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Theoretical analysis and experimental verification of a 3RR-3RRR multi-loop coupling mechanism based on geometric algebra

Published online by Cambridge University Press:  26 June 2025

Xinxue Chai ,
Guochang Zheng ,
Shuyin Zheng ,
Feng Wen ,
Yu Xiao ,
Lingmin Xu Open the ORCID record for Lingmin Xu [Opens in a new window]  and
Qinchuan Li Open the ORCID record for Qinchuan Li [Opens in a new window]
Xinxue Chai
Affiliation:
School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, China
Guochang Zheng
Affiliation:
School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, China
Shuyin Zheng
Affiliation:
School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, China
Feng Wen
Affiliation:
School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, China
Yu Xiao
Affiliation:
School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, China
Lingmin Xu*
Affiliation:
School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, China
Qinchuan Li
Affiliation:
School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, China
*
Corresponding author: Lingmin Xu; Email: xulm@zstu.edu.cn
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Abstract

Multi-loop coupling mechanisms (MCMs) are extensively utilized in the aerospace and aviation industries. This paper analyzes the mobility, singularity, and optimal actuation selection of a 3RR-3RRR MCM on the basis of geometric algebra (GA), where R denotes revolute joint. First, the principle of the shortest path is employed to identify the basic limbs and ascertain the type of coupling limbs. The analytical expression for the twist space and mobility characteristics of the mechanism is obtained by calculating the intersection of the limb’s twist space. The blade of limb constraint is subsequently employed to construct the singular polynomials of the mechanism. The singular configurations of the 3RR-3RRR MCM are analyzed in accordance with the properties of the outer product, resulting in the identification of two distinct types of boundary singularities. Next, the local transmission index is employed to evaluate the motion/force transmission performance of the two actuation schemes and finalize the selection of the superior actuation scheme for the mechanism. Finally, a prototype is developed to evaluate the energy loss resulting from the two actuation schemes, which verifies the correctness of the actuation selection scheme.

Keywords

multi-loop coupling mechanismgeometric algebramobilitysingularitymotion/force transmission index

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Type
Research Article
Information
Robotica , First View , pp. 1 - 23
Copyright
© The Author(s), 2025. Published by Cambridge University Press

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