A Novel Geometric Modeling and Solution Method for Forward Displacement Analysis of 6-3 Stewart Platforms

Abstract

In this paper, we propose a novel modeling and solution method for the forward displacement analysis of 6-3 Stewart platforms based on Conformal Geometric Algebra (CGA). First of all, one of three unknown vertices on the moving platform is expressed with the angle that measuring the elevation of a triangular face relative to the base reference system. Then, the other two unknown vertices are established with the aforementioned angle and the scale ratio based on CGA. Finally, a 16th-degree univariate polynomial equation is reduced from two geometric constraint equations by constructing a 4 by 4 Sylvester resultant matrix. At last, a numerical example is deployed to verify the procedure. The novelty of this paper lies in that only one step elimination procedure is required to derive the 16th-degree polynomial equation and the modeling formulation and the elimination procedure can be understood with geometric intuition.