Singularity Analysis Of A 3-RPS Parallel Manipulator Using Geometric Algebra

Lower-mobility parallel manipulators have been popular because they have advantages over conventional 6-DOF(degrees of freedom) parallel manipulators under certain circumstances. A lower-mobility parallel manipulator has advantages of simple structure, low cost in manufacturing, easier control and rapid dynamic response over traditional parallel manipulators with six DOF.Singularity analysis of lower-mobility parallel manipulators is basic and challenging. It is an inherent characteristic of parallel mechanism, and an essential kinematic property. Under singular configurations, a mechanism loses control, and large joint forces occur in the vicinity of its singularity. It is detrimental to the safe operation of a mechanism. Singularity region should be avoided.Geometric algebra is employed in analyzing the singularity of a 3-RPS parallel manipulator. The content of this thesis is organized as follows:Basics of geometric algebra needed to analyze singularity are reviewed in detail. And the method based on geometric algebra for singularity analysis of lower-mobility parallel mechanisms is detailed. Geometric algebra is the fusion of geometry and algebra. It has the advantage of expressing geometrically and computing algebraically.Second, Tilt & Torsion angles are used to express the orientation of the moving platform of the 3-RPS parallel manipulator. Then, the kinematics of the parallel manipulator is modeled. The positions of three spherical joints of a 3-RPS parallel manipulator are solved by using the Tilt & Torsion angles to build the mapping between inputs and singular configurations. All the screws of the 3-RPS parallel manipulator are expressed in geometric algebra.Further, geometric algebra approach is applied to obtain the general singularity locus of the 3-RPS manipulator through numerical method developed in MAPLE. The results are collated with the literature.The constraint singularity of the 3-RPS parallel manipulator is also investigated in a similar way to compare with the literature, numerical search method is adopted here, and several typical singular configurations are listed.This paper provides profound theoretical implications for the singularity analysis of other limited-mobility parallel manipulators.