How Hidden Geometric Symmetries in Origami Generate New Folding Mechanisms
Rocklin, David Zeb
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The traditional Japanese art of paper folding has inspired various foldable materials, some now realizable at the atomic scale. These thin sheets use engineered crease patterns to provide a desired mechanical response governed by the crease pattern geometry. We consider the entire class of triangulated origami, where global symmetries come paired with force-bearing modes that correspond to linear folding motions. We find triangulated origami generally has two such folding modes that extend into the non-linear regime and transform the origami sheet into cylindrical sections. The key feature of this class of origami is its matching number of constraints and degrees of freedom; hence, our methods are applicable to sheets allowing cuts and folds called kirigami, and continuous sheets satisfying this condition.
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