Abstract

Origami is the art of creating a three-dimensional (3D) shape by folding paper. It has drawn much attention from researchers, and the designs that origami has inspired are used in various engineering applications. Most of these designs are based on familiar origami patterns and their known deformations, but origami patterns were originally intended for materials of near-zero thickness, primarily paper. To use the designs in engineering applications, it is necessary to simulate origami in a way that enables designers to explore and understand the designs while taking the thickness of the material to be folded into account. Because origami is primarily a problem in geometric design, this paper develops a geometric simulation for thick origami. The actuation, constraints, and assignment of mountain and valley folds in origami are also incorporated into the geometric formulation. The experimental results show that the proposed method is efficient and accurate. The method can successfully simulate a flat-foldable degree-four vertex, two different action origami, the bistable property of a waterbomb base, and the elasticity of non-rigid origami panels.