Motion/Force constraint indices of redundantly actuated parallel manipulators with over constraints

Abstract

Abstract Redundantly actuated and overconstrained parallel manipulators (ROPMs) have several advantages, such as reduced singularity and higher stiffness. This paper proposes several motion/force constraint indices for the performance analysis and optimization of ROPMs. First, a method is proposed to extract a multiple-degree-of-freedom (DOF) ROPM into several one-DOF mechanisms by “losing” some wrenches in an ergodic manner. Then, a new output constraint index (OCI) is proposed that considers the influence of all the one-DOF mechanisms with multiple wrenches on the original ROPM. Combining the input and output constraint performance indices, a total constraint index (TCoI) is defined to evaluate the constrainability of certain configurations. A good constraint index (GCoI) and a poor constraint index (PCoI) based on the TCoI are then established to reveal the overall constrainability of certain workspace. The proposed TCoI, GCoI and PCoI are coordinate-free and range from zero to unity. Finally, the feasibility and generality of these new indices are demonstrated by the performance analysis of three ROPMs, including one planar case and two spatial cases. Using these proposed indices, the dimensional optimization of one spatial ROPM is also discussed.