Shape-Morphing Mechanism Arrays (SMMAs) can be made by arraying harmonic four-bar mechanisms, i.e. four-bar mechanisms with a particular structure that insures high levels of symmetry. This paper discusses a particular genre of harmonic mechanism array that can forms rectangular grids without requiring the exclusive use of parallel mechanisms. Such arrays can be designed to preserve their harmonic (highly symmetric) structure through-out their range of motion, producing arrays capable of large deformations that nevertheless can be characterized by a 2D tensor, specifically, rectangular arrays deform as parallelograms.

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