Dynamic analysis of parallel manipulators under the singularity-consistent parameterization

Based on the singularity-consistent parameterization framework, we analyze motion at direct kinematics singularities for a broad class of parallel manipulators. It will be shown that taking into account the instantaneous motion direction of the output link, additional insight can be gained for the possibility to move through such singularities. We argue that direct kinematics singularities should be analyzed over the dual space which, in turn, involves the state of the passive joints. We perform such an analysis based on the conditioning of the equation of motion. It is shown that, depending on the instantaneous motion direction, at certain direct kinematics singularities it is possible to obtain a consistent solution in terms of torque. This implies that in combination with the continuity of the singularity-consistent inverse kinematic solution, motion through such direct kinematics singularities is feasible.