 30 and April 13, 1877, vol.

43, pp. 211-212, 247-248.]

[Footnote 84: It is perhaps significant that the first paper of the First Conference on Mechanisms at Purdue University was Allen S. Hall's "Mechanisms and Their Cla.s.sification," which appeared in _Machine Design_, December 1953, vol. 25, pp. 174-180. The place of cla.s.sification in kinematic synthesis is suggested in Ferdinand Freudenstein's "Trends in Kinematics of Mechanisms," _Applied Mechanics Reviews_, September 1959, vol. 12, pp. 587-590.]

[Ill.u.s.tration: Figure 31.--Alexander Blackie William Kennedy (1847-1928), translator of Reuleaux' _Theoretische Kinematik_ and discoverer of Kennedy's "Law of Three Centers." From _Minutes of the Proceedings of the Inst.i.tution of Civil Engineers_ (1907, vol. 167, frontispiece).]