Classification of RRSS linkages

This paper classifies the movement of the RRSS spatial linkage in terms of its link dimensions. The constraint equation for this chain relates the rotation angles of the input crank and coupler around the two revolute joints. The condition for a real valued solution for the coupler angle as a function of the input angle yields a quartic polynomial. We use three polynomial discriminants obtained from this quartic to find explicit conditions for the cases available for the movement of the input crank. A similar analysis characterizes the coupler movement by determining conditions that ensure real solutions for the input angle as a function of the coupler angle. Combining the results we obtain parameters that characterize movement of the RRSS linkage. Examples for the various cases are provided.