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This paper proposes a two-step optimization procedure for resolving the actuation forces of a kinematically redundant planar parallel manipulator following a specified trajectory. Simulation results compare the performance of the manipulator when different degrees of kinematic redundancy are used. It is seen that the required forces are generally lower when there are more degrees of kinematic redundancy; however, more mechanical energy is required. In some cases, fewer degrees of kinematic redundancy can produce similar results from a force point of view, while requiring less energy. Furthermore, the importance of correctly choosing an initial configuration is presented. The proposed method finds an optimal initial configuration by considering a performance index along the entire trajectory. The evolution of the singularity loci as the manipulator moves along the trajectory demonstrates why certain initial configurations should not be used, even if they are optimal at the initial pose.

The effect of the number of degrees of kinematic redundancy on the actuation forces of a planar parallel manipulator