Research on Forward Position Solutions for 6-SPS Parallel Mechanisms Based on Topology Structure Analysis

Abstract

The relationship between complexity of mechanism topology structure and difficulty of solving forward position is discussed and established. A general numerical method, which is used to separately solve all real forward position solutions of parallel mechanism according to the value of coupling degree, is also presented. This method makes solving forward solution easy and the details can be listed as follows: 39 kinds of configurations of 6-SPS mechanism are analyzed and classified into four categories,i.e. k=0、1、2、3 according to their coupling degree. At the same time, the law that the numbers of geometric side of moving platform and chain types can affect coupling degree is found. The definite analysis direction for solving forward positions of parallel mechanism with different k is indicated, that is: For mechanisms with k=0, it is easy to directly obtain their analytical forward solutions. For mechanisms with k0, they are transformed into mechanisms with k=0 by virtually setting k SPS chain, then based on the condition of link length, establish k geometric compatibility equations, each of which contains only one variable. At last, k-dimensional search method is used to obtain all real forward solutions. Taking 6-DOF Stewart spherical mechanism as an example, the detailed steps of solving forward kinematics of any 6-DOF SPS parallel mechanisms with k=1 by using one-dimensional search method are listed. This general numerical method used to solve forward position solutions of 6-SPS parallel mechanism based on analyzing the complexity of topology structure has many advantages such as clear geometry meaning, simple solving principle, less calculation and good adaptability.