Branch reconfiguration of Bricard loops based on toroids intersections: Plane-symmetric case

[+] Author and Article Information
Pablo C. Lopez-Custodio

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

Jian S Dai

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

José M. Rico

Mechanical Engineering Department, DICIS, Universidad de Guanajuato, Salamanca, Guanajuato, Mexico

1Corresponding author.

ASME doi:10.1115/1.4039002 History: Received August 16, 2017; Revised December 21, 2017


This paper for the first time investigates a family of plane-symmetric Bricard mechanisms by means of two generated toroids. By means of their intersection, a set of special Bricard mechanisms with various branches of reconfiguration are designed. An analysis of the intersection of these two toroids reveals the presence of coincident conical singularities which lead to the design of plane-symmetric linkages that evolve to spherical 4R mechanisms. By examining the tangents to the curves of intersection at the conical singularities it is found that the mechanism can be reconfigured between the two possible branches of spherical 4R motion without disassembling it and without needing the usual special configuration connecting the branches. The study of tangent intersections between concentric singular toroids also reveals the presence of isolated points in the intersection which suggests that some linkages satisfying the Bricard plane-symmetry conditions are actually structures with zero finite degrees of freedom but with higher instantaneous mobility. This paper is the second part of a paper submitted in parallel by the authors in which the method is applied to the line-symmetric case.

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