Scholars and Machines

When, in 1829, André-Marie Ampère (1775-1836) was called upon to prepare a course in theoretical and experimental physics for the Collège de France, he first set about determining the limits of the field of physics. This exercise suggested to his wide-ranging intellect not only the definition of physics but the classification of all human knowledge. He prepared his scheme of classification, tried it out on his physics students, found it incomplete, returned to his study, and produced finally a two-volume work wherein the province of kinematics was first marked out for all to see and consider. Only a few lines could be devoted to so specialized a branch as kinematics, but Ampère managed to capture the central idea of the subject.

Cinématique (from the Greek word for movement) was, according to Ampère, the science "in which movements are considered in themselves [independent of the forces which produce them], as we observe them in solid bodies all about us, and especially in the assemblages called machines." Kinematics, as the study soon came to be known in English, was one of the two branches of elementary mechanics, the other being statics.

In his definition of kinematics, Ampère stated what the faculty of mathematics at the Ecole Polytechnique, in Paris, had been groping toward since the school's opening some 40 years earlier. The study of mechanisms as an intellectual discipline most certainly had its origin on the left bank of the Seine, in this school spawned, as suggested by one French historian, by the great Encyclopédie of Diderot and d'Alembert.

Because the Ecole Polytechnique had such a far-reaching influence upon the point of view from which mechanisms were contemplated by scholars for nearly a century after the time of Watt, and by compilers of dictionaries of mechanical movements for an even longer time, it is well to look for a moment at the early work that was done there. If one is interested in origins, it might be profitable for him to investigate the military school in the ancient town of Mézières, about 150 miles northeast of Paris. It was here that Lazare Carnot, one of the principal founders of the Ecole Polytechnique, in 1783 published his essay on machines, which was concerned, among other things, with showing the impossibility of "perpetual motion"; and it was from Mézières that Gaspard Monge and Jean Hachette came to Paris to work out the system of mechanism classification that has come to be associated with the names of Lanz and Bétancourt.

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.

Figure 28.—Hachette's synoptic chart of elementary mechanisms, 1808. This was the first of many charts of mechanical movements that enjoyed wide popularity for over 100 years.

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.

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.

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 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.

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—was another graduate of the Ecole Polytechnique who wrote on the subject of machines. His book, 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.

Michel Chasles (1793-1880), another graduate of the Ecole Polytechnique, contributed some incisive ideas in his papers on instant centers published during the 1830's, but their tremendous importance in kinematic analysis was not recognized until much later.

Figure 30.—Franz Reuleaux (1829-1905). His Theoretische Kinematik, published in 1875, provided the basis for modern kinematic analysis. Photo courtesy Deutsches Museum, Munich.

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 and commenced at Cambridge his lectures on kinematics of mechanisms that culminated in his 1841 book Principles of Mechanism.

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."

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."

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. 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.

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.

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. 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."

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. 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....

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.

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.

The book was enthusiastically reviewed by the weekly London journal Engineering, 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." 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.

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 Institution of Civil Engineers (1907, vol. 167, frontispiece).

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."

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." 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.

Figure 32.—Robert Henry Smith (1852-1916), originator of velocity and acceleration polygons for kinematic analysis. 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. 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.

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 analytical 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 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.