Geometry of Curved Folded Developables

Abstract

Origami inspired structures are gaining traction in the aerospace community. Often ignored, these structures exhibit an additional degree of freedom beyond rigid folding due to facet bending, leading to so called non-rigid Origami. A thin, initially plane inextensible sheet can be folded or creased along a general curve to form two concatenated developable surfaces that are not rigid or flat foldable. In the literature, theorems of differential geometry have been used to calculate the shape of a curved-line folded sheet by identifying kinematic constraints between the pair of developable surfaces. Two special cases; one in which the fold curve remains planar and the other in which the fold angle is constant, have been identified. In this work, we revisit these special cases through practical experiments and finite element analysis to quantify and validate the effectiveness of the analytical approach based on differential geometry. The results show excellent correlations with both elastic numerical modelling and differential geometry-based analysis able to capture the shape of the creased sheet influenced by crease rotation and facet bending. We then extend our methods to a special case of a curved creased disk and compare our predictions to experimental results. Agreement shows robustness and effectiveness of the differential geometric approach and also validates our numerical model, which may be applied to Origami structures with more complex extended curved crease networks.