A new homogeneous manipulability measure of robot manipulators, based on power concept

Abstract

Kinetostatic performance indices have been commonly used for many potential applications in robotics, i.e. optimal design purpose, trajectory planning, manipulation programming, redundancy treatment and dexterity analysis. This has been successful when the mechanism has either fully rotational or translational joints. However, in case of a mechanism having both rotational and translational degrees of freedom; performance indices, such as Jacobian matrix, manipulability or condition number, may not be used due to the dimensional inconsistency with its elements. In this paper, by means of the power concept, a new kinetostatic performance index of robot manipulators is proposed. The power has the same physical units in either translations or rotations. Therefore, we can make use of it as a homogeneous or natural performance index of manipulators. Although it has never been considered as a subject matter of kinetostatic performance criteria, exploiting the behaviour of its basic components namely, force and speed, along the mechanism was likely interesting. On the other hand, the new concept of Oriented Power was introduced, in order to formulate the quadrivector of apparent power, leading to the final homogeneous performance index, which is no longer susceptible to the physical units’ choice. The main benefits of this approach are as follows: firstly there is no need for any restriction on the kinematics’ limits; secondly, the new formalism is insensitive to joint types of mechanism, as well as it has the possibility of grouping translations and rotations of the operational space together. The new index is then both applied in a simple serial mechanism dexterity analysis, and extended to a planar parallel mechanism.