Wrench Capabilities of Planar Parallel Manipulators and their Effects Under Redundancy

Abstract

where J is referred to as the Jacobian matrix. In addition, an extended problem can be formulated as the analysis of the maximum twist or wrench that the end-effector can perform in the twist or wrench spaces, respectively. The knowledge of maximum twist and wrench capabilities is an important tool for achieving the optimum design of manipulators. For instance, by being able to graphically visualize the twist and wrench capabilities, comparisons between different design parameters, such as the actuator torque capabilities and the dimensions of the links, can be explored. Also, the performance of an existing manipulator can be improved by identifying the optimal capabilities based on the configuration of the branches and the pose of the end-effector. This work focuses on the wrench capabilities of planar parallel manipulators (PPMs), the geometric interpretation of their wrench polytopes, the derivation of wrench performance indices, and how the inclusion of redundancy affects the performance of parallel manipulators (PMs). The wrench capability analysis of a manipulator depends on its design, posture, and actuator torque capabilities.