A Kinematic Synthesis Methodology for P-Drivable Spatial Single Degree of Freedom Mechanisms to Avoid Singularities

For a single degree of freedom spatial mechanism, a reference frame attached to any of its links produces a continuous motion of this frame. Given the progression of this frame from the start through the end of the mechanism's motion, this paper seeks to identify specific points relative to this moving reference frame. The points of interest are those that can be coupled with a second point determined in the fixed frame to act as the end joint locations for a spherical-prismatic-spherical (SPS) driving chain. If the selection of the point pair is made such that the change in distance between them as the mechanism moves is strictly monotonic, then the SPS chain they define is potentially capable of driving the mechanism over the desired range of motion. This motion is referred to as locally P-drivable because a global solution is not ensured by the process proposed herein. This synthesis process can avoid singularities encountered by actuating the mechanism at one of its original joints. The proposed approach enables the dimensional synthesis of a single degree-of-freedom mechanism to focus on creating circuit-defect-free solutions without concern for potential singular positions. The actuating chain can then be determined as a separate step in the synthesis process. This paper also considers motions that are not P-drivable and the specialization to planar systems with the synthesis of a P-drivable RPR chain.