Natural motion analysis based on the singularity-consistent parametrization

This work adds some new insight into the singularity-consistent parametrization of the inverse kinematics of a nonredundant robot tracing a reference path. We show that in the general case (e.g. motion with constant end-effector velocity on the path) there is a nonintegrable motion component. When the end-effector moves with a velocity proportional to the determinant of the Jacobian, the nonintegrable motion component is removed. At the same time, the order of the equation of motion is reduced. We call this type of motion “natural”. Furthermore, from the simplified equation of natural motion, we derive the mechanical power measure. This is an instantaneous-motion performance measure defined over the phase space of the system, and thus, can be useful to evaluate the dynamic performance for the specified instantaneous motion direction