CGA-based Approach to Solve the Forward Position Solution of the (4SPS+SPR)+(2RPS+SPR) Serial-parallel Manipulator

doi:10.3901/JME.2021.13.102

Abstract

Abstract: Conformal geometric algebra (CGA) is introduced into the forward position solution of the series-parallel mechanism. Taking the (4SPS+SPR)+(2RPS+SPR) serial-parallel mechanism as an example, for each parallel manipulator, through reasonably selecting the kinematic parameters, some basic geometric elements, such as sphere and plane, are constructed based on the specific operation rules of CGA, and the geometric expressions of the vertex position for the moving platform can be obtained by the intersection and duality operations of the basic geometric elements. Then, combined with the dimension, geometric constraints of the mechanism and the inner product operation in CGA, the univariate higher order equation of the forward kinematics for each mechanism can be derived, and then the pose of the moving platform relative to the base for each mechanism can be obtained. Based on this result, combined with the rigid body motion transformation in CGA, the position of the moving platform for the serial-parallel mechanism is obtained. The CGA-based method can avoid the complex elimination operations in the traditional method, and the analysis process is more geometric intuitive, which shows great advantages in simplifying the geometric modeling of the forward solution for serial-parallel mechanism.

Key words: serial-parallel mechanism, conformal geometric algebra, forward kinematics

CLC Number:

TG156

HU Bo, ZHANG Da, GAO Junlin, GENG Xuewen, YE Nijia, YAO Jiantao, YI Wangmin. CGA-based Approach to Solve the Forward Position Solution of the (4SPS+SPR)+(2RPS+SPR) Serial-parallel Manipulator[J]. Journal of Mechanical Engineering, 2021, 57(13): 102-113.

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