Bending and twisting with a pinch: Shape morphing of creased sheets

Abstract

In this letter, we introduce a unique behavior seen in creased sheets where localized changes in the folding (i.e., a pinch) result in global bending and twisting deformations. Using isometric deformation theory, we identify the connections between pinching, crease curvature, and crease torsion that begin to explain the shape-morphing behavior. Given the limitations of isometric deformations, we expand our understanding of the behavior using a mechanics-based bar and hinge model of creased sheets, where the sheet is allowed to stretch. With this tool, we found that the increase in crease curvature and torsion due to pinching are proportional to the curvature of the crease before folding and that curved creases facilitate the bending and twisting. Additionally, we explored the bending and twisting of sheets with more than one crease. We found that sheets with an even number of creases generate more intense twisting than those with an odd number of creases and experience twisting even when the creases are straight. The number of creases had little effect on the pinch-induced bending of the origami. The stiffness of the sheets had little effect on the amount of bending and twisting, but greater spacing between the creases resulted in more bending with little effect on the twisting. Based on these results, we created a framework to design crease patterns to have desirable bending and twisting that can be coupled or not, and demonstrated this programmability with simulations and by pinching physical prototypes. Our findings enable shape morphing of creased sheets with a low-complexity input and a versatile output.