Kinematic design of the RSSR-SC spatial linkage based on rotatability conditions

This paper studies the relationship between the physical dimensions of the RSSR-SC spatial linkage and the range of motion of its input link. The study results in a quartic equation that defines any configuration of the linkage for given values of the input link angle. Obtained from this quartic equation, we use three polynomial discriminants in order to find the corresponding rotatability condition for all cases available for the motion of the input link. Examples for each case are provided. Moreover, during the design process, a branching analysis is also conducted, since the main goal of this work is to design the RSSR-SC linkage in such a way that its input link has full rotatability without the undesirable branching problem.