Quasi-Periodic Shape-Morphing Mechanism Array Based on Penrose Tiles

A novel design technique is described for creating quasi-periodic, plane-filling, tessellated mechanism arrays. Such arrays may be of value in the creation of shape-morphing objects for aerospace, deployment and storage, and wind-load mitigation. The tessellation technique is derived from a Penrose tiling using angular-velocity-colored mechanism graphs. This technique allows the identification of a Penrose tiling with the graph of a redundantly constrained parallel mechanism. A general design technique is presented as well as a specific prototype. For Penrose tiles, the method produces seven distinct types of links that can be configured to move relative to each other and be tessellated with arbitrarily many links. The current prototype is redundantly constrained with twenty-one links, and thirty-five revolute joints, which allows the removal of up to five joints without introducing additional mobility. The prototype has a single degree-of-freedom and can undergo approximately a 30.7% increase in area from its smallest to largest configuration. As the mechanism array moves, the Penrose tiling lattice changes size and rotates but does not distort.