Twist and finite twist analysis of 2UPR-SPR parallel mechanism based upon screw theory

Abstract

This paper discusses the issue on mobility analysis of parallel mechanism. The analysis is focused on the two-rotational and one-translational 2UPR-SPR parallel mechanism which has interesting motion properties that one rotation of this mechanism has fixed direction, while the other rotation and the translation have variable directions. Twist analysis is conducted to obtain the feasible velocities of the moving platform at any configuration of the mechanism, and finite twist analysis is carried out to obtain the feasible displacements of the moving platform when the mechanism moves away from the initial configuration to any configuration. The obtained parametric velocity space at any configuration and parametric displacement manifold from the initial configuration to any configuration are formulated, which are proved to contain the same motion information and have the same effect in mobility analysis. Through analyzing the 2UPR-SPR mechanism, it is revealed that both twist and finite twist are effective to describe continuous motions of rigid body or mechanism. This enriches the relation between twist and finite twist, and unifies the applications of these two kinds of screws in mobility analysis.