Parallel Platform Mechanism Based on

This paper addresses the determination of the singularity loci of a six-degree-of-freedom spatial parallel platform mechanism of a new type that can be statically balanced. The mechanism consists of a base and a mobile platform that are connected by three legs using five-bar linkages. A general formulation of the Jacobian ma-trix is first derived that allows one to determine the Plücker vectors associated with the six input angles of the architecture. The lin-ear dependencies between the corresponding lines are studied using Grassmann line geometry, and the singular configurations are pre-sented using simple geometric rules. It is shown that most of the singular configurations of the three-leg six-degree-of-freedom par-allel manipulator can be reduced to the generation of a general linear complex. Expressions describing all the corresponding sin-gularities are then obtained in closed form. Thus, it is shown that for a given orientation of the mobile platform, the singularity locus cor-responding to the general complex is a quadratic surface (i.e., either a hyperbolic, a parabolic, or an elliptic cylinder) oriented along the z-axis. Finally, three-dimensional representations that show the in-tersection between the singularity loci and the constant-orientation workspace of the mechanism are given. KEY WORDS—static balancing, parallel manipulator, sin-gularities, Grassmann line geometry, singularity loc