Geometry, mechanics and actuation of intrinsically curved folds

TL;DR

This paper combines theory and experiments to understand the geometry, mechanics, and actuation of intrinsically curved folds (ICFs) in developable shells, revealing their bending mechanisms, energy minimization, and potential for soft robotic applications.

Contribution

It introduces a theoretical framework for ICFs based on intrinsic geometry and demonstrates their fabrication and actuation in liquid crystal elastomers, highlighting new insights into their mechanics and design.

Findings

ICFs are bending mechanisms with a continuous isometry family.

Symmetric ICFs can fully fold into a deployable flat state.

Asymmetric ICFs lock with a finite, strong fold angle.

Abstract

We combine theory and experiments to explore the kinematics and actuation of intrinsically curved folds (ICFs) in otherwise developable shells. Unlike origami folds, ICFs are not bending isometries of flat sheets, but arise via non-isometric processes (growth/moulding) or by joining sheets along curved boundaries. Experimentally, we implement both, first making joined ICFs from paper, then fabricating flat liquid crystal elastomer (LCE) sheets that morph into ICFs upon heating/swelling via programmed metric changes. Theoretically, an ICF's intrinsic geometry is defined by the geodesic curvatures on either side, $\kappa_{g_i}$. Given these, and a target 3D fold-line, one can construct the entire surface isometrically, and compute the bending energy. This construction shows ICFs are bending mechanisms, with a continuous family of isometries trading fold angle against fold-line curvature. In ICFs with symmetric $\kappa_{g_i}$, straightening the fold-line culminates in a fully-folded flat state that is deployable but weak, while asymmetric ICFs ultimately lock with a mechanically strong finite-angle. When unloaded, freely-hinged ICFs simply adopt the (thickness $t$ independent) isometry that minimizes the bend energy. In contrast, in LCE ICFs a competition between flank and ridge selects a ridge curvature that, unusually, scales as $t^{-1/7}$. Finally, we demonstrate how multiple ICFs can be combined in one LCE sheet, to create a versatile stretch-strong gripper that lifts $\sim$40x its own weight.