Symmetry Adapted Analysis of the Hoberman Switch-Pitch Ball

The Hoberman Switch-Pitch ball is used as the inspiration for a symmetry analysis of a novel type of deployable structure. The underlying structure of the Switch-Pitch is essentially cubic, consisting of eight nodes that are connected via revolute joints to twelve linking bars, each of which is connected to two nodes. A simple mobility count suggests that the structure is over- constrained, but a symmetry mobility analysis shows that the structure is in fact mobile, and retains tetrahedral symmetry as it folds.