Singularity-Free RPR and SPS Chains for Actuating Single Degree of Freedom Planar and Spherical Mechanisms

This paper presents a method of selecting joints relative to a fixed and moving (coupler) frame that can be used to actuate a single degree of freedom planar mechanism using a revolute-prismatic-revolute (RPR) chain or a spherical mechanism via a spherical-prismatic-spherical (SPS) chain. Given a single degree of freedom mechanism, a moving reference frame attached to any link has a motion that can be described with a single parameter. A point relative to this moving frame is sought such that it either continually increases or decreases in distance from a point in the fixed frame over the entire motion. The mechanism can then be moved by placing an actuated prismatic joint between the two points. Moreover, the singularities relative to the joints in the original mechanism are not a concern and the dimensional synthesis can focus on creating the set of circuit-defect free solutions. From this analysis, a unique fixed point is determined relative to two positions and their velocities with the following characteristic. All points in the moving reference frame that are moving away from it in the first position are approaching it in the second position, and vice versa.