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

P C López-Custodio,J M Rico,J S Dai

doi:10.1115/1.4039002

Abstract

This paper for the first time reveals a set of special plane-symmetric Bricard linkages with various branches of reconfiguration by means of intersection of two generating toroids, and presents a complete theory of the branch reconfiguration of the Bricard plane-symmetric linkages. An analysis of the intersection of these two toroids reveals the presence of coincident conical singularities, which lead to design of the plane-symmetric linkages that evolve to spherical 4R linkages. By examining the tangents to the curves of intersection at the conical singularities, it is found that the linkage can be reconfigured between the two possible branches of spherical 4R motion without disassembling it and without requiring 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 (DOF) but with higher instantaneous mobility. This paper is the second part of a paper published in parallel by the authors in which the method is applied to the line-symmetric case.

Highlights

Among the reported overconstrained linkages, the Bricard linkages are the most studied due to their very special geometry that allow the mobility of these 6R loops
If these connected components of the configuration space are of different dimensions, the linkage is able to change its degrees of freedom or local mobility and it is said to be a kinematotropic linkage [8, 9]
The plane-symmetric case of Bricard loops was analyzed using the intersection of two concentric singular toroids, allowing the design of reconfigurable linkages with several motion branches which can be either planesymmetric 6R branches or spherical 4R branches

Summary

Institutional Repository Cover Sheet

ASME Paper Title: Branch reconfiguration of Bricard linkages based on toroids intersections. Branch reconfiguration of Bricard linkages based on toroids intersections: Plane-symmetric case. This paper for the first time investigates a family of planesymmetric Bricard linkages studying two generated toroids. By means of their intersection, a set of special Bricard linkages 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 linkages. 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

Introduction

None of these four symmetric configurations coincide since

Conclusions