Branch Reconfiguration of Bricard Linkages Based on Toroids Intersections: Line-Symmetric Case

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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