The art and science of folding intricate three-dimensional structures out of paper has occupied artists, designers, engineers, and mathematicians for decades, culminating in the design of deployable structures and mechanical metamaterials. Here we investigate the axial compressibility of origami cylinders, i.e., cylindrical structures folded from rectangular sheets of paper. We prove, using geometric arguments, that a general fold pattern only allows for a finite number of isometric cylindrical embeddings. Therefore, compressibility of such structures requires either stretching the material or deforming the folds. Our result considerably restricts the space of constructions that must be searched when designing new types of origami-based rigid-foldable deployable structures and metamaterials.
On the Incompressibility of Cylindrical Origami Patterns
37081 Göttingen, Germany
The University of Texas at Austin,
Austin, TX 78712
Cambridge, MA 02138
Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 5, 2016; final manuscript received September 19, 2016; published online December 22, 2016. Assoc. Editor: Nam H. Kim.
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Bös, F., Wardetzky, M., Vouga, E., and Gottesman, O. (December 22, 2016). "On the Incompressibility of Cylindrical Origami Patterns." ASME. J. Mech. Des. February 2017; 139(2): 021404. https://doi.org/10.1115/1.4034970
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