Robust Folding of Elastic Origami

Abstract

Self-folding origami, structures that are engineered flat to fold into targeted, three-dimensional shapes, have many potential engineering applications. Though significant effort in recent years has been devoted to designing fold patterns that can achieve a variety of target shapes, recent work has also made clear that many origami structures exhibit multiple folding pathways, each of which can compete with the desired one. This can lead to structures that are programmed for one shape, yet fold incorrectly. To disentangle the features that lead to misfolding, we introduce a model of self-folding origami that accounts for the finite stretching rigidity of the origami faces and allows the computation of energy landscapes that lead to misfolding. We find that, in addition to the geometrical features of the origami, the finite elasticity of the nearly-flat origami configurations regulates the proliferation of potential misfolded states through a series of saddle-node bifurcations. We apply our model to one of the most common origami motifs, the symmetric "bird's foot," a single vertex with four folds. We show that though even a small error in programmed fold angles induces metastability in rigid origami, elasticity allows one to tune resilience to misfolding. In a more complex design, the "Randlett flapping bird," which has thousands of potential competing states, we further show that the number of actual observed minima and folding robustness is strongly determined by the structure's elasticity.

Learning to self-fold at a bifurcation

“…However, bifurcations can also make the system hard to control [30]. For example, folding outcomes at these singularities can be unpredictable and depend on the precise spatial pattern of forces used [26,[31][32][33]. While generic mechanical systems show bifurcations in some parts of configuration space [34][35][36], bifurcations are especially a problem for thin creased sheets because the flat state configuration is necessarily degenerate [26,31].…”