Page:The Kinematics of Machinery.djvu/591

 SYNTHESIS OF COMPOUND CHAINS. 669

160. Compound Chains.

Our synthetic investigation lias now brought us, in a number of different directions, to the limits of the simple chains and to the ground covered by the compound ones. We see at once that the latter include so many important practical cases that it would be impossible to leave their synthetic treatment untouched. But there is no end to the possible combinations which can be made by join- ing one kinematic chain to another, and it is therefore very necessary to inquire if every problem arising in this way must necessarily fall within the region of kinematic synthesis, or if some distinction which may simplify our work does not exist between different classes of problems.

A distinction of this kind is, fortunately, furnished by the way in which the compounding has been carried out. A compounding may be a mere placing in sequence of known motions or chains, giving us therefore nothing new, or it may be so arranged as to give us some result in itself quite different from before. It is evident that these two methods of compounding may be treated in quite different ways. Let us first examine a few examples of them.

To take first a very simple case ; we obviously obtain nothing kinematically new by placing one belt-train or one wheel-train behind another. The relative velocities of rotation of the different parts may be altered, the nature of these rotations is, however, exactly the same as in the simple chain, and the advantage of the compounding in such cases is connected simply with the repeated use of one and the same form of train.

Fig. 423 is a sketch of the leading train of a beam-engine. The chain here used, which consists of the seven links a, b, c, d, b v a x and d lt is clearly compound. It consists of a lever-crank a, b,c,d = (Cy and a crossed swinging slider-crank ({/JP+), The latter is shown separately, in a form already known to us, in Fig. 424. The com- pounding has been carried out by combining the fixed links d and q of the two chains into one frame, and the links c and \ into a ternary link, the " beam " of the engine. The angle of swing of the lever c and the coupler \ becomes therefore equal, and the stroke of the slide rf t is made dependent upon the length of the crank a.

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