A novel criterion for singularity analysis of parallel mechanisms

A novel criterion for singularity analysis of parallel robots is presented. It relies on screw theory, the 3-dimensional Kennedy theorem, and the singular properties of minimal parallel robots. A parallel robot is minimal if in any generic configuration, activating any leg/limb causes a motion in all its joints and links. For any link of the robot, a pair of legs is removed. In the resulting 2 degrees-of-freedom mechanism, all possible instantaneous screw axes belong to a cylindroid. A center axis of this cylindroid is determined. This algorithm is performed for three different pairs of legs. The position is singular, if the instantaneous screw axis of the chosen link crosses and is perpendicular to three center axes of the cylindroids. This criterion is applied to a 6/6 Stewart Platform and validated on a 3/6 Stewart Platform using results known in the literature. It is also applied to two-platform minimal parallel robots and verified through the Jacobian; hence demonstrating its general applicability to minimal robots. Since any parallel robot is decomposable into minimal robots, the criterion applies to all constrained parallel mechanisms.