Perfectly Imperfect Origami: How the imperfections in self-folding origami allow robust folding*

Self-folding origami are engineered flat sheets that can fold into three dimensional structures when external stimuli are applied. In application, these structures are vulnerable to misfolding. To attempt to understand this misfolding problem, we introduce a bar and hinge model for self-folding, triangulated origami that allows both face stretching and face bending. Using this model, we use a single vertex four-fold origami called the birdsfoot to probe how the addition of these imperfections influence when the birdsfoot is bi-stable for given sets of programmed equilibrium angles. In both our theoretical predictions and a set of experiments where two of the birdsfoot’s faces are intentionally weakened, we see two competing effects. More face stretching leads to fewer sets of programmed angles in which the birdsfoot is bi-stable, while weakening faces leads to more bi-stable sets of programmed angles. We then turn to the Randlett bird, a more complex origami, and simulate its misfolding rates with different allowed amounts of face stretching and bending, and again see an interplay between the two effects. Collectively, these results seem to indicate that it is actually the imperfections in our experimental systems that allow robust folding.