Self-Foldability of Rigid Origami

When actuating a rigid origami mechanism by applying moments at the crease lines, we often confront the bifurcation problem where it is not possible to predict the way the model will fold when it is in a flat state. In this paper, we develop a mathematical model of self-folding and propose the concept of self-foldability of rigid origami when a set of moments, which we call a driving force, are applied. In particular, we desire to design a driving force such that a given crease pattern can uniquely self-fold to a desired mode without getting caught in a bifurcation. We provide necessary conditions for selffoldability that serve as tools to analyze and design self-foldable crease patterns. Using these tools, we analyze the unique self-foldability of several fundamental patterns and demonstrate the usefulness of the proposed model for mechanical design.