Threefold-symmetric Bricard linkages for deployable structures

A closed-loop overconstrained spatial mechanism composed of six hinge-jointed bars, which has three planes of symmetry in any position, is called a threefold-symmetric Bricard linkage. In this paper a kinematic analysis of these linkages is presented. It is pointed out that for particular parameter values, kinematic bifurcation of the linkages can occur. Features of the kinematic bifurcation are discussed in detail. The applicability of threefold-symmetric Bricard linkages and of their alternative forms to deployable structures is investigated. In addition, by using the theory of kinematic bifurcation, a snap-through phenomenon appearing in a deployable hexagonal ring is explained.