Self-motion in Spatial Parallel Mechanisms with More than Three Legs

Parallel mechanisms frequently possess an unstable type of singularity that has no counterpart in serial mechanisms. When the mechanism is at or near this type of singularity, it loses the ability to counteract external forces in certain directions. The determination of unstable singular configurations in parallel robots is challenging, and in the past has been tackled by exhaustive numerical searches of the mechanism workspace using an accurate analytical model of the mechanism kinematics. This paper considers the singularity determination problem from a geometric perspective for n-legged spatial parallel mechanisms. By using the constraints on the passive joint velocities, a necessary condition for unstable singularity is derived that identifies the reason for such singularities.