Topological transitions in the configuration space of non-Euclidean origami

Abstract

Origami structures have been proposed as a means of creating three-dimensional structures from the micro- to the macroscale, and as a means of fabricating mechanical metamaterials. The design of such structures requires a deep understanding of the kinematics of origami fold patterns. Here, we study the configurations of non-Euclidean origami, folding structures with Gaussian curvature concentrated on the vertices. The kinematics of such structures depends crucially on the sign of the Gaussian curvature. The configuration space of non-intersecting, oriented vertices with positive Gaussian curvature decomposes into disconnected subspaces; there is no pathway between them without tearing the origami. In contrast, the configuration space of negative Gaussian curvature vertices remain connected. This provides a new mechanism by which the mechanics and folding of an origami structure could be controlled.

References in corpus (6)

• Geometric Mechanics of Periodic Pleated Origami
• Making the Cut: Lattice Kirigami Rules
• Geometrically controlled snapping transitions in shells with curved creases
• Branches of triangulated origami near the unfolded state
• Origami building blocks: generic and special 4-vertices
• Rigid Foldability is NP-Hard

Cited by in corpus (9)

• The designs and deformations of rigidly and flat-foldable quadrilateral mesh origami
• An additive algorithm for origami design
• Non-Euclidean Origami
• Hidden symmetries generate rigid folding mechanisms in periodic origami
• Non-Hermitian topological phases and skin effects in kagome lattices
• Controlling the configuration space topology of mechanisms
• Classifying topological floppy modes in the continuum
• Explicit kinematic equations for degree-4 rigid origami vertices, Euclidean and non-Euclidean
• Thermal Fluctuations of Singular Bar-Joint Mechanisms