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.