Reprogrammable origami through bistable buckled hinges
Origami structures typically have a multiplicity of folded states that are connected to a flat sheet, making the folding protocol for specific end shapes challenging to design and deploy. Here, we introduce reprogrammable origami hinges that use bistable buckled shims to reversibly control their preferred folding direction. A shim embedded across a hinge produces an asymmetric torque-angle response that favors either mountain or valley folding. Switching the shim between its two stable states reverses this response, allowing the folding direction of each hinge to be reprogrammed after fabrication. By independently controlling the states and geometries of the shims, we enable a single origami sheet to access multiple folding branches and transform into prescribed three-dimensional shapes. We further introduce self-switching hinges in which folding causes the shims to snap between their stable states. These elements allow the sheet to reprogram its folding pathway under global mechanical inputs applied to the boundaries. Our approach embeds both shape selection and transition rules directly within the mechanics of the hinges, providing a versatile framework for creating multifunctional, deployable, and reconfigurable structures.