QUATERNION REPRESENTATION OF THE POWER MANIPULABILITY

Abstract

In this paper, a quaternion formulation of the power manipulability is developed. Quantifying the mechanical transmissibility of a mechanism, this parameter was previously introduced as a new homogeneous performance index of robot manipulators; however, its evaluation requires complex manipulations, particularly those of quadri-vectors. Furthermore, the quadri-vector form fits exactly with the structure of quaternions. Hence, a quaternion based method may be useful for power performance indices evaluation. It will be shown that this method leads to a recursive algorithm that manipulates kinematics’ parameters as matrices defined over the real quaternion space. Therefore, a new mostly simplified procedure is elaborated, which is suitable to robots performance analysis related issues. The resultant algorithm is largely simpler and more efficient to evaluate the power based performance indices.