Dynamic Analysis ofParallel Manipulators under the Singularity-Consistent Parameterization

Abstract

Based on the singularity-consistent parameterization framework, weanalyze motion at direct kinematics singularities for a broad class of parallelmanipulators. It will be shown that taking into account the instantaneous motiondirection of the output link, additional insight can be gained for thepossibility to move through such singularities. We argue that direct kinematicssingularities should be analyzed over the dual space which, in turn, involvesthe state of the passive joints. We perform such an analysis based on theconditioning of the equation of motion. It is shown that, depending on theinstantaneous motion direction, at certain direct kinematics singularities it ispossible to obtain a consistent solution in terms of torque. This implies thatin combination with the continuity of the singularity-consistent inversekinematic solution, motion through such direct kinematics singularities isfeasible.