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CONTRIBUTIONS FROM
THE MUSEUM OF HISTORY AND TECHNOLOGY
PAPER 27
KINEMATICS OF MECHANISMS FROM THE TIME OF WATT
_Eugene S. Ferguson_
JAMES WATT, KINEMATIC SYNTHESIST 187
TO DRAW A STRAIGHT LINE 199
SCHOLARS AND MACHINES 209
MECHANICIANS AND MECHANISMS 216
MECHANISMS IN AMERICA, 1875-1955 223
ADDITIONAL REFERENCES 229
KINEMATICS OF MECHANISMS FROM THE TIME OF WATT
_In an inventive tour de force that seldom, if ever, has been equalled
for its brilliance and far-reaching consequences, James Watt radically
altered the steam engine not only by adding a separate condenser but by
creating a whole new family of linkages. His approach was largely
empirical, as we use the word today._
_This study suggests that, despite the glamor of today's sophisticated
methods of calculation, a highly developed intuitive sense, reinforced
by a knowledge of the past, is still indispensable to the design of
successful mechanisms._
THE AUTHOR: _Eugene S. Ferguson, formerly curator of mechanical and
civil engineering in the United States National Museum, Smithsonian
Institution, is now professor of mechanical engineering at Iowa State
University of Science and Technology._
In engineering schools today, a student is introduced to the kinematics
of mechanisms by means of a course of kinematic analysis, which is
concerned with principles underlying the motions occurring in
mechanisms. These principles are demonstrated by a study of mechanisms
already in existence, such as the linkage of a retractable landing gear,
computing mechanisms, mechanisms used in an automobile, and the like. A
systematic, if not rigorous, approach to the design of gears and cams
also is usually presented in such a course. Until recently, however, no
serious attempt was made to apply the principles developed in kinematic
analysis to the more complex problem of kinematic synthesis of linkages.
By kinematic synthesis is meant the designing of a linkage to produce a
given series of motions for a particular purpose.
That a rational--numerical or geometrical--approach to kinematic
synthesis is possible is a relatively recent idea, not yet fully
accepted; but it is this idea that is responsible for the intense
scholarly interest in the kinematics of mechanisms that has occurred in
this country within the last 10 years.
This scholarly activity has resulted in the rediscovery of many earlier
works on the subject, and nearly all the scholars now working in this
field have acknowledged in one way or another their debt to those who
arrived on the scene at an earlier time than they. There have been
occasional reviews of the sequence and nature of developments, but the
emphasis naturally has been upon the recent past. It seems to me that
there is something to be gained in looking beyond our own generation, or
even beyond the time of Franz Reuleaux (1829-1905), who is generally
credited with originating many of our modern concepts of mechanism
analysis and design, and to inquire into the ideas that made possible
Reuleaux's contributions.
_Take to Kinematics. It will repay you. It is more fecund than
geometry; it adds a fourth dimension to space._
--Chebyshev to Sylvester, 1873
While no pretense of completeness is made, I have tried in this paper to
trace the high points in the development of kinematic analysis and
synthesis, both in academic circles and in the workshop, noting where
possible the influence of one upon the other. If I have devoted more
space to particular people and episodes than is warranted by their
contributions to the modern treatment of the subject, it is because I
have found that the history of kinematics of mechanisms, like the
history of any other branch of engineering, is more interesting and more
plausible if it is recognized that its evolutionary development is the
result of human activity. This history was wrought by people like us, no
less intelligent and no less subject than we are to environment, to a
subjective way of looking at things, and to a heritage of ideas and
beliefs.
I have selected the period from the time of Watt because modern
mechanisms originated with him, and I have emphasized the first century
of the period because by 1885 many of the ideas of modern kinematics of
mechanisms were well developed. Linkages are discussed, to the virtual
exclusion of gears and cams, because much of the scholarly work in
kinematic synthesis is presently directed toward the design of linkages
and because linkages provide a convenient thread for a narrative that
would have become unnecessarily complex if detailed treatment of gears
and cams had been included. I have brought the narrative down to the
present by tracing kinematics as taught in American engineering
schools, closing with brief mention of the scholarly activity in
kinematics in this country since 1950. An annotated list of additional
references is appended as an encouragement to further work in the
history of the subject.
James Watt, Kinematic Synthesist
James Watt (1736-1819), improver of the steam engine, was a highly
gifted designer of mechanisms, although his background included no
formal study of mechanisms. Indeed, the study of mechanisms, without
immediate regard to the machines in which they were used, was not
introduced until after Watt's important work had been completed, while
the actual design of mechanisms had been going on for several centuries
before the time of Watt.
Mechanisms that employed screws, cams, and gears were certainly in use
by the beginning of the Christian era. While I am not aware of
unequivocal evidence of the existence of four-bar linkages before the
16th century, their widespread application by that time indicates that
they probably originated much earlier. A tantalizing 13th-century sketch
of an up-and-down sawmill (fig. 1) suggests, but does not prove, that
the four-bar linkage was then in use. Leonardo da Vinci (1452-1519)
delineated, if he did not build, a crank and slider mechanism, also for
a sawmill (fig. 2). In the 16th century may be found the conversion of
rotary to reciprocating motion (strictly speaking, an oscillation
through a small arc of a large circle) and vice versa by use of linkages
of rigid members (figs. 3 and 4), although the conversion of rotary to
reciprocating motion was at that time more frequently accomplished by
cams and intermittent gearing. Nevertheless, the idea of linkages was a
firmly established part of the repertory of the machine builder before
1600. In fact one might have wondered in 1588, when Agostino Ramelli
published his book on machines,[1] whether linkages had not indeed
reached their ultimate stage of development. To illustrate my point, I
have selected the plate of Ramelli that most appeals to me (fig. 5),
although the book exhibits more than 200 other machines of comparable
complexity and ingenuity.
[Footnote 1: Agostino Ramelli, _Le Diverse et Artificiose Machine_,
Paris, 1588.]
[Illustration: Figure 1.--Up-and-down sawmill of the 13th century. The
guide mechanism at lower left, attached to the saw blade, appears to be
a 4-bar linkage. After Robert Willis, trans. and ed., _Facsimile of the
Sketch-Book of Wilars de Honecort_ (London, 1859, pl. 43).]
[Illustration: Figure 2.--Slider-crank mechanism of Leonardo da Vinci
(1452-1519), redrawn from his manuscript notebooks. A frame saw is
depicted at the lower end of the guides. From Theodor Beck, _Beiträge
zur Geschichte des Maschinenbaues_ (Berlin, 1899, p. 323).]
[Illustration: Figure 3.--Blowing engine by Vanuccio Biringuccio, about
1540, showing conversion of motion of the waterwheel shaft from rotation
to oscillation. From Theodor Beck, _Beiträge zur Geschichte des
Maschinenbaues_ (Berlin, 1899, p. 120).]
[Illustration: Figure 4.--Grain mill, 1588, showing conversion of motion
of the operating bars from oscillation to rotation. Note the
fly-weights, predecessors of the flywheel. From Agostino Ramelli, _Le
Diverse et Artificiose Machine_ (Paris, 1588, pl. opposite p. 199).]
[Illustration: Figure 5.--Machine for raising water. Such a machine was
built in Spain during the 16th century and was operated for some 80
years. From Agostino Ramelli, _Le Diverse et Artificiose Machine_
(Paris, 1588, p. 199).]
There was a vast difference, both in conception and execution, between
the linkages of Ramelli and those of James Watt some 200 years later.
Watt was responsible for initiating profound changes in mechanical
technology, but it should be recognized that the mechanic arts had,
through centuries of slow development, reached the stage where his
genius could flourish. The knowledge and ability to provide the
materials and tools necessary for Watt's researches were at hand, and
through the optimism and patient encouragement of his partner, Matthew
Boulton, they were placed at his disposal.
Watt's genius was nowhere more evident than in his synthesis of
linkages. An essential ingredient in the success of Watt's linkages,
however, was his partner's appreciation of the entirely new order of
refinement that they called for. Matthew Boulton, who had been a
successful manufacturer of buttons and metal novelties long before his
partnership with Watt was formed, had recognized at once the need for
care in the building of Watt's steam engine. On February 7, 1769, he had
written Watt:[2] "I presumed that your engine would require money,
very accurate workmanship and extensive correspondence to make it turn
out to the best advantage and that the best means of keeping up the
reputation and doing the invention justice would be to keep the
executive part of it out of the hands of the multitude of empirical
engineers, who from ignorance, want of experience and want of necessary
convenience, would be very liable to produce bad and inaccurate
workmanship; all of which deficiencies would affect the reputation of
the invention." Boulton expected to build the engines in his shop "with
as great a difference of accuracy as there is between the blacksmith and
the mathematical instrument maker." The Soho Works of Boulton and Watt,
in Birmingham, England, solved for Watt the problem of producing "in
great" (that is, in sizes large enough to be useful in steam engines)
the mechanisms that he devised.[3]
[Footnote 2: Henry W. Dickinson, _James Watt, Craftsman & Engineer_,
Cambridge, Cambridge University Press, 1936, pp. 52-53.]
[Footnote 3: James P. Muirhead, _The Origin and Progress of the
Mechanical Inventions of James Watt_, London, 1854, vol. 1, pp. 56, 64.
This work, in three volumes, contains letters, other documents, and
plates of patent specification drawings.]
The contributions of Boulton and Watt to practical mechanics "in great"
cannot be overestimated. There were in the 18th century instrument
makers and makers of timekeepers who had produced astonishingly
accurate work, but such work comprised relatively small items, all being
within the scope of a bench lathe, hand tools, and superb handwork. The
rapid advancement of machine tools, which greatly expanded the scope of
the machine-building art, began during the Boulton and Watt partnership
(1775-1800).
In April 1775 the skirmish at Concord between American colonists and
British redcoats marked the beginning of a war that was to determine for
the future the course of political events in the Western Hemisphere.
Another event of April 1775 occurring in Birmingham now appears to have
been one that marked the beginning of a new era of technological
advance. It was near the end of this month that Boulton, at the Soho
Works, wrote to his partner and commented upon receiving the cast iron
steam engine cylinder that had been finished in John Wilkinson's boring
mill:
... it seems tolerably true, but is an inch thick and weighs about
10 cwt. Its diameter is about as much above 18 inches as the tin
one was under, and therefore it is become necessary to add a brass
hoop to the piston, which is made almost two inches broad.[4]
[Footnote 4: _Ibid._, vol. 2, p. 84.]
This cylinder indeed marked the turning point in the discouragingly long
development of the Watt steam engine, which for 10 years had occupied
nearly all of Watt's thoughts and all the time he could spare from the
requirements of earning a living. Although there were many trials ahead
for the firm of Boulton and Watt in further developing and perfecting
the steam engine, the crucial problem of leakage of steam past the
piston in the cylinder had now been solved by Wilkinson's new boring
mill, which was the first large machine tool capable of boring a
cylinder both round and straight.
The boring mill is pertinent to the development of linkages "in great,"
being the first of a new class of machine tools that over the next 50 or
60 years came to include nearly all of the basic types of heavy
chip-removing tools that are in use today. The development of tools was
accelerated by the inherent accuracy required of the linkages that were
originated by Watt. Once it had been demonstrated that a large and
complex machine, such as the steam engine, could be built accurately
enough so that its operation would be relatively free of trouble, many
outstanding minds became engaged in the development of machines and
tools. It is interesting, however, to see how Watt and others grappled
with the solutions of problems that resulted from the advance of the
steam engine.
During the 1770's the demand for continuous, dependable power applied to
a rotating shaft was becoming insistent, and much of Boulton's and
Watt's effort was directed toward meeting this demand. Mills of all
kinds used water or horses to turn "wheel-work," but, while these
sources of power were adequate for small operations, the quantity of
water available was often limited, and the use of enormous horse-whims
was frequently impracticable.
The only type of steam engine then in existence was the Newcomen beam
engine, which had been introduced in 1712 by Thomas Newcomen, also an
Englishman. This type of engine was widely used, mostly for pumping
water out of mines but occasionally for pumping water into a reservoir
to supply a waterwheel. It was arranged with a vertical steam cylinder
located beneath one end of a large pivoted working beam and a vertical
plunger-type pump beneath the other end. Heavy, flat chains were secured
to a sector at each end of the working beam and to the engine and pump
piston rods in such a way that the rods were always tangent to a circle
whose center was at the beam pivot. The weight of the reciprocating pump
parts pulled the pump end of the beam down; the atmosphere, acting on
the open top of the piston in the steam cylinder, caused the engine end
of the beam to be pulled down when the steam beneath the piston was
condensed. The chains would of course transmit force from piston to beam
only in tension.
It is now obvious that a connecting rod, a crank, and a sufficiently
heavy flywheel might have been used in a conventional Newcomen engine in
order to supply power to a rotating shaft, but contemporary evidence
makes it clear that this solution was by no means obvious to Watt nor to
his contemporaries.
At the time of his first engine patent, in 1769, Watt had devised a
"steam wheel," or rotary engine, that used liquid mercury in the lower
part of a toroidal chamber to provide a boundary for steam spaces
successively formed by flap gates within the chamber. The practical
difficulties of construction finally ruled out this solution to the
problem of a rotating power source, but not until after Boulton and
Watt had spent considerable effort and money on it.[5]
[Footnote 5: Henry W. Dickinson and Rhys Jenkins, _James Watt and the
Steam Engine_, Oxford, Clarendon Press, 1927, pp. 146-148, pls. 14, 31.
This work presents a full and knowledgeable discussion, based on primary
material, of the development of Watt's many contributions to mechanical
technology. It is ably summarized in Dickinson, _op. cit._ (footnote
2).]
In 1777 a speaker before the Royal Society in London observed that in
order to obtain rotary output from a reciprocating steam engine, a crank
"naturally occurs in theory," but that in fact the crank is impractical
because of the irregular rate of going of the engine and its variable
length of stroke. He said that on the first variation of length of
stroke the machine would be "either broken to pieces, or turned
back."[6] John Smeaton, in the front rank of English steam engineers of
his time, was asked in 1781 by His Majesty's Victualling-Office for his
opinion as to whether a steam-powered grain mill ought to be driven by a
crank or by a waterwheel supplied by a pump. Smeaton's conclusion was
that the crank was quite unsuited to a machine in which regularity of
operation was a factor. "I apprehend," he wrote, "that no motion
communicated from the reciprocating beam of a fire engine can ever act
perfectly equal and steady in producing a circular motion, like the
regular efflux of water in turning a waterwheel." He recommended,
incidentally, that a Boulton and Watt steam engine be used to pump water
to supply the waterwheel.[7] Smeaton had thought of a flywheel, but he
reasoned that a flywheel large enough to smooth out the halting, jerky
operation of the steam engines that he had observed would be more of an
encumbrance than a pump, reservoir, and waterwheel.[8]
[Footnote 6: John Farey, _A Treatise on the Steam Engine_, London, 1827,
pp. 408-409.]
[Footnote 7: _Reports of the Late John Smeaton, F.R.S._, London, 1812,
vol. 2, pp. 378-380.]
[Footnote 8: Farey, _op. cit._ (footnote 6), p. 409.]
The simplicity of the eventual solution of the problem was not clear to
Watt at this time. He was not, as tradition has it, blocked merely by
the existence of a patent for a simple crank and thus forced to invent
some other device as a substitute.
Matthew Wasbrough, of Bristol, the engineer commonly credited with the
crank patent, made no mention of a crank in his patent specification,
but rather intended to make use of "racks with teeth," or "one or more
pullies, wheels, segments of wheels, to which are fastened rotchets and
clicks or palls...." He did, however, propose to "add a fly or flys, in
order to render the motion more regular and uniform." Unfortunately for
us, he submitted no drawings with his patent specification.[9]
[Footnote 9: British Patent 1213, March 10, 1779.]
James Pickard, of Birmingham, like Boulton, a buttonmaker, in 1780
patented a counterweighted crank device (fig. 6) that was expected to
remove the objection to a crank, which operated with changing leverage
and thus irregular power. In figure 6, the counterweighted wheel,
revolving twice for each revolution of the crank (A), would allow the
counterweight to descend while the crank passed the dead-center position
and would be raised while the crank had maximum leverage. No mention of
a flywheel was made in this patent.[10]
[Footnote 10: British Patent 1263, August 23, 1780.]
[Illustration: Figure 6.--One of the steam engine "Crank Patents" that
hindered James Watt's progress. This patent, granted to James Pickard in
1780, claimed only the arrangement of counterweights, not the crank. The
crank pin to which the connecting rod was attached is at _Aa_. From
British Patent 1263, August 23, 1780.]
Wasbrough, finding that his "rotchets and clicks" did not serve,
actually used, in 1780, a crank with a flywheel. Watt was aware of this,
but he remained unconvinced of the superiority of the crank over other
devices and did not immediately appreciate the regulating ability of a
flywheel.[11] In April 1781 Watt wrote to Boulton, who was then out of
town: "I know from experiment that the other contrivance, which you saw
me try, performs at least as well, and has in fact many advantages over
the crank."[12] The "other contrivance" probably was his swash wheel
which he built and which appeared on his next important patent
specification (fig. 7a). Also in this patent were four other devices,
one of which was easily recognizable as a crank, and two of which were
eccentrics (fig. 7a, b). The fourth device was the well-known
sun-and-planet gearing (fig. 7e).[13] In spite of the similarity of the
simple crank to the several variations devised by Watt, this patent drew
no fire from Wasbrough or Pickard, perhaps because no reasonable person
would contend that the crank itself was a patentable feature, or perhaps
because the similarity was not at that time so obvious. However, Watt
steered clear of directly discernible application of cranks because he
preferred to avoid a suit that might overthrow his or other patents. For
example, if the Wasbrough and Pickard patents had been voided, they
would have become public property; and Watt feared that they might
"get into the hands of men more ingenious," who would give Boulton and
Watt more competition than Wasbrough and Pickard.[14]
[Footnote 11: Dickinson and Jenkins, _op. cit._ (footnote 5), pp. 150,
154.]
[Footnote 12: _Ibid._, p. 154.]
[Footnote 13: William Murdock, at this time a Boulton and Watt erector,
may have suggested this arrangement. _Ibid._, p. 56.]
[Footnote 14: Muirhead, _op. cit._ (footnote 3), vol. 3, note on p. 39.]
[Illustration: Figure 7.--James Watt's five alternative devices for the
conversion of reciprocating motion to rotary motion in a steam engine.
(British Patent 1306, October 25, 1781). From James P. Muirhead, _The
Origin and Progress of the Mechanical Inventions of James Watt_ (London,
1854, vol. 3, pls. 3-5, 7).]
[Illustration: (a) "Inclined wheel." The vertical shaft at _D_ is
rotated by action of wheels _H_ and _J_ on cam, or swash plate, _ABC_.
Boulton and Watt tried this device but discarded it.]
[Illustration: (b) Counterweighted crank wheel.]
[Illustration: (c) "Eccentric wheel" with external yoke hung from
working beam. The wheel pivots at _C_.]
[Illustration: (d) "Eccentric wheel" with internal driving wheel hung
from working beam. Wheel _B_ is pivoted at center of shaft _A_.]
[Illustration: (e) Sun-and-planet gearing. This is the idea actually
employed in Boulton and Watt engines. As the optional link _JK_ held the
gearwheel centers always equidistant, the annular guide _G_ was not
used.]
The sun-and-planet arrangement, with gears of equal size, was adopted by
Watt for nearly all the rotative engines that he built during the term
of the "crank patents." This arrangement had the advantage of turning
the flywheel through two revolutions during a single cycle of operation
of the piston, thus requiring a flywheel only one-fourth the size of the
flywheel needed if a simple crank were used. The optional link (JK of
fig. 7e) was used in the engines as built.
From the first, the rotative engines were made double-acting--that is,
work was done by steam alternately in each end of the cylinder. The
double-acting engine, unlike the single-acting pumping engine, required
a piston rod that would push as well as pull. It was in the solution of
this problem that Watt's originality and sure judgment were most clearly
demonstrated.
A rack and sector arrangement (fig. 8) was used on some engines. The
first one, according to Watt, "has broke out several teeth of the rack,
but works steady."[15] A little later he told a correspondent that his
double-acting engine "acts so powerfully that it has broken all its
tackling repeatedly. We have now tamed it, however."[16]
[Footnote 15: James Watt, March 31, 1783, quoted in Dickinson and
Jenkins, _op. cit._ (footnote 5), p. 140.]
[Footnote 16: Watt to De Luc, April 26, 1783, quoted in Muirhead, _op.
cit._ (footnote 3), vol. 2, p. 174.]
[Illustration: Figure 8.--Watt engine of 1782 (British Patent 1321,
March 12, 1782) showing the rack and sector used to guide the upper end
of the piston rod and to transmit force from piston to working beam.
This engine, with a 30-inch cylinder and an 8-foot stroke, was arranged
for pumping. Pump rod _SS_ is hung from sector of the working beam. From
James P. Muirhead, _The Origin and Progress of the Mechanical Inventions
of James Watt_ (London, 1854, vol. 3, pl. 15).]
It was about a year later that the straight-line linkage[17] was thought
out. "I have started a new hare," Watt wrote to his partner. "I have
got a glimpse of a method of causing the piston-rod to move up and down
perpendicularly, by only fixing it to a piece of iron upon the beam,
without chains, or perpendicular guides, or untowardly frictions,
arch-heads, or other pieces of clumsiness.... I have only tried it in a
slight model yet, so cannot build upon it, though I think it a very
probable thing to succeed, and one of the most ingenious simple pieces
of mechanism I have contrived...."[18]
[Footnote 17: Watt's was a four-bar linkage. All four-bar straight-line
linkages that have no sliding pairs trace only an approximately straight
line. The exact straight-line linkage in a single plane was not known
until 1864 (see p. 204). In 1853 Pierre-Frédéric Sarrus (1798-1861), a
French professor of mathematics at Strasbourg, devised an accordion-like
spatial linkage that traced a true straight line. Described but not
illustrated (Académie des Sciences, Paris, _Comptes rendus_, 1853, vol.
36, pp. 1036-1038, 1125), the mechanism was forgotten and twice
reinvented; finally, the original invention was rediscovered by an
English writer in 1905. For chronology, see Florian Cajori, _A History
of Mathematics_, ed. 2, New York, 1919, p. 301.]
[Footnote 18: Muirhead, _op. cit._ (footnote 3), vol. 2, pp. 191-192.]
Watt's marvelously simple straight-line linkage was incorporated into a
large beam engine almost immediately, and the usually pessimistic and
reserved inventor was close to a state of elation when he told Boulton
that the "new central perpendicular motion answers beyond expectation,
and does not make the shadow of a noise."[19] This linkage, which was
included in an extensive patent of 1784, and two alternative devices are
illustrated here (fig. 9). One of the alternatives is a guided crosshead
(fig. 9, top right).
[Footnote 19: _Ibid._, p. 202.]
[Illustration: Figure 9.--Watt's mechanisms for guiding the upper end of
the piston rod of a double-acting engine (British Patent 1432, April 28,
1784). _Top left_, straight-line linkage; _top right_, crosshead and
guide arrangement; _lower left_, piston rod _A_ is guided by sectors _D_
and _E_, suspended by flexible cords. From James P. Muirhead, _The
Origin and Progress of the Mechanical Inventions of James Watt_ (London,
1854, vol. 3, pls. 21, 22).]
Brilliant as was the conception of this linkage, it was followed up by a
synthesis that is very little short of incredible. In order to make the
linkage attached to the beam of his engines more compact, Watt had
plumbed his experience for ideas; his experience had yielded up the work
done much earlier on a drafting machine that made use of a
pantograph.[20] Watt combined his straight-line linkage with a
pantograph, one link becoming a member of the pantograph.
[Footnote 20: "It has only one fault," he had told a friend on December
24, 1773, after describing the drafting machine to him, "which is, that
it will not do, because it describes conic sections instead of straight
lines." _Ibid._, p. 71.]
The length of each oscillating link of the straight-line linkage was
thus reduced to one-fourth instead of one-half the beam length, and the
entire mechanism could be constructed so that it would not extend
beyond the end of the working beam. This arrangement soon came to be
known as Watt's "parallel motion" (fig. 10).[21] Years later Watt told
his son: "Though I am not over anxious after fame, yet I am more proud
of the parallel motion than of any other mechanical invention I have
ever made."[22]
[Footnote 21: Throughout the 19th century the term "parallel motion" was
used indiscriminately to refer to any straight-line linkage. I have not
discovered the origin of the term. Watt did not use it in his patent
specification, and I have not found it in his writings or elsewhere
before 1808 (see footnote 22). _The Cyclopaedia_ (Abraham Rees, ed.,
London, 1819, vol. 26) defined parallel motion as "a term used among
practical mechanics to denote the rectilinear motion of a piston-rod,
&c. in the direction of its length; and contrivances, by which such
alternate rectilinear motions are converted into continuous rotatory
ones, or _vice versa_...." Robert Willis in his _Principles of
Mechanism_ (London, 1841, p. 399) described parallel motion as "a term
somewhat awkwardly applied to a combination of jointed rods, the purpose
of which is to cause a point to describe a straight line...." A. B.
Kempe in _How to Draw a Straight Line_ (London, 1877, p. 49) wrote: "I
have been more than once asked to get rid of the objectionable term
'parallel motion.' I do not know how it came to be employed, and it
certainly does not express what is intended. The expression, however,
has now become crystallised, and I for one cannot undertake to find a
solvent."]
[Footnote 22: Muirhead, _op. cit._ (footnote 3), vol. 3, note on p. 89.]
[Illustration: Figure 10.--Watt's "parallel motion." Engine's working
beam is pivoted at _A_. Pivot _F_ is attached to the engine frame. From
Dyonysius Lardner, _The Steam Engine_ (Philadelphia, 1852), pl. 5
(American ed. 5 from London ed. 5).]
The Watt four-bar linkage was employed 75 years after its inception by
the American Charles B. Richards when, in 1861, he designed his first
high-speed engine indicator (fig. 11). Introduced into England the
following year, the Richards Indicator was an immediate success, and
many thousands were sold over the next 20 or 30 years.[23]
[Footnote 23: Charles T. Porter, _Engineering Reminiscences_, New York,
1908, pp. 58-59, 90.]
[Illustration: Figure 11.--Richards high-speed engine indicator of 1861,
showing application of the Watt straight-line linkage. (_USNM 307515_;
_Smithsonian photo 46570_).]
In considering the order of synthetic ability required to design the
straight-line linkage and to combine it with a pantograph, it should be
kept in mind that this was the first one of a long line of such
mechanisms.[24] Once the idea was abroad, it was only to be expected
that many variations and alternative solutions should appear. One
wonders, however, what direction the subsequent work would have taken
if Watt had not so clearly pointed the way.
[Footnote 24: At least one earlier straight-line linkage, an arrangement
later ascribed to Richard Roberts, had been depicted before Watt's
patent (Pierre Patte, _Mémoirs sur les objets les plus importants de
l'architecture_, Paris, 1769, p. 229 and pl. 11). However, this linkage
(reproduced here in figure 18) had no detectable influence on Watt or on
subsequent practice.]
In 1827 John Farey, in his exhaustive study of the steam engine, wrote
perhaps the best contemporary view of Watt's work. Farey as a young man
had several times talked with the aging Watt, and he had reflected upon
the nature of the intellect that had caused Watt to be recognized as a
genius, even within his own lifetime. In attempting to explain Watt's
genius, Farey set down some observations that are pertinent not only to
kinematic synthesis but to the currently fashionable term "creativity."
In Farey's opinion Watt's inventive faculty was far superior to that of
any of his contemporaries; but his many and various ideas would have
been of little use if he had not possessed a very high order of
judgment, that "faculty of distinguishing between ideas; decomposing
compound ideas into more simple elements; arranging them into classes,
and comparing them together...."
Farey was of the opinion that while a mind like Watt's could produce
brilliant new ideas, still the "common stock of ideas which are current
amongst communities and professions, will generally prove to be of a
better quality than the average of those new ideas, which can be
produced by any individual from the operation of his own mind, without
assistance from others." Farey concluded with the observation that "the
most useful additions to that common stock, usually proceed from the
individuals who are well acquainted with the whole series."[25]
[Footnote 25: Farey, _op. cit._ (footnote 6), pp. 651, 652.]
To Draw a Straight Line
During most of the century after James Watt had produced his parallel
motion, the problem of devising a linkage, one point of which would
describe a straight line, was one that tickled the fancies of
mathematicians, of ingenious mechanics, and of gentlemanly dabblers in
ideas. The quest for a straight-line mechanism more accurate than that
of Watt far outlasted the pressing practical need for such a device.
Large metal planing machines were well known by 1830, and by midcentury
crossheads and crosshead guides were used on both sides of the Atlantic
in engines with and without working beams.
By 1819 John Farey had observed quite accurately that, in England at
least, many other schemes had been tried and found wanting and that "no
methods have been found so good as the original engine; and we
accordingly find, that all the most established and experienced
manufacturers make engines which are not altered in any great feature
from Mr. Watt's original engine...."[26]
[Footnote 26: In Rees, _op. cit._ (footnote 21), vol. 34 ("Steam
Engine"). John Farey was the writer of this article (see Farey, _op.
cit._, p. vi).]
Two mechanisms for producing a straight line were introduced before the
Boulton and Watt monopoly ended in 1800. Perhaps the first was by Edmund
Cartwright (1743-1823), who is said to have had the original idea for a
power loom. This geared device (fig. 12), was characterized
patronizingly by a contemporary American editor as possessing "as much
merit as can possibly be attributed to a gentleman engaged in the
pursuit of mechanical studies for his own amusement."[27] Only a few
small engines were made under the patent.[28]
[Footnote 27: _Emporium of Arts and Sciences_, December 1813, new ser.,
vol. 2, no. 1, p. 81.]
[Footnote 28: Farey, _op. cit._ (footnote 6), p. 666.]
[Illustration: Figure 12.--Cartwright's geared straight-line mechanism
of about 1800. From Abraham Rees, _The Cyclopaedia_ (London, 1819,
"Steam Engine," pl. 5).]
The properties of a hypocycloid were recognized by James White, an
English engineer, in his geared design which employed a pivot located on
the pitch circle of a spur gear revolving inside an internal gear. The
diameter of the pitch circle of the spur gear was one-half that of the
internal gear, with the result that the pivot, to which the piston rod
was connected, traced out a diameter of the large pitch circle (fig.
13). White in 1801 received from Napoleon Bonaparte a medal for this
invention when it was exhibited at an industrial exposition in
Paris.[29] Some steam engines employing White's mechanism were built,
but without conspicuous commercial success. White himself rather agreed
that while his invention was "allowed to possess curious properties, and
to be a _pretty_ thing, opinions do not all concur in declaring it,
essentially and generally, a _good_ thing."[30]
[Footnote 29: H. W. Dickinson, "James White and His 'New Century of
Inventions,'" _Transactions of the Newcomen Society_, 1949-1951, vol.
27, pp. 175-179.]
[Footnote 30: James White, _A New Century of Inventions_, Manchester,
1822, pp. 30-31, 338. A hypocycloidal engine used in Stourbridge,
England, is in the Henry Ford Museum.]
[Illustration: Figure 13.--James White's hypocycloidal straight-line
mechanism, about 1800. The fly-weights (at the ends of the diagonal arm)
functioned as a flywheel. From James White, _A New Century of
Inventions_ (Manchester, 1822, pl. 7).]
The first of the non-Watt four-bar linkages appeared shortly after 1800.
The origin of the grasshopper beam motion is somewhat obscure, although
it came to be associated with the name of Oliver Evans, the American
pioneer in the employment of high-pressure steam. A similar idea,
employing an isosceles linkage, was patented in 1803 by William
Freemantle, an English watchmaker (fig. 14).[31] This is the linkage
that was attributed much later to John Scott Russell (1808-1882), the
prominent naval architect.[32] An inconclusive hint that Evans had
devised his straight-line linkage by 1805 appeared in a plate
illustrating his _Abortion of the Young Steam Engineer's Guide_
(Philadelphia, 1805), and it was certainly used on his Columbian engine
(fig. 15), which was built before 1813. The Freemantle linkage, in
modified form, appeared in Rees's _Cyclopaedia_ of 1819 (fig. 16), but
it is doubtful whether even this would have been readily recognized as
identical with the Evans linkage, because the connecting rod was at the
opposite end of the working beam from the piston rod, in accordance with
established usage, while in the Evans linkage the crank and connecting
rod were at the same end of the beam. It is possible that Evans got his
idea from an earlier English periodical, but concrete evidence is
lacking.
[Footnote 31: British Patent 2741, November 17, 1803.]
[Footnote 32: William J. M. Rankine, _Manual of Machinery and Millwork_,
ed. 6, London, 1887, p. 275.]
[Illustration: Figure 14.--Freemantle straight-line linkage, later
called the Scott Russell linkage. From British Patent 2741, November 17,
1803.]
[Illustration: Figure 15.--Oliver Evans' "Columbian" engine, 1813,
showing the Evans, or "grasshopper," straight-line linkage. From
_Emporium of Arts and Sciences_ (new ser., vol. 2, no. 3, April 1814,
pl. opposite p. 380).]
[Illustration: Figure 16.--Modified Freemantle linkage, 1819, which is
kinematically the same as the Evans linkage. Pivots _D_ and _E_ are
attached to engine frame. From Abraham Rees, _The Cyclopaedia_ (London,
1819, "Parallel Motions," pl. 3).]
If the idea did in fact originate with Evans, it is strange that he did
not mention it in his patent claims, or in the descriptions that he
published of his engines.[33] The practical advantage of the Evans
linkage, utilizing as it could a much lighter working beam than the Watt
or Freemantle engines, would not escape Oliver Evans, and he was not a
man of excessive modesty where his own inventions were concerned.
[Footnote 33: Greville and Dorothy Bathe, _Oliver Evans_, Philadelphia,
1935, pp. 88, 196, and _passim_.]
Another four-bar straight-line linkage that became well known was
attributed to Richard Roberts of Manchester (1789-1864), who around 1820
had built one of the first metal planing machines, which machines helped
make the quest for straight-line linkages largely academic. I have not
discovered what occasioned the introduction of the Roberts linkage, but
it dated from before 1841. Although Roberts patented many complex
textile machines, an inspection of all of his patent drawings has failed
to provide proof that he was the inventor of the Roberts linkage.[34]
The fact that the same linkage is shown in an engraving of 1769 (fig.
18) further confuses the issue.[35]
[Footnote 34: Robert Willis (_op. cit._ [Footnote 21] p. 411) credited
Richard Roberts with the linkage. Roberts' 15 British patent drawings
exhibit complex applications of cams, levers, guided rods, cords, and so
forth, but no straight-line mechanism. In his patent no. 6258 of April
13, 1832, for a steam engine and locomotive carriage, Roberts used
Watt's "parallel motion" on a beam driven by a vertical cylinder.]
[Footnote 35: This engraving appeared as plate 11 in Pierre Patte's 1769
work (_op. cit._ footnote 24). Patte stated that the machine depicted in
his plate 11 was invented by M. de Voglie and was actually used in
1756.]
[Illustration: Figure 17.--Straight-line linkage (before 1841)
attributed to Richard Roberts by Robert Willis. From A. B. Kempe, _How
to Draw a Straight Line_ (London, 1877, p. 10).]
[Illustration: Figure 18.--Machine for sawing off pilings under water,
about 1760, designed by De Voglie. The Roberts linkage operates the bar
(_Q_ in detailed sketch) at the rear of the machine below the operators.
The significance of the linkage apparently was not generally recognized.
A similar machine depicted in Diderot's _Encyclopédie_, published
several years later, did not employ the straight-line linkage. From
Pierre Patte, _Memoirs sur les objets plus importants de l'architecture_
(Paris, 1769, pl. 11).]
The appearance in 1864 of Peaucellier's exact straight-line linkage went
nearly unnoticed. A decade later, when news of its invention crossed
the Channel to England, this linkage excited a flurry of interest, and
variations of it occupied mathematical minds for several years. For at
least 10 years before and 20 years after the final solution of the
problem, Professor Chebyshev,[36] a noted mathematician of the
University of St. Petersburg, was interested in the matter. Judging by
his published works and his reputation abroad, Chebyshev's interest
amounted to an obsession.
[Footnote 36: This is the Library of Congress spelling]
Pafnutï[)i] L'vovich Chebyshev was born in 1821, near Moscow, and
entered the University of Moscow in 1837. In 1853, after visiting France
and England and observing carefully the progress of applied mechanics in
those countries, he read his first paper on approximate straight-line
linkages, and over the next 30 years he attacked the problem with new
vigor at least a dozen times. He found that the two principal
straight-line linkages then in use were Watt's and Evans'. Chebyshev
noted the departure of these linkages from a straight line and
calculated the deviation as of the fifth degree, or about 0.0008 inch
per inch of beam length. He proposed a modification of the Watt linkage
to refine its accuracy but found that he would have to more than double
the length of the working beam. Chebyshev concluded ruefully that his
modification would "present great practical difficulties."[37]
[Footnote 37: _Oeuvres de P. L. Tchebychef_, 2 vols., St. Petersburg,
1899-1907, vol. 1, p. 538; vol. 2, pp. 57, 85.]
At length an idea occurred to Chebyshev that would enable him to
approach if not quite attain a true straight line. If one mechanism was
good, he reasoned, two would be better, _et cetera, ad infinitum_. The
idea was simply to combine, or compound, four-link approximate linkages,
arranging them in such a way that the errors would be successively
reduced. Contemplating first a combination of the Watt and Evans
linkages (fig. 19), Chebyshev recognized that if point D of the Watt
linkage followed nearly a straight line, point A of the Evans linkage
would depart even less from a straight line. He calculated the deviation
in this case as of the 11th degree. He then replaced Watt's linkage by
one that is usually called the Chebyshev straight-line mechanism (fig.
20), with the result that precision was increased to the 13th
degree.[38] The steam engine that he displayed at the Vienna Exhibition
in 1873 employed this linkage--the Chebyshev mechanism compounded with
the Evans, or approximate isosceles, linkage. An English visitor to the
exhibition commented that "the motion is of little or no practical use,
for we can scarcely imagine circumstances under which it would be more
advantageous to use such a complicated system of levers, with so many
joints to be lubricated and so many pins to wear, than a solid guide of
some kind; but at the same time the arrangement is very ingenious and in
this respect reflects great credit on its designer."[39]
[Footnote 38: _Ibid._, vol. 2, pp. 93, 94.]
[Footnote 39: _Engineering_, October 3, 1873, vol. 16, p. 284.]
[Illustration: Figure 19.--Pafnutï[)i] L'vovich Chebyshev (1821-1894),
Russian mathematician active in analysis and synthesis of straight-line
mechanisms. From _Ouvres de P. L. Tchebychef_ (St. Petersburg, 1907,
vol. 2, frontispiece).]
[Illustration: Figure 20.--Chebyshev's combination (about 1867) of
Watt's and Evans' linkages to reduce errors inherent in each. Points
_C_, _C'_, and _C"_ are fixed; _A_ is the tracing point. From _Oeuvres
de P. L. Tchebychef_ (St. Petersburg, 1907, vol. 2, p. 93).]
[Illustration: Figure 21.--_Top_: Chebyshev straight-line linkage, 1867;
from A. B. Kempe, _How to Draw a Straight Line_ (London, 1877, p. 11).
_Bottom_: Chebyshev-Evans combination, 1867; from _Oeuvres de P. L.
Tchebychef_ (St. Petersburg, 1907, vol. 2, p. 94). Points _C_, _C'_, and
_C"_ are fixed. _A_ is the tracing point.]
There is a persistent rumor that Professor Chebyshev sought to
demonstrate the impossibility of constructing any linkage, regardless of
the number of links, that would generate a straight line; but I have
found only a dubious statement in the _Grande Encyclopédie_[40] of the
late 19th century and a report of a conversation with the Russian by an
Englishman, James Sylvester, to the effect that Chebyshev had "succeeded
in proving the nonexistence of a five-bar link-work capable of producing
a perfect parallel motion...."[41] Regardless of what tradition may have
to say about what Chebyshev said, it is of course well known that
Captain Peaucellier was the man who finally synthesized the exact
straight-line mechanism that bears his name.
[Footnote 40: _La Grande Encyclopédie_, Paris, 1886 ("Peaucellier").]
[Footnote 41: James Sylvester, "Recent Discoveries in Mechanical
Conversion of Motion," _Notices of the Proceedings of the Royal
Institution of Great Britain_, 1873-1875, vol. 7, p. 181. The fixed link
was not counted by Sylvester; in modern parlance this would be a
six-link mechanism.]
[Illustration: Figure 22.--Peaucellier exact straight-line linkage,
1873. From A. B. Kempe, _How to Draw a Straight Line_ (London, 1877, p.
12).]
[Illustration: Figure 23.--Model of the Peaucellier "Compas Composé,"
deposited in Conservatoire National des Arts et Métiers, Paris, 1875.
Photo courtesy of the Conservatoire.] [Illustration: Figure 24.--James
Joseph Sylvester (1814-1897), mathematician and lecturer on
straight-line linkages. From _Proceedings of the Royal Society of
London_ (1898, vol. 63, opposite p. 161).]
Charles-Nicolas Peaucellier, a graduate of the Ecole Polytechnique and a
captain in the French corps of engineers, was 32 years old in 1864 when
he wrote a short letter to the editor of _Nouvelles Annales de
mathématiques_ (ser. 2, vol. 3, pp. 414-415) in Paris. He called
attention to what he termed "compound compasses," a class of linkages
that included Watt's parallel motion, the pantograph, and the polar
planimeter. He proposed to design linkages to describe a straight line,
a circle of any radius no matter how large, and conic sections, and he
indicated in his letter that he had arrived at a solution.
This letter stirred no pens in reply, and during the next 10 years the
problem merely led to the filling of a few academic pages by Peaucellier
and Amédée Mannheim (1831-1906), also a graduate of Ecole Polytechnique,
a professor of mathematics, and the designer of the Mannheim slide rule.
Finally, in 1873, Captain Peaucellier gave his solution to the readers
of the _Nouvelles Annales_. His reasoning, which has a distinct flavor
of discovery by hindsight, was that since a linkage generates a curve
that can be expressed algebraically, it must follow that any algebraic
curve can be generated by a suitable linkage--it was only necessary to
find the suitable linkage. He then gave a neat geometric proof,
suggested by Mannheim, for his straight-line "compound compass."[42]