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. If a mechanism only owns limbs with Lie group motions, it is convenient to predict how a limb arrangement determines 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 find the influence of a limb arrangement. On this regard, this paper provides an in-depth investigation by focusing on motion analysis of parallel mechanisms consisting of three PRS limbs with planar-spherical 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 presents results in expressions of new types of manifold motions, providing a foundation for design and application of parallel mechanisms having the various three-planar-spherical manifolds' intersection motions.