Structure, Design, and Mechanics of a Pop-Up Origami with Cuts

Abstract

The rotational erection system (RES) is an origami-based design method to generate a three-dimensional (3D) structure from a planar sheet. Its rotational and translational kinematics are fully encoded in the form of prescribed cuts and folds. Here we characterize the mechanical properties of a threefold symmetric RES by combining finite element analysis and a physical experiment. Whereas the crease and cut patterns imply that the system is not rigid foldable, we demonstrate that plate bending creates a physical route connecting the two energetically separated configurations. The elasticity of the RES allows the RES to morph into a 3D shape via a snapthrough transition. We show that the energy barrier for bistability is independent of the entire span of the structure, and depends solely on its aspect ratio. We also indicate that the standing RES has structural rigidity and resilience, owing to its unique self-locking mechanism, indicating its superior load-bearing performance in a range of applications. The present study clarifies the fundamental actuation mechanism of an origami-based deployable structure extended with chiral patterned cuts, which facilitates a way to use the optimally designed RES in a variety of human-made systems.