The motion isotropy hypersurface: a characterization of acceleration capability

The study of acceleration capability is concerned with the responsiveness of a manipulator to controller commands. We present a general model for the analysis of end-effector linear and angular accelerations that accounts for the velocity effects. The separate treatment of linear and angular motion directly addresses the inhomogeneities of end-effector motions, avoiding the use of indeterminate scaling factors. The velocity effects considered are the Coriolis and centrifugal forces, as well as the relationships associated with actuator's speed-torque performance curves. This study results in a characterization referred to as the "motion isotropy hypersurface" which describes the relationships between isotropic end-effector linear and angular velocities and accelerations. The utility of this surface and its associated information is demonstrated in a design application involving the PUMA 560 manipulator.