Self-Foldability of Rigid Origami

When actuating a rigid origami mechanism by applying a driving force (moment) at their 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 driving forces are given. In particular, we desire to design a driving force such that a given crease pattern can uniquely self-fold to a desired mode without bifurcation. We provide necessary conditions for self-foldability that serve as tools to analyze and design self-foldable crease patterns. Using these tools, we analyze unique self-foldability of several fundamental patterns and demonstrate the usefulness of the proposed model for mechanical design.