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]

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.

Figure 30

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[[70] and commenced at Cambridge his lectures on kinematics of mechanisms that culminated in his 1841 book Principles of Mechanism.[71]

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]

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]

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.

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]

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]

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]

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]

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]

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]

Figure 31

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."[85]

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]

Figure 32

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.[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.

Figure 33

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.

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]

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]

Figure 34

Figure 34.—Hachette's ferryboat of 1808, a "machine" for converting continuous rectilinear motion into alternating circular motion. From Phillipe Louis Lanz and Augustin de Bétancourt, Essai sur la composition des machines (Paris, 1808, pl. 2).

Figure 35

Figure 35.—Ferryboat from Gardner D. Hiscox, ed., Mechanical Movements (ed. 10, New York, 1903, p. 151).

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]

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.

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.

Figure 36

Figure 36.—Typical mechanisms from E. F. and N. Spon, Dictionary of Engineering (London, 1873, pp. 2426, 2478).

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

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]

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.

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 unmaking 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]

Figure 37

Figure 37.—Johnson's "converting motion," 1841. The linkage causes the flywheel to make two revolutions for each double-stroke of the engine piston rod B. From 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]