Design of Kinematically Redundant Linkage Following a Desired Trajectory

Abstract

This paper presents an optimum design approach for selecting the base-joint locations of a kinematically redundant parallel linkage following a desired trajectory by minimizing the active joint torques. Kinematically redundant parallel mechanisms offer several advantages such as reduced singularity loci, high dexterity indices etc. However, in path tracking problems, selection of redundant joint positions is tedious procedure due to existence of multiple solutions for inverse kinematics. Some criteria can be employed to resolve the complexity of identifying these extra degrees of freedom. In present task, joint torque minimization is considered and the problem is resolved as a static analysis formulation. The static analysis gives joint torques for known applied wrench vector and resulting torque-norm which is a function of redundant degrees of freedom (DOF) is minimized using genetic algorithms (GA). Interactive computer programs are developed for kinematics and static analysis along with binary coded GA. Results are presented using a 6-DOF, 3-PRRR planar parallel mechanism following predefined trajectories