Modelling of the Waterbomb Origami Pattern and its Applications

The waterbomb pattern is a well-known origami pattern and has been employed to construct foldable cylinders as stent grafts and deformable robot wheels. It is known that the cylinders made from the waterbomb pattern are, in general, not rigidly foldable. This feature makes construction and numerical simulation of those cylinders difficult because a distortion-free initial configuration for the cylinders cannot be identified. A geometrical analysis of the cylinders formed from the waterbomb pattern reveals that by properly selecting pattern geometry, there exist particular configurations at which a cylinder of a uniform radius can be rigidly assembled out of the pattern. In other words, the pattern can be perfectly connected together to form a cylinder without distortion. Those particular configurations can be used as the initial configuration of the cylinders when they are constructed and as the starting configuration of the cylinders in a numerical analysis.