Abstract: The position sub-manifold and orientation sub-man- ifold are defined for the redundant robots in which the end manipulator’s position and orientation are decoupled. The end manipulator’s workspace is divided into three subspaces accor- ding to the difference of position sub-manifold and orientation sub-manifold. The position sub-manifold and the orientation sub-manifold in all subspaces are expressed as parameter equations by vector algebra, so the self-motion manifold can be obtained as the matched pair that is formed by position sub-manifold and orientation sub-manifold. A simulation is carried out in the first subspace to obtain the self-motion manifolds for a given point, and the result is verified by forward kinematics. The method to solve self-motion manifold with position sub-manifold and orientation sub-manifold is also valid for other kinds of redundant robots in which the end manipulator’s position and orientation are decoupled.

Key words: Self-motion manifold, Inverse kinematics, Redundant robot, Self-motion