MULTIPLE POINTS ON THE COUPLER CURVE OF TRANSITIONAL 4-HINGE PLANAR LINKAGES

In the present paper a detailed analysis is made of the conditions gov erning the existence and position of multiple points on the coupler cu rves of a four-hinge linkage. It is shown that apart from the circle o f singular foci there exists another ''complementary curve'' on which also there may be multiple points. An analysis is made of the case of transitional mechanisms, in which there are double points outside the circle of singular foci but lying on the complementary curve. A detail ed look is then taken at the conditions for the position of threefold points and cusps, which must be both on the circle of singular foci an d on the complementary curve. In addition there is a description of tw o simple procedures for the graphic synthesis of transitional mechanis ms with threefold points on their coupler curve.