Page:The Kinematics of Machinery.djvu/305

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QUADRIC CRANK CHAIN. 283

appears in modern text-books ; and we see also the reason of the neglectful treatment they have received from the higher mechanics, but our investigations have shown us something which helps to explain the attachment to these old and well preserved problems. This no doubt rests chiefly upon the fact that three of them, the lever, inclined-plane and screw, represent pairs of elements, perhaps also upon the existence in another, the pulley, of a timid step towards a free and exhaustive treatment of a kinematic chain.

It was therefore in the first place an indistinct feeling that the motions of a machine were founded upon those of pairs of bodies, which led to the " simple machines." In point of fact they have, as it were, felt the way in this direction. It is this that has allowed the lever, inclined-plane and screw to which we arrived by a priori reasoning as the three lower pairs (15) to take such deep root. The faint trace of the law of the kinematic chain which appears in the two forms of pulley is both interesting and striking only to this extent do the venerable problems seem justified. I think, however, that our examination of them has shown that this whole department of elementary Mechanics, whether treated by itself or as a part of Physics, in text-books or orally, absolutely requires a very searching revision.

65. The Quadric (Cylindric) Crank Chain (C'[\

The kinematic chain which consists of four links connected by parallel cylinder pairs, and which has already repeatedly engaged our attention, is one of the most important chains occur- ring in practical machine-construction, and we shall now proceed to its analysis. Its complete treatment belongs to applied and not to theoretic Kinematics ; our purpose here is not its exhaustive treatment, but simply the examination of the various forms in which it is applied as a mechanism. We shall find that they have very great variety.

We may look first at the train already described in G2 and shown in Fig. 201, where the four links are so proportioned that,