TWO-ORBIT SWITCH-PITCH STRUCTURES

摘要

The Hoberman 'switch-pitch' ball is a transformable structure with a single folding and unfolding path. The underlying cubic structure has a novel mechanism that retains tetrahedral symmetry during folding. Here, we propose a generalized class of structures of a similar type that retain their full symmetry during folding. The key idea is that we require two orbits of nodes for the structure: within each orbit, any node can be copied to any other node by a symmetry operation. Each member is connected to two nodes, which may be in different orbits, by revolute joints. We will describe the symmetry analysis that reveals the symmetry of the internal mechanism modes for a switch-pitch structure. To follow the complete folding path of the structure, a nonlinear iterative predictor-corrector algorithm based on the Newton method is adopted. First, a simple tetrahedral example of the class of two-orbit structures is presented. Typical configurations along the folding path are shown. Larger members of the class of structures are also presented, all with cubic symmetry. These switch-pitch structures could have useful applications as deployable structures.