Page:The Kinematics of Machinery.djvu/217

 HIGHER PAIRING AT CHANGE-POINTS.

�195

�in Fig. 145, the length of the link I be made equal to that of the crank a, then when the crank makes a quarter revolution the centre of the block c has been brought up to the axis 1 of the crank, and it would be moved forward symmetrically as the rotation continued, were it not that a change-point here occurred. The centre of the

��FIG. 155.

�pin 3 coincides with the centre 1, a and b cover each other, and can together turn about their common axis 1. The chain thus becomes at its point of change simply a pair of elements. This can be prevented by pairing the link b with the opposite one d, for which purpose we must find the centroids of both links.

��FIG. 156.

�An examination of the relative motions of b and d shows at once that these centroids are Cardanic circles (Fig. 157), the smaller having a radius a = b, and described about the point 2 (which is a point always of the link b), the larger having a radius twice as great, described about the point 1 of the link d. It is easy to see that the pairing at the point of change can be effected by supplying b and d with such small portions of toothed profiles as can come into action at that point.

o 2

�