Design of Origami Structures With Smooth Folds

Origami provides inspiration and solutions to the fabrication and functionality of various structures. Origami design methods in the literature are limited to the idealization of the folds as creases of zeroth-order geometric continuity. This idealization is not proper for origami structures having non-negligible fold thickness or maximum curvature at the folds restricted by material or structural limitations. For these structures, the folds are not accurately represented as creases but instead as bent regions of higher-order geometric continuity. These fold regions of arbitrary order of continuity are denoted in this work as smooth folds. A method for the design of a single planar sheet and its associated pattern of smooth folds that morphs into a given three-dimensional goal shape represented as a polygonal mesh is proposed. The parameterization of the planar sheet and the constraints allowing for a valid smooth fold pattern and matching of the goal shape in a folded configuration are presented. The folding deformation of the determined sheet designs is simulated using a previously derived kinematic model for origami with smooth folds. Various testing examples considering diverse goal shapes are presented. The results demonstrate that each considered sheet design matches its corresponding goal shape in a known folded configuration having fold angles determined from the geometry of the goal mesh. The proposed method can be used for the design of origami structures having folds of arbitrary order of geometric continuity such as origami-inspired active structures.