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Research Papers

First- and Second-Order Kinematics-Based Constraint System Analysis and Reconfiguration Identification 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, China
e-mail: 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 2 LS, UK
e-mail: 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, China;
Advanced Kinematics and Reconfigurable
Robotics Lab,
School of Natural and Mathematical Sciences,
King's College London,
Strand, London WC2R 2 LS, UK
e-mail: jian.dai@kcl.ac.uk

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received April 21, 2018; final manuscript received September 9, 2018; published online November 12, 2018. Assoc. Editor: Leila Notash.

J. Mechanisms Robotics 11(1), 011004 (Nov 12, 2018) (15 pages) Paper No: JMR-18-1113; doi: 10.1115/1.4041486 History: Received April 21, 2018; Revised September 09, 2018

Reconfiguration identification of a mechanism is essential in design and analysis of reconfigurable mechanisms. However, reconfiguration identification of a multiloop reconfigurable mechanism is still a challenge. This paper establishes the first- and second-order kinematic model in the queer-square mechanism to obtain the constraint system by using the sequential operation of the Lie bracket in a bilinear form. Introducing a bilinear form to reduce the complexity of first- and second-order constraints, the constraint system with first- and second-order kinematics of the queer-square mechanism is attained in a simplified form. By obtaining 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.

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Figures

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Fig. 1

The 3D structure of the queer-square mechanism

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Fig. 2

The singularity configuration of the mechanism

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Fig. 3

The directed graph of topology

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Fig. 4

Loop II of the mechanism in a configuration of a parallelogram and the connotative parallelogram

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Fig. 5

Loop III of the mechanism in a configuration of a parallelogram and the connotative parallelogram

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Fig. 6

Motion branch I with two parallelograms and two connotative parallelograms

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Fig. 7

The prototype of the mechanism in motion branch I

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Fig. 8

Initial configuration space of the motion branches

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