Comparison of Methods for Determining Screw Parameters of Infinitesimal Rigid Body Motion From Position and Velocity Data

Abstract

Five methods are outlined in this paper for determining the screw parameters of the instantaneous motion of rigid bodies from given velocity and position data of three noncollinear points. The five methods are compared on the basis of their computational efficiency and accuracy. It is found that the method based on vector algebra is much more efficient computationally than any of the other four methods, but has some limitations of applicability. In terms of accuracy, the methods are equivalent when working with exact data. It is recommended that the method based on vector algebra be used for computing screw parameters from position and velocity data when this computation is performed frequently, as in the case of trajectory planning for robotics application. But method hopping be employed where inexact data are used, employing the method which gives the best speed/accuracy combination.