Finite Displacement Screw-Based Group Analysis of 3PRS Parallel Mechanisms  

When limbs of a parallel mechanism have been selected, the geometric relation among limbs determines the mechanism’s motion. The limb arrangement which affects the mechanism’s motion raises a fundamental and significant issue in the study of parallel mechanisms. If a mechanism only owns limbs with Lie group motions, it is convenient to find the influence a limb arrangement brings to the mechanism’s motion. However, if a mechanism is mainly or purely constituted by limbs with motions of general differential manifolds, it is difficult to predict how a limb arrangement determines the mechanism’s motion. On this regard, this paper provides an in-depth investigation by focusing on motion analysis of parallel mechanisms consisting of three PRS limbs with general differential manifolds. By formulating and comparing the motion characteristics of these mechanisms which though could be modeled difficultly by a mathematical tool without using the finite displacement screw, a finite displacement screw-based group method is proposed in this paper to resolve the raised issue. The novel approach presented results in expressions of new types of manifold motions, providing a foundation for design and application of parallel mechanisms having the various three-G-S manifolds’ intersection motions.