End-Effector Motion Capabilities of Serial Manipulators

Abstract

This article introduces an invariant measure to quantify the motion of a rigid body attached to the end effector of a serial manipulator. The measure arises as a natural consequence of the properties of the Euclidean group. It is invariant with respect to the position and orientation of the fixed and moving coordinate systems used to parameterize the motion of the manipulator. It is independent of the type and number of joints in the chain and the dimensions used to parameterize the chain. The singularities of the manipulator are also predicted by the measure. Finally, it is shown that, when applied to redundant manipulators, the measure quantifies the importance of each joint of the manipulator.