Synthesis of spherical four-bar path generator satisfying the prescribed tangents at two cusps

Design equations for spherical four-bar linkages to trace a coupler curve with two prescribed cusps are derived in this study by using a special case of spherical Burmester curves. For the case in which the tangents at two cusps are also prescribed, an analytical method is proposed with the aid of the foregoing design equations associated with the concept of the spherical cross ratio and spherical Bobillier theorem. The proposed method is straightforward and quite useful for those cases in which the tangents at two cusps are neither on the same plane nor on parallel planes. Numerical examples are also provided for illustrating the entire technique.