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.]
[Illustration: 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]
[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.]
[Illustration: 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.
[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.]
[Illustration: 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]
[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.]
[Illustration: 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).]
[Illustration: 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]
[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.]