Self-folding Origami Surfaces of Non-Zero Gaussian Curvature

This paper presents a framework for the design, fabrication, and experimental testing of self-folding origami structures that deform from two-dimensional forms towards three-dimensional goal shapes of arbitrary local Gaussian curvature via uniform heating. Due to the general inability of the widely employed unfolding polyhedra method to generate origami designs for structures having negative Gaussian curvature, a tuck-folding method is implemented for self-folding composites driven by shape memory polymer actuation. As implementation examples, meshes of a pyramid, a saddle, and a combination of both are chosen to represent surfaces of positive and negative Gaussian curvature, and all three structures are shown to successfully fold towards their intended goal shape. The presented framework can be applied to origami design problems that consider other goal shapes and active materials.