Bifurcation Motion and Configuration Toroid of Classical Mobility-One Single Loop Linkages

[+] Author and Article Information
Xuesi Ma

PhD Candidate, MoE Key Laboratory for Mechanism Theory and Equipment Design, International Centre for Advanced Mechanisms and Robotics, School of Mechanical Engineering, Tianjin University, Tianjin 300072, PR China

Xinsheng Zhang

PhD, Center for Robotics Research, King's College London, University of London, Strand, London WC2R 2LS, UK

Jian S Dai

Chair of Mechanisms and Robotics, International Centre for Advanced Mechanisms and Robotics, Tianjin University, Center for Robotics Research, King's College London, Strand, London WC2R 2LS, UK

1Corresponding author.

ASME doi:10.1115/1.4040357 History: Received October 31, 2017; Revised May 10, 2018


Classical mobility-one loop linkages usually have different assembled conditions, each of which has a configuration and a motion cycle. In normal circumstance, the linkage experienced a full cycle when the input joint completes a joint cycle. But some mechanisms have a motion cycle larger than 2pi because of the bifurcation motion. Bennett plano-spherical hybrid linkage is an over-constrained spatial 6R linkage with one degree of freedom. Its motion cycle can expand to , four times of a normal motion cycle. By mapping the two-dimensions of input-output relationship to a three-dimension configuration toroid, the motion cycle can be observed. Using intersection of the constraint curve with the bottom plane, top plane and equatorial plane, this linkage's motion can be divided into four parts, which are connected by the motion. During each part, the linkage will pass through configurations with a same joint input angular. Further, Myard plane-symmetry 5R linkage can have a motion cycle under a special condition. By mapping the input-output relationship onto the configuration toroid using the same method, the linkage's motion can be divided into two parts, during each of which the input joint angle accomplishes a full cycle, but the linkage itself only accomplishes half a cycle. In both linkages, the bifurcations connect different parts of motion curves and make them transform continuously and smoothly. This has been revealed in this paper though the motion branches transformation is not so apparent.

Copyright (c) 2018 by ASME
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