A Novel Dual-Matrix Method for Displacement Analysis of Spatial Linkages

Abstract

In view of the limitation of general dual algebra approach to kinematic analysis, this paper proposes a novel dual-matrix method as a unified procedure for displacement analysis of spatial linkages. By this mean, the Euler angles computation of spherical joints is avoided, and the coordinate transformation equation of spatial linkages which contain varied kinds of joints can be solved more easily and efficiently. Firstly, the transformation equation of spatial linkages is established by dual-matrix method. Secondly, according to the positional relation of the spherical joint and linkages, the rotation transformation matrix containing Euler angles in the equation is eliminated. Finally, the spatial linkages kinematic equation is obtained after rearranging and simplifying matrix equation. This paper takes RSSR mechanism as an example to illustrate the improved dual-matrix approach, and kinematic formulas are derived. The kinematic simulation is performed in computer and then compared with the results of formula calculation, which proves that this method is completely correct.