Abstract
This paper presents a geometric synthesis procedure for spherical (6, 7) linkages, often known as spherical six-bar linkages, based on adding two spherical RR constraints to a spherical 3R serial chain. The design can use the spherical 3R chain to shape the movement of the linkage and identify a set of task positions that shape the trajectory of the end-effector. We use five task positions to completely specify the two RR chains that constrain the system to one degree-of-freedom. This procedure yields spherical versions of the various topologies for the planar Watt and Stephenson six-bar linkages. We find that for any design problem we obtain at a minimum of two design candidates for the Watt-type linkage, and as many as 185 different design for all of the topologies obtained by constraining the spherical 3R chain. Wampler's method for the analysis of spherical loops is used to analyze these linkages. An example design is presented in detail.