Overconstraint Reduction for Mechanism Networks of Threefold-Symmetric Bricard Linkages

Abstract Mechanism networks constructed by spatial overconstrained linkages can offer great potential for deployable mechanisms, such as the great stiffness and large folding ratio, yet their inherent overconstrained characteristic could hinder engineering applications due to the strict geometric conditions. Hence, it is important to reduce or even eliminate the redundant constraints of the original overconstrained mechanisms while maintaining their original kinematic behaviors. In this article, we propose an overconstraint reduction method for the multiloop mechanism network of threefold-symmetric Bricard linkages by a topology reduction operation. By extending the Hamiltonian-path-based reduction method into the planar topological graph of overconstrained mechanisms, the less-overconstrained one-DOF mechanism network constructed by threefold-symmetric Bricard linkages is generated by removing redundant links and joints. Meanwhile, the original equivalent motion and the threefold-symmetric motion characteristic are preserved in the reduced forms. Furthermore, based on the reduced results, the large-scale, even ultra-large-scale, less-overconstrained Bricard mechanism networks are presented, resulting in a great decrease of overconstraints, still with equivalent kinematics. The reduction strategy proposed in this article can not only guide the reduction of the known multiloop mechanism network but also provide inspiration for the construction of new deployable mechanisms with appropriate overconstraints, to facilitate their practical applications in deployable architectures, space exploration, and so on.