in nineteenth-century engineering.
Newton’s celestial objects were moving along straight-line paths, or on paths that could be analyzed as the result of forces jointly impacting an imaginary center where all mass was concentrated. Rotary motion, by contrast, had to be conceived as the impact of two forces at separate points of an extended body. To reiterate, it makes no sense to speak of the rotation of a point, but neither does it make sense to speak of a single rotating force.12 Louis Poinsot, also a product of the new French education system, argued that rotation should be viewed as the result of a “couple” of forces, acting equally from opposite directions on a line drawn through the center of a rotating body. Thus rotation can be quantified as the product of the forces times the length of the line on which they act: this is the measure of torque—a quantity unknown to the eighteenth century—which even today is the true measure of the output of machines, most prominently the automobile engine.13 (A good example is turning a car’s steering wheel: one hand pulls downward, the other pushes upward, and both are at an equal distance from the center of the wheel. Before the introduction of power steering, the diameter of steering wheels in heavy trucks was particularly large to help the driver expend less force in turning the vehicle.)
Kinematics relies on a still more restricted description of motion than that outlined by Newton and amplified by Poinsot. It is defined as a view of motion independent from the forces causing it. Since machines are, from one point of view, manifest attempts to eliminate random, or, as Franz Reuleaux would say, “cosmic,” forces, kinematics is always “kinematics of machinery.”14 The text that is most often mentioned as the declaration of independence of kinematics, André-Marie Ampère’s Essai sur la philosophie des sciences (1834), clearly recognizes this interdependence of machinery and geometric description:
It [i.e., the new science of kinematics] should treat in the first place of spaces passed over, and of times employed in different motions, and of the determination of velocities according to the different relations which may exist between those spaces and times. Furthermore it should study the various instruments by means of which one motion can be changed into another; so that if one conceives of these instruments as machines (as is usually the case) one must define a machine not, as one customarily does, as an instrument by means of which one can change the direction and the intensity of a given force, but as an instrument by means of which one can change the direction and the speed of a given motion.15
While French theorists put serious efforts into founding and institutionalizing kinematics as a deductive science, British engineers were attacking its practical problems. Kinematically speaking, the rise of the steam engine as the motor of the Industrial Revolution was the result of a specific mechanism to “change the direction and speed of a given motion,” more precisely the (reciprocating) translational motion of the piston, into the rotational motion of the working beam. It was invented by James Watt in 1784 and was immediately patented so that it could reach the open market at the very beginning of the nineteenth century. Only then could the proliferation of cylindrical machines in the nineteenth century really begin.16
This mechanism, commonly called “Watt’s parallel motion,” changed the steam engine from a pendulum into a fully rigid mechanism. It connected the piston that rose from and was pushed into the cylinder with the beam that pivoted on a central column.
The pivoting beam was part of the early architecture of steam engines, which were primarily used to pump water. Before Watt, only the downward stroke of the engine was powered: either the rapid cooling of the steam under the piston created a vacuum that pulled the piston down, or steam was injected above the piston. In this configuration, where the piston pulled on the beam (and the beam pulled on the pumping vessel), it was enough to use chains or ropes as a connection; they were run across the ends of the beam, and the kinematic conflict between the semicircular motion of the beam and the straight motion of the piston was reconciled—just as it was in Kleist’s marionettes—by the slackness in the connection (fig. 1).
FIGURE 1. Watt’s 1774 engine. The piston (and the valve gear) are connected to the beam by a chain; the power stroke can only be downward. Reprinted from Thurston (1902, 98).
This paradigm had to be changed when Watt began to power both the up- and the downstroke of the piston by using steam as a positive (expanding) rather than as a negative medium. Now the piston was pushing up on the beam as well as pulling it down; ropes and chains did no longer work, and a simple rigid rod without a mediating mechanism would have destroyed the machines in a very short time—if the piston were pushed along a line that deviated from the cylinder’s axis, it would scrape against the inside walls, destroying its symmetry and losing the ability to seal and maintain pressure.17 Even without these difficulties, the practical problems of boring or casting accurate enough cylinders in sufficiently strong materials and of finding lubricants to minimize the inevitable friction proved very hard to overcome for most machine builders in the late eighteenth and the very early nineteenth centuries.18 One of Watt’s many advantages in the race for efficient engines was that through his partner Matthew Boulton he could intervene directly in the manufacturing of cylinders, asking for more precision in boring and for stronger alloys.19 To Boulton he first announced his discovery that a rigid linkage configured the right way could guide both the up-and the downstroke of a double-acting steam engine without stressing the materials involved.
In a formulation at once revelatory of the truly empirical process of engineering and of the stunning novelty of motion conversion, Watt wrote of the contraption he called “parallel motion”: “When I saw it work for the first time, I felt truly all the pleasure of novelty, as if I was examining the invention of another man.”20 Yet like so many engineering advances in the nineteenth century, parallel motion was an avoidance of conflict rather than an invention of something entirely new. The mechanism simply caught two semicircular movements at the point where they intersected along a seemingly straight path (fig. 2). One was the movement of the beam OA—A, which in kinematic nomenclature was called the crank (the Kurbel, of which Kleist’s Herr C. dreamed); the other was the link OB—B affixed to an opposite wall, called the follower. Both were connected by a third link A—B, the coupler. As the crank moved up and down, it led the follower into a mirror image of its own motion whereby a point M on the coupler was forced to trace out an elongated figure eight, the sign of infinity. If the proportions of the links were chosen appropriately and the movement of the crank was restricted accordingly, M traced a line that was approximately parallel to the beam’s support column. A piston rod, attached to C, could push and pull in a line extending from the cylinder’s axis. Depending on the machine’s architecture and size, Watt translated this parallel motion horizontally by means of pantographs—linkages based on the parallelograms that had long been used to translate writing and drawing across a plane—which yielded other parallel points M′ able to drive a valve train or an auxiliary pump (fig. 3).21
Watt’s mechanism not only allowed for a potentially infinite increase in power output but also universalized the use of steam engines just as much as fossil fuel rendered them independent of natural location. The four-bar linkage (the hatched line at OB and OA on the left of figure 2 indicates a fixed frame and counts as one bar, just like the “floor and datum” on the right) is the most economical way of mediating between translational and rotational motion. To repeat, such mediation is necessary because in a finite mechanism (unlike in the universe or in a gun) every translational motion needs to be “returned,” every straight motion needs to be reciprocal or oscillating.22 Using variants of the four-bar linkage, engineers could
