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

TY - JOUR

T1 - Branch Reconfiguration of Bricard linkages Based on Toroids Intersections: Line-Symmetric Case.

AU - Lopez-Custodio, Pablo Cesar

AU - Dai, Jian

AU - Rico, Jose

PY - 2018

Y1 - 2018

N2 - This paper for the first time investigates a family of linesymmetric Bricard linkages by means of two generated toroids and reveals their intersection that leads to a set of special Bricard linkages with various branches of reconfiguration.The disc very is made in the concentric toroid-toroid intersection. By manipulating the construction parameters of the toroids all possible bifurcation points are 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 a pair of different types of Bennett linkage 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 linkage studied in this paper. The method is applied to the plane-symmetric case in a different paper submitted by the authors in parallel with this paper.

AB - This paper for the first time investigates a family of linesymmetric Bricard linkages by means of two generated toroids and reveals their intersection that leads to a set of special Bricard linkages with various branches of reconfiguration.The disc very is made in the concentric toroid-toroid intersection. By manipulating the construction parameters of the toroids all possible bifurcation points are 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 a pair of different types of Bennett linkage 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 linkage studied in this paper. The method is applied to the plane-symmetric case in a different paper submitted by the authors in parallel with this paper.

U2 - DOI: 10.1115/1.4038981

DO - DOI: 10.1115/1.4038981

M3 - Article

SN - 1942-4302

JO - Transactions of the ASME Journal of Mechanisms and Robotics

JF - Transactions of the ASME Journal of Mechanisms and Robotics

ER -