Ring Origami
Ring origami uses a snap-folding mechanism triggered by the buckling instability of rods under external loads that can induce out-of-plane deformation (e.g., bending and twisting). It is demonstrated that the snap-through instability leads to a self-guided folding behavior while showing a high packing ratio for rings with different geometries.
MATLAB code for curved-sided hexagram based on the Kirchoff rod model
Tutorial video that shows the fabrication of a curved-sided hexagram ring with four equilibrium states
Here, we propose a 2D-to-3D shape transformation strategy for ring origami by introducing out-of-plane natural curvature (i.e., the stress-free curved state lies in a plane perpendicular to the planar ring) into the rod segments. Due to natural curvature-induced out-of-plane bending moments, a 2D elastic ring spontaneously snaps out-of-plane and reaches equilibrium in a 3D configuration. These snapping-induced out-of-plane shape transitions not only enable self-guided, spontaneous shape morphing, but also allow the construction of complex structures from simple geometries, making them promising for the design of functional deployable and foldable structures.
DetailsHere, we introduce a concept of segmented rings with intrinsic multistability by programming the natural curvature of the rod segments. Guided by theoretical modeling, simulation, and experimental validation, we demonstrate that a segmented ring with a rectangular cross-section can exhibit up to six distinct planar stable states characterized by uniform bending in each segment. The segmented rings constitute what are probably the simplest elastic structural entities with multiple stable states, and they will serve to expand the application space of functional multistable structures.
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Part I investigates the stability of the multiple equilibrium states of a hexagram ring with six curved sides. Rods with circular and rectangular crosssections will be analyzed using a specialized form of Kirchhoff rod theory, and properties will be detailed such that all four of the states of interest are mutually stable. Experimental demon strations of the various states and their stability are presented.
Detailss. In Part I, the classical stability criterion based on energy variation was used to study the elastic stability of the curved-sided hexagram and identify the natural curvature range for the stability of each state with circular and rectangular rod cross-sections. Here, we combine a multisegment Kirchhoff rod model, finite element simulations, and experiments to investigate the transitions between four basic equilibrium states of the curved-sided hexagram.
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Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states are investigated analytically
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The initial curvature of the rings is tuned to study how this initial curvature affects the folded configurations of the rings
DetailsMotivated by this significant packing, we utilize a combination of experiments and finite element analysis to study effective folding strategies and packing abilities of various 2D and 3D hexagonal ring assemblies
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Motivated by the large area change and the self-guided deformation through snap-folding of the rings (circular, elliptical, rounded rectangular, and rounded triangular shapes), this work introduces ring origami assemblies with unprecedented packing ratios
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