Force/Motion transmissibility analysis of a 3-degree-of-freedom parallel mechanism with offset joints

Abstract Force/motion transmissibility serves as an essential performance metric in the kinematic analysis of parallel mechanisms. The initial step in evaluating force/motion transmissibility involves identifying the basis elements of twist and wrench spaces. In parallel mechanisms consisting of PRS, RPS, SPR, and PU limbs, the identification of the basis elements of a given limb is relatively straightforward, as the limb constraints can be evaluated as pure forces and torques. However, in limbs where the axes of the joints are offset, determining these basis elements becomes quite complex. Typically, the constraints of these limbs involve the interconversion between general screws and line vectors or couples. This paper focuses on a 3- P RRU parallel mechanism. Procedures for identifying the basis elements are investigated. Screw theory is used to elucidate the relationships between the variations in the basis elements and the configurations of the mechanism. Moreover, the influence of an offset between two revolute joint axes on the force/motion transmissibility is systematically analyzed. The results indicate that, compared to the case without offsets, the introduction of offsets enhances the force transmissibility of the mechanism.