motor to the tool; they followed the same “phoronomic” laws as their elements and were fully determined (even though describing them mathematically remained difficult).
Mechanisms that employed the three cylindrical pairs were at once the basis and the ideal of Reuleaux’s kinematics because they excluded all interference by outside (in Reuleaux’s terms, “cosmic”) forces and thus allowed for a coherent logic of machine elements. By calling his pairs Umschlusspaare and their combination “chains” (Ketten), Reuleaux invoked an embodied logic of material elements—Kettenschluss is, after all, the German word for syllogism.41 The overall goal of Theoretische Kinematik was “kinematic synthesis”—which, in the wake of Kant’s distinction between analysis and synthesis and with a view of making good on Monge’s and Ampère’s program, Reuleaux conceived as the science of deducing kinematic assemblages a priori, regardless of material or even of purpose.42 Reuleaux coined a word to invoke both the exclusion of cosmic forces and the a priori necessity of kinematic design: zwang(s)läufig. It has since entered the German vernacular with the meaning “inevitable”; Kennedy translates it as “constrained,” and Reuleaux in a note offers the Greek “desmodromic,” which has caught on in certain engineering circles.43
Reuleaux was too much of a practitioner not to know that many mechanical linkages cannot be converted into cylinder chains with fully constrained pairs—ropes and belts and springs, for example, could not be enclosed, and the strain on the material in enclosed links often exceeded the metallurgical capacities of his time. Nonetheless, he understood the history of machine design to be a logical—a zwangsläufig—development from “force-closure” to “pair-closure.” Force-closure, like the link between a cam lobe and a valve or between the wheel of a locomotive and the rail, is open to “cosmic” interference (valve float or wheel slip); pair-closure—its basic forms being embodied in the three cylindrical enclosed pairs—eliminates such interferences by systematically forcing motion in one direction to the exclusion of all others. The change from one to the other provides, according to Reuleaux, a parameter by which to measure progress in machine design: “The question now arises:—what is the special kinematic meaning or nature of the changes by which the machine has been advanced to its present degree of completeness? . . . I believe the answer to this question is:—the line of progress is indicated in the manner of using force-closure, or more particularly, in the substitution of pair-closure, and the closure of the kinematic chain obtained by it, for force-closure.”44 One way of describing this development in kinematic terms—and in terms provocatively contrary to liberal philosophies of history—is to chart it as the successive elimination of freedoms. For engineers, an object within three-dimensional Euclidean space has six degrees of freedom: it can move along the three axes of space and it can rotate around them. The motions of mechanisms (as opposed to those of a ship or a plane, from which many of the technical terms for the degrees of freedom are taken) are constrained to one plane, as in Watt’s parallel mechanism, thus eliminating all freedoms except rotation around an axis and translation along it. These two freedoms, as well as their combination in the motion of a screw, are embodied, as Reuleaux had casually remarked, in the body of the cylinder.
Against this backdrop, the history of machine development, which Reuleaux inserted as a compact chapter into his Theoretische Kinematik and later dispersed over the second volume of the Kinematik, which appeared in 1900, amounts to a history of the progressive elimination of “cosmic” freedom.45 “We have recognized and examined in certain pairs of kinematic elements the property of force-closure, by which a certain amount of kosmic freedom is left in the machinal system, and seen that it has been for thousands of years the aim of invention to limit or destroy this freedom.”46 Reuleaux’s Ur-machine is a single cylinder: the fire drill, a pointed stick twirled by hands on a wooden cavity with the purpose of igniting the wood itself or fibers placed around it. So long as human hands twirl the stick, there is pair-closure only between the recess and the point of the stick. The next step consists in replacing the hands by a rope, which does not alter the nature of the closure but speeds up the rotation. Then a stone or a fitted piece of wood is placed on top of the rotating stick in such a way that all motion except rotation is eliminated. Now the twirling stick is part of a pair-closed chain that produces fire in a fully predictable manner.
A more contemporary but perhaps not equally felicitous example is the steam locomotive. It replaced the horse-carriage, which had been improved upon in various ways, for example in shock absorption and in the development of steering gear, but which was still beset by the potential disturbance of cosmic forces, such as uneven roads or drunken coachmen.
Force-closure still remained, if nowhere else at least in the preservation of the direction of motion, which still demanded accustomed animals and an intelligent driver. Men naturally attempted to replace this force-closure by pair-closure. In the Railway the rails are paired with the wheels,—force-closure is used only to neutralize vertical disturbing forces. The step thus made in the direction of machinal completeness . . . was in reality no other than the uniting of the carriage and the road into a machine. The rail forms a part of this machine, it is the fixed element of the kinematic chain of which the mechanism really exists. . . . In opposition to this we have the problem of steam locomotion on common roads, which has been so feverishly taken up again within the last few years, but the solutions of which seem doomed to eternal incompleteness, for they are self-contradictory. It is desired to make something which shall be a machine, but in which at the same time the special characteristic of the machine—the pairing of elements—may be disregarded.47
To be sure, the pair-closure between the locomotive and the rail is only approximate: it is achieved by the weight of the engine (and in fact often breaks when the train has to climb a steep incline). What Reuleaux means by the inner contradictoriness of the automobile is that the wheels of the car cannot form a pair-closure with the road if the automobile is defined as a vehicle that can go anywhere by itself; he mentions the recent discovery of wheels made of “India-rubber,” which try to emulate rails insofar as “vulcanized India-rubber, externally flattened upon the road, serves as a smooth uniform surface for the rigid tread to run upon, thus corresponding generally to the rail of the railway”;48 kinematically speaking, however, the automobile is a failure because the pair-closure of its engine (the slider-crank-linkage) is stunted by the weak force-closure of its contact to the road. The further development of rubber wheels and the improvement of roads by means of another cylindrical machine, the steamroller, will alleviate this weakness, but every instance when a car spins its wheels or swerves off the road or just out of its lane is a testimony to the justness of Reuleaux’s observation.
Although in the use of his terminology Reuleaux seemed to emulate Kant’s critical philosophy, his view on the history of machines was Hegelian. Very much in the tradition of Hegel, Reuleaux tried to understand the history of machines and mechanisms as a slow but logically driven and often dialectical process toward maximum efficiency. His ideal was a machine, consisting of absolutely rigid elements connected by cylindrical pair-closures, that would capture and convert the energy flowing through the cosmos with as little noise and as little loss as possible. But this historical dialectic was the limit of his Hegelian leanings; in cosmological terms Reuleaux was thoroughly modern. Like Poinsot, like Auguste Comte, and like the foremost physicists of his time, he conceived of the cosmos, not as a living being (as Hegel still did), but as a vast machine driven by heat, in which the planets were the remnants of a linked planar mechanism. Perfecting transmissions, from this perspective, meant combating entropy in the only arena possible, namely by slowing down the dissipation of energy in fully linked, “pair-closed” machines.
Reuleaux also paid attention to the devaluation of human work. Like most engineers and scientists in the latter half of the nineteenth century, he was keenly aware of the destructive and dehumanizing potential of industrial modes of production and sought to confront the “burning question of our time, the question of the worker,” with proposals of his own.49 Characteristically, he saw the problem in the motor end of the machine: it is the logic of capital, he argued, that requires ever more powerful motors,
