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research-article

First and Second-Order Kinematics Based Constraint System Analysis and Reconfiguration Recognition for the Queer-Square Mechanism

[+] Author and Article Information
Xi Kang

MOE Key Laboratory for Mechanism Theory and Equipment Design, International Centre for Advanced Mechanisms and Robotics, Tianjin University, Tianjin 300350, PR China
xikang@tju.edu.cn

Xinsheng Zhang

Advanced Kinematics and Reconfigurable Robotics Lab, School of Natural and Mathematical Sciences, King's College London, Strand, London WC2R 2LS, UK
xinsheng.zhang@kcl.ac.uk

Jian S Dai

Chair of Mechanisms and Robotics, MOE Key Laboratory for Mechanism Theory and Equipment Design, International Centre for Advanced Mechanisms and Robotics, Tianjin University, Tianjin 300350, PR China, Advanced Kinematics and Reconfigurable Robotics Lab, School of Natural and Mathematical Sciences, King's College London, Strand, London WC2R 2LS, UK
jian.dai@kcl.ac.uk

1Corresponding author.

ASME doi:10.1115/1.4041486 History: Received April 21, 2018; Revised September 09, 2018

Abstract

Reconfiguration identification of the reconfigurable mechanisms is essential in design and analysis of a reconfigurable mechanism. However, reconfiguration identification of the multi-loop reconfigurable mechanisms is still a challenge. For the queer-square mechanism, a typical multi-loop reconfigurable mechanism, this paper establishes the first and second-order kinematic model to obtain the constraint system by using the sequential operation of Lie bracket in bilinear form. Introducing bilinear forms to reduce the complexity of the first and second-order constraints, the constraint system with the first and second-order kinematics of the queer-square mechanism is attained in a simplified form. By solving the solutions of the constraint system, six motion branches of the queer-square mechanism are identified and their corresponding geometric conditions are presented. Moreover, the initial configuration space of the mechanism is obtained.

Copyright (c) 2018 by ASME
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