Kinematic analysis of parallel mechanisms at singular points where a connecting chain has local mobility

In the present paper, singular point of parallel mechanisms where a connecting chain has local mobility has been investigated. Through inverse kinematics of each connecting chain, the presence of such a singular point has been revealed. The kinematic relationship between the output velocity and the velocities of both active and passive joints in the connecting chain with local mobility has been derived. Utilizing this relationship, a method generating a trajectory to pass through such a singular point has been proposed. Numerical examples of a planar parallel mechanism with three degrees of freedom have been shown and discussed.