Inverse Position Analysis of Two Kinds of 6-DOF Serial-parallel Manipulators Based on Conformal Geometric Algebra

doi:10.3901/JME.2022.21.060

Abstract

Abstract: Based on the basic theory of conformal geometric algebra (CGA), the inverse displacement of (3-PRS)+(3-SPR) and (3-RPS)+(3-SPS+UP) typical serial-parallel manipulators are solved. First, a single unknown is selected according to the geometrical structure of the manipulators, and based on the basic operation of CGA, the mathematical expression of a vertex of the intermediate platform of the manipulators related to this parameter is established. Secondly, according to the coordinate expression of the this vertex and the geometric and dimensional constraints in the manipulators, some basic geometric elements including planes and spheres are constructed, and the conformal geometric expression of the coordinates of other two vertices of the intermediate platform are obtained using the outer product intersection operation. At last, combined with the expressions of the obtained vertices and the inner product operation in CGA, the input-output polynomial equation with a single unknown can be derived and all the inverse position solutions of the manipulators are obtained. The method has the characteristics of simple calculation, high efficiency and remarkable geometric intuition. It avoids the tedious and complicated calculation process compared with traditional methods, and provides a reference for the study of the inverse position analysis of serial-parallel manipulators.

Key words: conformal geometric algebra, serial-parallel manipulator, inverse displacement

CLC Number:

TG156

HU Bo, GAO Junlin, HUO Yan, ZHANG Da, ZENG Daxing, LU Wenjuan. Inverse Position Analysis of Two Kinds of 6-DOF Serial-parallel Manipulators Based on Conformal Geometric Algebra[J]. Journal of Mechanical Engineering, 2022, 58(21): 60-68.

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