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Origami, the ancient art of paper folding, embodies techniques for transforming a flat sheet of paper into shapes of arbitrary complexity. Although this makes origami a conceptually attractive source of inspiration when designing foldable structures and reconfigurable metamaterials for multiple functionalities, their designs are still based on a set of well-studied patterns leaving the full potential of origami inaccessible for design practitioners and researchers. Here, we present a generalized approach for the algorithmic design of rigidly-foldable origami structures exhibiting a single kinematic degree of freedom. We build on generalized conditions for rigid foldability of degree- n  vertices to design origami patterns of arbitrary size and complexity. The versatility of the approach is demonstrated by its capability to not only generate, analyze and optimize regular origami patterns, but also generate and analyze kirigami, generic three-dimensional panel-hinge assemblages and their tessellations. Due to its versatility, the approach provides an inexhaustible source of foldable patterns to inspire the design of metamaterials for a wide range of applications.

Algorithmic design of origami mechanisms and tessellations