The effect of mountain-valley folds on the rigid foldability of double corrugated pattern

Abstract

Origami is able to create a 3D sculpture by folding a piece of paper by following the crease lines, which can be mountain or valley folds. Rigid origami is a subset of origami in which the panels, that are surrounded with the creases, do not stretch or bend during its folding sequence, but only rotate about the creases. Besides geometric design parameters, the mountain-valley fold assignments also affect the rigid-foldability of origami patterns. This paper proposes a general kinematic method to analyze the rigid-foldability of origami patterns by modelling them as assemblies of spherical linkages. The double corrugated pattern is taken as the study case. We first investigate the rigid-foldability of all possible mountain-valley fold assignments that can satisfy the condition of flat-foldability. Subsequently, we explore different rigid-foldable tessellations of the double corrugated patterns. This work will offer an in-depth understanding of the effect of mountain-valley folds on the rigid-foldability of origami patterns.