Page:The Kinematics of Machinery.djvu/337

 OLDHAMS COUPLING. 315

which is formed from the swinging block, we may call a swinging cross-block. The motion produced is very simple. The centroids of a and c are Cardanic circles, the smaller (for a) having a diameter = 1.2, and the larger described from the centre of the cross-block with a radius = a, as in Fig. 243. The primary centroids for b and d are infinite, and must be replaced by secondaries, which are here omitted ; they would show that every point in b describes circles relating to d, the whole piece moving always parallel to itself. The turning double slider-crank is not unfrequently used, its most common application being in the driving gear of steam pumps in the form (C^P^X- It is often of value also from the fact that if the crank revolve uni- formly, it imparts to the cross-block c a simple har- monic motion.

The mechanism ( C^P^Y- If the chain be placed on a, the links b and d move about fixed axes 2 and 1. The cross-block revolves, its centroid rolling always upon that of a. as is shown in FIG. 245.

Fig. 244. We shall call it a

turning cross-block* The links b and d are kinematically identical, although constructively different ; their angular motions are always the same.

There have been many practical applications of this train. The well known Old ham's coupling (Fig 245) gives us one inter- esting illustration. The object of this mechanism is the com- munication of a uniform rotation between two parallel shafts, its special formula is therefore (CJP-$ror (C'^P^. The bed-plate of the two shafts is the frame a (the crank originally), the middle disc is the link c,the cross-block P...J_...P; the two shafts and their con- nected discs are the links b and d. To make the construction of the coupling clearer, the three last-named links are shown sepa- rately in Fig. 246. The special property of the train (G" 2 P) a which is utilized in Oldham's coupling is the uniformity of the rotation


 * Compare " turning lilook " for (C" F) j> 2:9.