else utilize the transmission as the machine’s tool, as is the case in motorized vehicles. The slider-crank mechanism—an avatar of the four-bar linkage—became the most successful of these linkages: first in the locomotive, then in the internal combustion engine, it allowed the motor to produce nothing but rotation.
FIGURE 2. (a) Watt’s “parallel-motion” linkage in schematic form: OA—A is the beam’s arm, acting as a crank; A—B is the coupler; OB—B is the follower, anchored to a wall. The point M on the coupler will trace out a figure eight, part of which is “straight” and can be used to guide the piston rod. (b) The mechanism on Watt’s engine. Point M is transposed to M′ by means of a pantograph and there guides the rod of a pump. The sun-and-planet gear on the working side of the beam would be useless without the continuous motion provided by the parallel linkage. “Floor and datum” is what Reuleaux (and Heidegger) call Gestell. Reproduced with permission of The McGraw-Hill Companies from Richard Hartenberg, Kinematic Synthesis of Linkages,© 1964.
From a kinematic point of view, it is irrelevant where the motion of a mechanism originates and where it is utilized, as kinematics is not concerned with forces or with stresses on material that might result from the impact of forces.23 Kinematic transmission functions without a fixed origin (such as straight-line motion) and without a determined destination (such as pure rotation) but is concerned (to use Walter Benjamin’s term) with translatability (Übersetzbarkeit) as such. All that linkages, and machines in general, need is a frame that determines the orientation of their movements; it generally consists in anchoring one link to an immobile part that in figure 2 is called the “floor and datum” but that in Reuleaux’s seminal terminology becomes Gestell.24
FIGURE 3. Drawing of a Watt and Boulton steam engine, after 1784. The parallel-motion linkage is on the right; on the left is the sun-and-planet gear driving a flywheel. Also visible on the left side is a governor, another of Watt’s inventions. It rotates with the engine stroke and shuts down the steam supply if the machine runs too fast. © Science Museum / Science & Society Picture Library—All rights reserved.
FIGURE 4. Two of Reuleaux’s teaching models. The curve traced by a point on the coupler depends on the length of the links, and on which of them is immobilized by the Gestell. Reprinted from Reuleaux (1876, 68, 71).
The curves traced by a point on the coupler (the link d—e in the linkage on the left in fig. 4) are an instructive example of the irreducible empiricism and pragmatism in the construction of kinematic transmissions. They change in proportion to the length of the individual links and to the position of the Gestell, but the rate of this change and the bewildering variety of the resulting curves defeat attempts to describe them algebraically or in any other form of abstraction. This was true at least as long as the means of representing these curves were, like the mechanisms that produced them, analog; computer programs now can easily model coupler point curves, and the problem, like many others, has disappeared from the problem sets of kinematics students. Franz Reuleaux felt that the best way to teach the properties of four-bar (and other) linkages was to build (and license) an extensive collection of teaching models, which can still be admired, for example, in Cornell’s Sibley School of Mechanical and Aerospace Engineering. Seeing these models in motion—or seeing Theo Jansen’s fantastically inventive linkage “beasts” prowl the beaches in Holland—gives us a rare sight of kinematics liberated from the servitude to motor and tool.25 They show that there is distinct grace and beauty in forced motion, as Kleist’s Herr C. claimed with seeming contrariness. Uncovering the aesthetics of forced motion as an object of contemplation, as a driving force in mechanical engineering, and as an element in nineteenth-century literary culture is a goal of the following pages.
Such a goal was far from the mind of Franz Reuleaux, the great German synthesizer of machine design and kinematics; with his Theoretische Kinematik of 1875 he wanted to provide a space for kinematics on the curriculum of German research universities, which had been founded by men around Friedrich Schiller for whom all things mechanical were anathema. While experimental physiologists, despite operating with rather gruesome empirical remainders themselves, had managed to secure for themselves a prestigious place in the German research university, mechanical engineering was still relegated to professional schools and para-academic institutions. Reuleaux, who had traveled widely in Europe and in the United States, felt that German engineering products stood no chance in an increasingly globalized market and that it would behoove the Second Reich to centralize engineering training and raise it to a par with other academic disciplines.26
In the German context, any discipline wanting to graduate to a full-fledged science had to meet two fundamental requirements: it had to be in discursive control of its own principles and presuppositions, and it had to be able to give a coherent account of its own history. In the case of experimental physiology, for example, this meant that the dubious principle of Lebenskraft (vital force) had to be abandoned in favor of the first law of thermodynamics and that a careful rewriting of its history, especially with regard to Romantic visions of vitality (including Goethe’s), would integrate physiology into the context of German intellectual history. Many of Herrmann von Helmholtz’s popular lectures were devoted to this task.27 In the case of mechanical engineering this meant that all contingent factors in machine design—such as the metallurgy of machine parts, the turbulences of power generation, the economic concerns of the manufacturing process, the social conditions of factory workers—would have to be bracketed, and the logic of machines developed deductively. Relying on the definitions by Ampère and other theorists, Reuleaux realized that an a priori deduction of the logic of machines could proceed only from the kinematics of machinery. The Theoretische Kinematik (translated into English in 1876 as Kinematics of Machinery) seeks to unfold this logic beginning with the most fundamental givens of material contact, and it invents a symbolic language in which machine elements can be classified and their combination be taught. At the same time—hidden in the vast body of his book—Reuleaux sketched a history of machines and mechanisms that emulated in scope the grand historico-philosophical designs of German historicism.28
With a good measure of irony, though not without systematic pride, Reuleaux reached back to the pre-Socratic sage Heraclitus for his most fundamental statement: “Everything rolls.”29 Everything in a machine is in contact with everything else in a motion that is at the same time rotational and translational. Motion in and of machines is always relative motion (anchored by the Gestell of its frame), and the successive positions of one extended body in relation to another can always be configured as one curve rolling off another. In the part entitled—with obvious reference to the opening chapter of Immanuel Kant’s Metaphysical Foundations of Natural Science—“Phoronomic Propositions,” Reuleaux demonstrates this relationship first as that between a moving and a fixed line. The successive positions of the moving line P—Q (or of any other figure through which a line can be drawn) with respect to the line A—B can be described by two separate lines: first, as the line between the successive points around which the line rotates (its poles) as it moves along the x axis in an imaginary Cartesian coordinate system (the line O1, O2, O3 in the following illustration); and second, as the line between the successive points that indicate the rate of rotation along the y axis (the line M1, M2, M3) (fig. 5).
Contracted
