Computation of Dynamic Joint Reaction Forces of PKM and its Use for Load-Minimizing Trajectory Planning

Parallel kinematics machines (PKM) operate with maximal acceleration being designed for highly dynamic ma- nipulation tasks. This leads to extreme loads of the joints, which is usually not accounted for in the motion planning. In this paper an extended inverse dynamics method is introduced, which allows computing the joint reaction forces along with the actuation torques, and provides a basis for time optimal motion planning and control minimizing wear of the components. To this end, PKM are modeled using absolute coordinates. The joint constraints are complemented with servo constraints so that the motion can be described by the actuator motion or by the end-effector motion. The presented method is particularly advantageous when certain model parameters are unknown and allows for model simplification, which would not be possible for the relative coordinate formulation. The sparsity of the obtained velocity constraint Jacobian matrix, due to the use of absolute coordinates, can be efficiently exploited to minimize computation time. The method is demonstrated and numerical results are reported for a time-optimal pick and place movement of a 4-DOF Delta robot.