Branch Reconfiguration of Bricard Loops Based on Toroids Intersections: Line-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:10.1115/1.4038981 History: Received June 22, 2017; Revised December 14, 2017


This paper for the first time investigates a family of line-symmetric Bricard mechanisms by means of two generated toroids and reveals their intersection that leads to a set of special Bricard mechanisms with various branches of reconfiguration. The discovery is made in the concentric toroid-toroid intersection. By manipulating the construction parameters of the toroids any possible bifurcation point is explored. This leads to the common bi-tangent planes that present singularities in the intersection set. The study reveals the presence of Villarceau and secondary circles in the toroids intersection. Therefore, a way to reconfigure the Bricard linkage to two different types of Bennett mechanism is uncovered. Further a linkage with two Bricard and two Bennett motion branches is explored. In addition, the paper reveals the Altmann linkage as a member of the family of special line-symmetric Bricard linkages studied in this paper.

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