Chapter II: Part 2

[Footnote 61: Biographical notices of Monge and Hachette appear in _Encyclopaedia Britannica_, ed. 11. See also _L'Ecole Polytechnique, Livre du Centenaire_, Paris, 1895, vol. 1, p. 11ff.]

Gaspard Monge (1746-1818), who while a draftsman at Mézières originated the methods of descriptive geometry, came to the Ecole Polytechnique as professor of mathematics upon its founding in 1794, the second year of the French Republic. According to Jean Nicolas Pierre Hachette (1769-1834), who was junior to Monge in the department of descriptive geometry, Monge planned to give a two-months' course devoted to the elements of machines. Having barely gotten his department under way, however, Monge became involved in Napoleon's ambitious scientific mission to Egypt and, taking leave of his family and his students, embarked for the distant shores.

"Being left in charge," wrote Hachette, "I prepared the course of which Monge had given only the first idea, and I pursued the study of machines in order to analyze and classify them, and to relate geometrical and mechanical principles to their construction." Changes of curriculum delayed introduction of the course until 1806, and not until 1811 was his textbook ready, but the outline of his ideas was presented to his classes in chart form (fig. 28). This chart was the first of the widely popular synoptical tables of mechanical movements.[62]

[Footnote 62: Jean N. P. Hachette, _Traité élémentaire des machines_, Paris, 1811, p. v.]

From Jean N. P. Hachette, _Traité Élémentaire des Machines_ (Paris, 1811, pl. 1).]

Hachette classified all mechanisms by considering the conversion of one motion into another. His elementary motions were continuous circular, alternating circular, continuous rectilinear, and alternating rectilinear. Combining one motion with another--for example, a treadle and crank converted alternating circular to continuous circular motion--he devised a system that supplied a frame of reference for the study of mechanisms. In the U.S. Military Academy at West Point, Hachette's treatise, in the original French, was used as a textbook in 1824, and perhaps earlier.[63]

[Footnote 63: This work was among the books sent back by Sylvanus Thayer when he visited France in 1816 to observe the education of the French army cadets. Thayer's visit resulted in his adopting the philosophy of the Ecole Polytechnique in his reorganization of the U.S. Military Academy and, incidentally, in his inclusion of Hachette's course in the Academy's curriculum (U.S. Congress, _American State Papers_, Washington, 1832-1861, Class v, Military Affairs, vol. 2, p. 661: Sidney Forman, _West Point_, New York, 1950, pp. 36-60). There is a collection of miscellaneous papers (indexed under Sylvanus Thayer and William McRee, U.S. National Archives, RG 77, Office, Chief of Engineers, Boxes 1 and 6) pertaining to the U.S. Military Academy of this period, but I found no mention of kinematics in this collection.]

Lanz and Bétancourt, scholars from Spain at the Ecole Polytechnique, plugged some of the gaps in Hachette's system by adding continuous and alternating curvilinear motion, which doubled the number of combinations to be treated, but the advance of their work over that of Hachette was one of degree rather than of kind.[64]

[Footnote 64: Phillipe Louis Lanz and Augustin de Bétancourt, _Essai sur la composition des machines_, Paris, 1808. Hachette's chart and an outline of his elementary course on machines is bound with the Princeton University Library copy of the Lanz and Bétancourt work. This copy probably represents the first textbook of kinematics. Bétancourt was born in 1760 in Teneriffe, attended the military school in Madrid, and became inspector-general of Spanish roads and canals. He was in England before 1789, learning how to build Watt engines, and he introduced the engines to Paris in 1790 (see Farey, _op. cit._, p. 655). He entered Russian service in 1808 and died in St. Petersburg in 1826 J. C. Poggendorff, _Biographisches-literarisches Handwörterbuch für Mathematik ..._, Leipzig, 1863, vol. 1.]

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 _Traité complet de méchanique appliquée aux arts_, caused a bifurcation of the structure built upon Hachette's foundation of classification when he introduced six orders of machine elements and subdivided these into classes and species. His six orders were _récepteurs_ (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, _Théorie de la mécanique usuelle_ in _Traité complet de mécanique appliquée 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 _récepteurs_, _communicateurs_, and _operateurs_, Coriolis indicated by the title 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 systèmes 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: Grundzüge 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 analysis 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.).]

Acting upon Ampère's clear exposition of the province of kinematics and excluding, as Ampère had done, the consideration of forces, an Englishman, Robert Willis, made the next giant stride forward in the analysis 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 Institution 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 Institution 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, Massachusetts), 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 analyzing 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 principal 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 Ampère'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 classification and description that had gone before. He appraised the "celebrated system" of Lanz and Bétancourt 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 analysis. He was consistent in his pursuit of analytical 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 analysis, 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 titled _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 analysis, 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 classes 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 classmate, a textbook whose translated title 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 associate with the writings of a German scientific professor."[77]

[Footnote 76: See Weihe, _op. cit._ (footnote 75), p. 3; Hans Zopke, "Professor Franz Reuleaux," _Cassier'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 Beförderung 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,' 'analysis,' 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 classification, 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 Classification," which appeared in _Machine Design_, December 1953, vol. 25, pp. 174-180. The place of classification in kinematic synthesis is suggested in Ferdinand Freudenstein's "Trends in Kinematics of Mechanisms," _Applied Mechanics Reviews_, September 1959, vol. 12, pp. 587-590.]

Nevertheless, no earlier author had seen the problem of kinematic analysis 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 identity of one design after another of rotary steam engines, demolishing 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 analysis. 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 analysis 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 Institution of Mechanical Engineers and of the Institution of Civil Engineers. Smith, who had taught in the Imperial University of Japan, 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 analysis. 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 Beförderung des Gewerbefleisses in Preussen_, 1872, vol. 51, pp. 129-155. Kennedy's theorem is on pp. 137-138.]

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 Analysis 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.]

By 1885 nearly all the tools for modern kinematic analysis had been forged. Before discussing subsequent developments in analysis 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 "anchored 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 anchored in Hiscox's _Mechanical Movements_, although the tide had changed (fig. 35).[90]

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

During the upsurge of the Lyceum--or working-man's institute--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 Bétancourt, and Olinthus Gregory's mechanical dictionary, an English work in which Hachette's classification 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 Bétancourt[92] under the title _Analytical 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 Bétancourt's chart because the figures are in every case exact mirror images of the originals.

[Footnote 92: Rudolph Ackermann, _Analytical Essay on the Construction of Machines_, London, about 1820, a translation of Lanz and Bétancourt, _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 classic 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.]

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 entitled "Mechanical Movements," in which one or two mechanisms--borrowed from an English work that had borrowed from a French work--were illustrated 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 title _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.]

There was an interesting class of United States patents called "Mechanical Movements" that comprised scores of patents issued throughout the middle decades of the 19th century. A sampling of these patents shows that while some were for devices used in particular machines--such as a ratchet device for a numbering machine, a locking index for gunmaking machinery, and a few gear trains--the great majority were for converting reciprocating motion to rotary motion. Even a cursory examination of these patents reveals an appalling absence of sound mechanical sense, and many of them appear to be attempts at "perpetual motion," in spite of an occasional disclaimer of such intent.

Typical of many of these patented devices was a linkage for "multiplying" the motion of a flywheel, proposed in 1841 by Charles Johnson of Amity, Illinois (fig. 37). "It is not pretended that there is any actual gain of power," wrote Mr. Johnson; and probably he meant it. The avowed purpose of his linkage was to increase the speed of a flywheel and thus decrease its size.[103]

[Footnote 103: U.S. Patent 2295, October 11, 1841.]

An Englishman who a few years earlier had invented a "new Motion" had claimed that his device would supersede the "ordinary crank in steam engines," the beam, parallel motion, and "external flywheel," reduce friction, neutralize "all extra contending power," and leave nothing for the piston to do "but the work intended to be done."

A correspondent of the _Repertory of Patent Inventions_ made short work of this device: "There is hardly one assertion that can be supported by proof," he wrote, "and most of them are palpable misstatements." The writer attacked "the 'beetle impetus wheel,' which he [the inventor] thinks us all so beetle-headed, as not to perceive to be a flywheel," and concluded with the statement: "In short the whole production evinces gross ignorance either of machinery, if the patentee really believed what he asserted, or of mankind, if he did not."[104]

[Footnote 104: _Repertory of Patent Inventions_, ser. 3, October 1828, vol. 7, pp. 196-200, and December 1828, vol. 7, pp. 357-361.]

Although many of the mechanisms for which patents were taken out were designed by persons who would make no use of the principles involved even if such principles could at that time have been clearly stated, it is a regrettable fact that worthless mechanisms often got as much space as sound ones in patent journals, and objections such as the one above were infrequent. The slanted information thus conveyed to the young mechanician, who was just accumulating his first kinematic repertory, was at times sadly misleading.

From even this sketchy outline of the literature on the subject, it should be fairly evident that there has been available to the mechanician an enormous quantity of information about mechanical linkages and other devices. Whatever one may think of the quality of the literature, it has undoubtedly had influence not only in supplying designers with information but in forming a tradition of how one ought to supply the background that will enable the mind to assemble and synthesize the necessary mechanism for a given purpose.[105]

[Footnote 105: Some additional catalogs of "mechanical movements" are listed in the selected references at the end of this paper.]

Some of the mechanisms that have been given names--such as the Watt straight-line linkage and the Geneva stop--have appeared in textbook after textbook. Their only excuse for being seems to be that the authors must include them or risk censure by colleagues. Such mechanisms are more interesting to a reader, certainly, when he has some idea of what the name has to do with the mechanism, and who originated it. One such mechanism is the drag link.

After I had learned of the drag link (as most American engineering students do), I wondered for awhile, and eventually despaired of making any sense out of the term. What, I wanted to know, was being dragged? Recently, in Nicholson's _Operative Mechanic and British Machinist_ (1826), I ran across the sketch reproduced here as figure 38. This figure, explained Mr. Nicholson (in vol. 1, p. 32) "represents the coupling link used by Messrs. Boulton and Watt in their portable steam engines. A, a strong iron pin, projecting from one of the arms of the fly-wheel B; D, a crank connected with the shaft C; and E, a link to couple the pin A and the crank D together, so the motion may be communicated to the shaft C." So the drag link was actually a link of a coupling. Nothing could be more logical. A drag link mechanism now makes sense to me.

Directly related to the drag link coupling were the patents of John Oldham (1779-1840), an Irish engineer who is remembered mainly for the coupling that bears his name (fig. 39). His three patents, which were for various forms of steamboat feathering paddle wheels, involved linkages kinematically similar to the drag link coupling, although it is quite unlikely that Oldham recognized the similarity. However, for his well-known coupling, which employs an inversion of the elliptical trammel mechanism, I have found no evidence of a patent. Probably it was part of the machinery that he designed for the Bank of Ireland's printing house, of which Oldham was manager for many years. "Mr. Oldham and his beautiful system" were brought to the Bank of England in 1836, where Oldham remained until his death in 1840.[106]

[Footnote 106: Oldham's paddle-wheel patents were British Patents 4169 (October 10, 1817), 4429 (January 15, 1820), and 5445 (February 1, 1827). Robert Willis (_op. cit._ footnote 21, p. 167) noticed the existence of the coupling. Drawings or descriptions of the banknote machinery apparently have not been published though they probably still exist in the banks' archives. The quotation is from Frederick G. Hall, _The Bank of Ireland 1783-1946_, Dublin, 1949. John Francis in his _History of the Bank of England_ (London, 1848, vol. 2, p. 232) wrote: "The new machinery for printing the notes, which was introduced by Mr. Oldham ... is well worthy of a visit, but would be uninteresting to delineate."]

The Geneva stop mechanism (fig. 40) was properly described by Willis as a device to permit less than a full revolution of the star wheel and thus to prevent overwinding of a watch spring. It was called Geneva stop because it was used in Geneva watches. The Geneva wheel mechanism, which permits full rotation of the star wheel and which is frequently used for intermittent drives, was improperly called a Geneva stop in a recent textbook probably because the logical origin of the term had been lost.

The name for the Scotch yoke seems to be of fairly recent origin, the linkage being called by a Scotsman in 1869 a "crank and slot-headed sliding rod" (fig. 41). I suppose that it is now known as a Scotch yoke because, in America at least, a "Scotch" was a slotted bar that was slipped under a collar on a string of well-drilling tools to support them while a section was being added (fig. 42).

It was surprising to me to find that the Ackermann steering linkage, used today on most automobiles, was patented in 1818 when Detroit was still a frontier town.[107] Furthermore, the man who took out the patent described himself as Rudolph Ackermann, publisher and printseller. I thought I had the necessary clue to the linkage's origin when I noticed that the first English translation of the Lanz and Bétancourt treatise was published by Ackermann, but the connection finally proved to be more logical, if less direct. Ackermann (1764-1834), son of a Bavarian coach builder, had spent a number of years designing coaches for English gentlemen in London, where he made his home. One of his more notable commissions was for the design of Admiral Nelson's funeral car in 1805. The Ackermann steering linkage was not actually Ackermann's invention, although he took out the British patent in his name and promoted the introduction of the running gear of which the linkage was a part (fig. 43). The actual inventor was Ackermann's friend George Lankensperger of Munich, coachmaker to the King of Bavaria. The advantage of being able to turn a carriage around in a limited area without danger of oversetting was immediately obvious, and while there was considerable opposition by English coachmakers to an innovation for which a premium had to be paid, the invention soon "made its way from its own intrinsic merit," as Ackermann predicted it would.[108]

[Footnote 107: British Patent 4212, January 27, 1818.]

[Footnote 108: Rudolph Ackermann, _Observations on Ackermann's Patent Moveable Axles_, London, 1819. It was interesting to me to note an abstract of W. A. Wolfe's paper "Analytical Design of an Ackermann Steering Linkage" in _Mechanical Engineering_, September 1958, vol. 80, p. 92.]

The Whitworth quick-return mechanism (fig. 44) was first applied to a slotter, or vertical shaper, in 1849, and was exhibited in 1851 at the Great Exhibition in London.[109] Willis' comments on the mechanism are reproduced in figure 44. I hope that Sir Joseph Whitworth (1803-1887) will be remembered for sounder mechanical contrivances than this.

[Footnote 109: The quick-return mechanism (British Patent 12907, December 19, 1849) was perhaps first publicly described in Charles Tomlinson, ed., _Cyclopaedia of Useful Arts and Manufactures_, London, 1854, vol. 1, p. cxliv.]

Mechanisms in America, 1875-1955

Engineering colleges in the United States were occupied until the late 1940's with extending, refining, and sharpening the tools of analysis that had been suggested by Willis, Rankine, Reuleaux, Kennedy, and Smith. The actual practice of kinematic synthesis went on apace, but designers often declined such help as the analytical methods might give them and there was little exchange of ideas between scholars and practitioners.

The capability and precision of machine tools were greatly enhanced during this period, although, with the exception of the centerless grinder, no significant new types of tools appeared. The machines that were made with machine tools increased in complexity and, with the introduction of ideas that made mass production of complex mechanical products economically feasible, there was an accelerating increase in quantity. The adoption of standards for all sorts of component parts also had an important bearing upon the ability of a designer economically to produce mechanisms that operated very nearly as he hoped they would.

The study of kinematics has been considered for nearly 80 years as a necessary part of the mechanical engineer's training, as the dozens of textbooks that have been published over the years make amply clear. Until recently, however, one would look in vain for original work in America in the analysis or rational synthesis of mechanisms.

One of the very earliest American textbooks of kinematics was the 1883 work of Charles W. MacCord (1836-1915), who had been appointed professor of mechanical drawing at Stevens Institute of Technology in Hoboken after serving John Ericsson, designer of the _Monitor_, as chief draftsman during the Civil War.[110] Based upon the findings of Willis and Rankine, MacCord's _Kinematics_ came too early to be influenced by Kennedy's improvements upon Reuleaux's work.

[Footnote 110: A biographical notice and a bibliography of MacCord appears in _Morton Memorial: A History of the Stevens Institute of Technology_, Hoboken, 1905, pp. 219-222.]

When the faculty at Washington University in St. Louis introduced in 1885 a curriculum in "dynamic engineering," reflecting a dissatisfaction with the traditional branches of engineering, kinematics was a senior subject and was taught from Rankine's _Machinery and Millwork_.[111]

[Footnote 111: _Transactions of the American Society of Mechanical Engineers_, 1885-1886, vol. 7, p. 757.]

At Massachusetts Institute of Technology, Peter Schwamb, professor of machine design, put together in 1885 a set of printed notes on the kinematics of mechanisms, based on Reuleaux's and Rankine's works. Out of these notes grew one of the most durable of American textbooks, first published in 1904.[112] In the first edition of this work, acceleration was mentioned only once in passing (on p. 4). Velocities in linkages were determined by orthogonal components transferred from link to link. Instant centers were used only to determine velocities of various points on the same link. Angular velocity ratios were frequently noted. In the third edition, published in 1921, linear and angular accelerations were defined, but no acceleration analyses were made. Velocity analyses were altered without essential change. The fourth edition (1930) was essentially unchanged from the previous one. Treatment of velocity analysis was improved in the fifth edition (1938) and acceleration analysis was added. A sixth edition, further revised by Prof. V. L. Doughtie of the University of Texas, appeared in 1947.

[Footnote 112: Peter Schwamb and Allyne L. Merrill, _Elements of Mechanism_, New York, 1904. In addition to the work of Reuleaux and Rankine, the authors acknowledged their use of the publications of Charles MacCord, Stillman W. Robinson, Thomas W. Goodeve, and William C. Unwin. For complete titles see the list of selected references.]

Before 1900, several other books on mechanisms had been published, and all followed one or another of the patterns of their predecessors. Professors Woods and Stahl, at the Universities of Illinois and Purdue, respectively, who published their _Elementary Mechanism_ in 1885, said in their preface what has been said by many other American authors and what should have been said by many more. "We make little claim to originality of the subject-matter," wrote Woods and Stahl, "free use having been made of all available matter on the subject.... Our claim to consideration is based almost entirely on the manner in which the subject has been presented." Not content with this disclaimer, they continued: "There is, in fact, very little room for such originality, the ground having been almost completely covered by previous writers."[113]

[Footnote 113: Arthur T. Woods and Albert W. Stahl, _Elementary Mechanism_, New York, 1885.]

The similarity and aridity of kinematics textbooks in this country from around 1910 are most striking. The generation of textbook writers following MacCord, Woods and Stahl, Barr of Cornell, Robinson of Ohio State, and Schwamb and Merrill managed to squeeze out any remaining juice in the subject, and the dessication and sterilization of textbooks was nearly complete when my generation used them in the 1930's. Kinematics was then, in more than one school, very nearly as it was characterized by an observer in 1942--"on an intellectual par with mechanical drafting."[114] I can recall my own naïve belief that a textbook contained all that was known of the subject; and I was not disabused of my belief by my own textbook or by my teacher. I think I detect in several recent books a fresh, less final, and less tidy treatment of the kinematics of mechanisms, but I would yet recommend that anyone who thinks of writing a textbook take time to review, carefully and at first hand, not only the desk copies of books that he has accumulated but a score or more of earlier works, covering the last century at least. Such a study should result in a better appreciation of what constitutes a contribution to knowledge and what constitutes merely the ringing of another change.

[Footnote 114: _Mechanical Engineering_, October 1942, vol. 64, p. 745.]

The author of the contentious article that appeared in _Mechanical Engineering_ in 1942 under the title "What is Wrong with Kinematics and Mechanisms?" made several pronouncements 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 classroom 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 analysis 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 fictitious acceleration of Coriolis." The author's analysis 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 "fictitious," 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 Analysis 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 substitute 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 analysis, 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 analysis 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 titles 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 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.]

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, _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.]