Optimized Configurations of Kinematically Redundant Planar Parallel Manipulator following a Desired Trajectory

This paper presents an optimization methodology for achieving minimum actuation torques of a kinematically redundant planar parallel mechanism following a desired trajectory using binary coded Genetic Algorithms (GA). A user interactive computer program developed in present work helps for obtaining inverse kinematic solution and Jacobian matrices at a given Cartesian coordinate location of the end-effector. Furthermore, the joint torques are obtained from the end-effector forces (wrench) using Jacobian matrix at every location. The resultant joint torque vector can be used to describe the objective function. The variables of the optimization problem are redundant base prismatic joint displacements and the constraints include the variable bounds and the pre-defined trajectory lying within the original workspace. The outputs of the kinematically-redundant 3-PRRR manipulator are compared against the results for a non-redundant 3-RRR manipulator. The results show that the redundant manipulator gives relatively lower input torques. Also, it is observed that while passing through singular configurations on the trajectory, finite values of torques are achieved. Results are shown for a straight-line trajectory.