The power manipulability – A new homogeneous performance index of robot manipulators

Jacobian-based performance indices such as the manipulability ellipsoid, the condition number and the minimum singular value, have been very helpful tools both for mechanical manipulator design and for determining suitable manipulator postures to execute a given task. For a manipulator having complex degrees of freedom (translations and rotations), Jacobian matrix becomes non-homogeneous, i.e. it contains elements with different physical units; therefore, the evaluation of its determinant, eigenvalues or singular values needs the combination of quantities of different nature, which is physically inconsistent and moreover it corresponds to a noncommensurable system. In this paper, a new performance index of robot manipulators is proposed. It is fully homogeneous and it constitutes a physically consistent system whether the manipulator contains joints of different natures, or the task space combines both translation and rotation motion. The development is concerned with the study of power within the mechanism. Given that the power has the same physical units in translation and rotation, it can be used as a homogeneous or natural performance index of manipulators by examining the behaviour of its basic components namely, force and speed, at different kinematics configurations. Furthermore, the new concept of vectorial power is introduced, followed by to the quadrivector of apparent power, and leading to the final homogeneous performance index of the power manipulability (PM). This new approach matches perfectly with mechanisms having joints of different natures, as well as with a task space combining both translation and rotation.