A Theorem on the Manipulability of Redundant Serial Kinematic Chains

concept of 'manipulability' is particularly important to characterize the ability of a serial kinematic chain – artificial manipulator or natural limb – to move quickly its end-effector in any direction of its operational space in response to given joint velocities. Yoshikawa's manipulability definition has shown its benefit for robotics. According to him the robot manipulability can be measured, in any joint configuration q, by)] () (det[ q J q J T where J(q) denotes the robot Jacobian matrix. From this specific manipulability criterion an original theorem is derived which helps to express in closed-form the manipulability of a redundant serial kinematic chain in resolving it into manipulability factors associated to non-redundant subrobots of which the redundant original robot consists. The proposed approach is suitable for robotics but also for the analysis of naturally redundant biomechanical kinematic systems as illustrated in the study of a redundant 4R kinematic model defined as being the regional structure of a 7R anthropomorphic robot-arm.