Synthesis of Spherical Four-Bar Mechanisms for Two or Three Prescribed Coupler-Curve Cusps

This paper presents a new approach for the synthesis of spherical four-bar mechanisms with two or three prescribed coupler curve cusps. According to the configuration of a spherical four-bar mechanism whose coupler point coincides with the instant center at two separated positions, two kinds of degenerated curves for the corresponding spherical Burmester curves are obtained. For each degenerated curve, a synthesis procedure is proposed for the dimensional synthesis of spherical four-bar mechanisms to trace a coupler curve with two prescribed cusps. The possible types of spherical four-bar mechanisms with two-cusp coupler curves are discussed. Furthermore, special spherical double-rockers are also presented for tracing a symmetric coupler curve with two cusps, tracing a doubly symmetric coupler curve with two cusps or tracing a symmetric coupler curve with three cusps.