In a classical mobility-one single loop linkage, the motion begins from an original position determined by the assembled condition and runs in cycles. In normal circumstances, the linkage experiences a full cycle when the input-joint completes a full revolution. However, there are some linkages that accomplish a whole cycle with the input-joint having to go through multiple revolutions. Their motion cycle covers multiple revolutions of the input-joint. This paper investigates this typical phenomenon that the output angle is in a different motion cycle of the input angle that we coin this as the multiple input-joint revolution cycle. The paper then presents the configuration torus for presenting the motion cycle and reveals both bifurcation and double points of the linkage, using these mathematics-termed curve characteristics for the first time in mechanism analysis. The paper examines the motion cycle of the Bennett plano-spherical hybrid linkage that covers an range of an input-joint revolution, reveals its four double points in the kinematic curve, and presents two motion branches in the configuration torus where double points give bifurcations of the linkage. The paper further examines the Myard plane-symmetric 5R linkage with its motion cycle covering a range of the input-joint revolution. The paper, hence, presents a way of mechanism cycle and reconfiguration analysis based on the configuration torus.
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October 2018
Research-Article
Motion Cycle and Configuration Torus With Their Relationship to Furcation During Reconfiguration
Xuesi Ma,
Xuesi Ma
MoE Key Laboratory for Mechanism Theory and
Equipment Design,
International Centre for
Advanced Mechanisms and Robotics,
School of Mechanical Engineering
Tianjin University,
Tianjin 300072, China
e-mail: maxuesi@tju.edu.cn
Equipment Design,
International Centre for
Advanced Mechanisms and Robotics,
School of Mechanical Engineering
Tianjin University,
Tianjin 300072, China
e-mail: maxuesi@tju.edu.cn
Search for other works by this author on:
Xinsheng Zhang,
Xinsheng Zhang
Center for Robotics Research,
King's College London,
Strand WC2R 2 LS, London, UK
e-mail: xinsheng.zhang@kcl.ac.uk
King's College London,
Strand WC2R 2 LS, London, UK
e-mail: xinsheng.zhang@kcl.ac.uk
Search for other works by this author on:
Jian S. Dai
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 300072, China;
Center for Robotics Research,
King's College London,
Strand WC2R 2 LS, London, UK
e-mail: jian.dai@kcl.ac.uk
MoE Key Laboratory for Mechanism Theory
and Equipment Design,
International Centre for
Advanced Mechanisms and Robotics,
Tianjin University,
Tianjin 300072, China;
Center for Robotics Research,
King's College London,
Strand WC2R 2 LS, London, UK
e-mail: jian.dai@kcl.ac.uk
Search for other works by this author on:
Xuesi Ma
MoE Key Laboratory for Mechanism Theory and
Equipment Design,
International Centre for
Advanced Mechanisms and Robotics,
School of Mechanical Engineering
Tianjin University,
Tianjin 300072, China
e-mail: maxuesi@tju.edu.cn
Equipment Design,
International Centre for
Advanced Mechanisms and Robotics,
School of Mechanical Engineering
Tianjin University,
Tianjin 300072, China
e-mail: maxuesi@tju.edu.cn
Xinsheng Zhang
Center for Robotics Research,
King's College London,
Strand WC2R 2 LS, London, UK
e-mail: xinsheng.zhang@kcl.ac.uk
King's College London,
Strand WC2R 2 LS, London, 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 300072, China;
Center for Robotics Research,
King's College London,
Strand WC2R 2 LS, London, UK
e-mail: jian.dai@kcl.ac.uk
MoE Key Laboratory for Mechanism Theory
and Equipment Design,
International Centre for
Advanced Mechanisms and Robotics,
Tianjin University,
Tianjin 300072, China;
Center for Robotics Research,
King's College London,
Strand WC2R 2 LS, London, 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 October 31, 2017; final manuscript received May 10, 2018; published online July 9, 2018. Assoc. Editor: Philippe Wenger.
J. Mechanisms Robotics. Oct 2018, 10(5): 051006 (10 pages)
Published Online: July 9, 2018
Article history
Received:
October 31, 2017
Revised:
May 10, 2018
Citation
Ma, X., Zhang, X., and Dai, J. S. (July 9, 2018). "Motion Cycle and Configuration Torus With Their Relationship to Furcation During Reconfiguration." ASME. J. Mechanisms Robotics. October 2018; 10(5): 051006. https://doi.org/10.1115/1.4040357
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