Singular planes of serial wrist-partitioned manipulators and their singularity metrics

Current metrics measuring proximity to kinematic singularities are based on mathematical characteristics of the Jacobian matrix such as manipulability or the conditioning index. This paper develops a geometric representation of the kinematic singularities of wrist-partitioned manipulators in terms of singular planes. It is shown that the determinant of the Jacobian matrix is a product of the distances from the controlled points on the end-effector to these singular planes. The paper proposes that for wrist-partitioned manipulators these distances can be used as singularity metrics which directly measure proximity to kinematic singularities. The Puma manipulator is used as an example.