The Cylinder. Helmut Müller-Sievers

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 from polygons into smooth curves, these curves fully describe the instantaneous position of the translating and rotating line P—Q in relation to the line A—B, which lies on the same plane (it is “con-plane”). Reuleaux calls these curves Polbahnen; his translator Kennedy calls them centroids (later changed to “centrodes”).³⁰ The purpose of this abstraction is to show that the relative planar motion of any two bodies can be fully described once their centrodes are known, and that this relative motion can be described as a rolling.³¹

      Machine parts, then, just make actual what is potential in any relative motion of two rigid bodies in a plane. Reuleaux operates with the abstraction of moving points and lines only because he strives for maximum generality—for the justification of his law that everything rolls. He is fully aware, of course, that the subject of kinematics is machinery: that is, an assembly of rigid bodies that have additional properties, even if one abstracts from material and from the forces to which they are subject.³² The reciprocal rolling of the centrodes, as soon as it is conceived as being performed by two extended bodies moving in the same plane, must be understood as the rolling of one cylinder against another, for it is the cylinder alone that has an extended curved surface and a fixed axis of rotation.³³ Even if one of the bodies does not move, the other can roll on it, as a locomotive’s wheel rolls on its rail (which is conceived as a cylinder with infinitely large diameter). The application of the Heraclitean law of rolling to the real world of extended machine parts therefore reads: “We may extend the law just enunciated for plane figures equally to the relative motion of solids . . . : Every relative motion of two con-plane bodies may be considered to be a cylindric [sic] rolling, and the motions of any points in them may be determined so soon as their cylinders of instantaneous axes are known.”³⁴

      FIGURE 5. The relative translation and rotation of an extended body represented as the rolling of one body (P—Q) off another (A—B). Reprinted from Reuleaux (1876, 62).

      Even though the cylinder as an embodied motion is crucial for the understanding of the relative motion of extended bodies, Reuleaux introduces it in the first part of his theoretical kinematics without further comment or reflection. Far-reaching consequences of this conception could be explored: for example, the oscillation of rolling as an intransitive verb of motion and as a transitive verb denoting perhaps the most important industrial processes of the nineteenth century. Spheres, for example, can roll on one another (as they do in ball bearings), but only cylinders can roll something. Yet the cylinder, although everywhere present,