In this paper the zero dynamics corresponding to the self-motion of links in the null space of a redundant robot is derived based on the theory of feedback linearization. For a planar 4R redundant robot with the desired output to be a straight line
the relation between the self-motion and the vectors in the null space is obtained for the first time by means of several diagnostic criteria for chaos such as Poincare maps and Lyapunov exponents
and it is meaningful to improve the dynamic performance of redundant robots.