Abstract: Based on the control theoryof feedback linearization, the zero dynamics equation for a planar3R rigid redundant robotwas derived. Using Poincare maps and Lyapunov exponents, the motion state(regular or chaotic motion) of the redundant robotwas numerically simulated, and the relationship between its self- motion state and its vectors in the null space was obtained. The research result shows that the chaotic self- motion of a redundant robot is influenced by the initial conditions and has a direct relationwith its victors in the null space.