The dynamic capability equations: a new tool for analyzing robotic manipulator performance

Dynamic capability equations (DCE) provide a new description of robot acceleration and force capabilities. These refer to a manipulator´s ability to accelerate its end-effector and to apply forces to the environment at the end-effector. The key features in the development of these equations are that they combine the analysis of end-effector accelerations, velocities, and forces, while addressing the difference in units between translational and rotational quantities. The equations describe the magnitudes of translational and rotational acceleration and force guaranteed to be achievable in every direction, from a particular configuration, given the limitations on the manipulator´s motor torques. They also describe the effect of velocities on these capabilities contributed by the Coriolis and centrifugal forces, as well as the reduction of actuator torque capacity due to motor speed. This article focuses on nonredundant manipulators with as many actuators as degrees of freedom.