Kinematic manipulability of general constrained rigid multibody systems

This paper extends the kinematic manipulability concept commonly used for serial manipulators to general constrained rigid multibody systems. Examples of such systems include multiple cooperating manipulators, multiple fingers holding a payload, multileg walking robots, and variable geometry trusses. Explicit formulas for velocity and force manipulability ellipsoids are derived and their duality explained. Singularities are classified into two types: 1) unmanipulable singularity; 2) unstable singularity. The former is similar the singularities in serial chains where velocity manipulability ellipsoid is degenerate and force manipulability ellipsoid infinite. The latter is unique to parallel mechanisms, the velocity manipulability ellipsoid becomes infinite and force manipulability degenerate. In the case of multifinger grasp, these concepts correspond to unmanipulable or unstable grasps.