Kinematically redundant planar parallel mechanisms: Kinematics, workspace and trajectory planning

This paper introduces two general architectures of kinematically redundant planar parallel mechanisms. Their kinematic models are analyzed, an analytic workspace determination method is presented and a simple algorithm for their trajectory planning is provided for prescribed Cartesian trajectories. The trajectory planning algorithm uses the redundant degree of freedom to avoid singularities and optimize the actuator forces while taking into account the mechanical limits of the mechanism. The trajectory planning is computed globally in order to avoid local minima/maxima and to predict and take into account large variations in optimal values of the redundant degree of freedom. The algorithm guarantees that a solution will be found, if the Cartesian trajectory is feasible. Two planar parallel mechanisms with kinematic redundancy are used to demonstrate the algorithm. The kinematics of the mechanisms are derived, and the Jacobian matrices are obtained. The singularities and the mechanical limits of this type of mechanism are presented in order to establish the framework for the planning algorithm. Finally, example trajectories and results are shown to illustrate the algorithm and demonstrate its effectiveness.