A consistent approach to the instantaneous kinematics of redundant, non-redundant and in-parallel manipulators

A unified method for the instantaneous kinematics of redundant, nonredundant and in-parallel manipulators is developed. For redundant arms, we investigate the relationship between kinematic and algorithmic singularities when the method of extended Jacobian is used for task optimization. Under the same model, it is found that, for serial manipulators to move in a point-to-point fashion and for general motion of in-parallel manipulators, their instantaneous kinematics take a similar format as the method of extended Jacobian for redundant arms. Thus, our method of solution can be applied to these manipulators. Several features for the manipulators are demonstrated based on the concept of task separation in the row space of the Jacobian of these manipulators