Related papers: Rigid foldability of the augmented square twist

Non-Euclidean surfaces are ubiquitous in numerous engineering fields, such as automotive, aerospace, and biomedical engineering domains. Morphing origami has numerous potential engineering applications, including soft robots, mechanical…

We offer new insight into the folding kinematics of degree-4 rigid origami vertices by drawing an analogy to spacetime in special relativity. Specifically, folded states of the vertex, described by pairs of fold angles in terms of cotangent…

An efficient way to introduce elastic energy that can bias an origami structure toward desired shapes is to allow curved tiles between the creases. The bending of the tiles supplies the energy and the tiles themselves may have additional…

Origami structures enabled by folding and unfolding can create complex 3D shapes. However, even a small 3D shape can have large 2D unfoldings. The huge initial dimension of the 2D flattened structure makes fabrication difficult, and defeats…

Can folding a piece of paper flat make it larger? We explore whether a shape $S$ must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries $S\rightarrow R^2$).…

Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly…

We consider generalizations of the familiar fifteen-piece sliding puzzle on the 4 by 4 square grid. On larger grids with more pieces and more holes, asymptotically how fast can we move the puzzle into the solved state? We also give a…

We develop some design examples for approximating a target surface at the final rigidly folded state of a developable quadrilateral creased paper, which is folded with a 1-DOF rigid folding motion from the planar state. The final rigidly…

For origami structures, perforating or cutting slits along creases is an effective method to define fold lines and alleviate stress concentrations at vertices. In this letter we show numerically and experimentally that for…

This letter solves an open question of origami paper spring risen by Yoneda et al.(Phys. Rev. E 2019). By using both dimensional analysis and data fitting, a universal scaling law of a paper spring is formulated. The scaling law shows that…

In this paper we study twisted complexes on a ringed space and prove that it gives a new dg-enhancement of the derived category of perfect complexes on that space. A twisted complex is a collection of locally defined sheaves together with…

We present new examples of topologically convex edge-ununfoldable polyhedra, i.e., polyhedra that are combinatorially equivalent to convex polyhedra, yet cannot be cut along their edges and unfolded into one planar piece without overlap.…

Kirigami, the Japanese art of paper cutting, has recently enabled the design of stretchable mechanical metamaterials that can be easily realized by embedding arrays of periodic cuts into an elastic sheet. Here, we exploit kirigami…

Motivated by a question in origami, we consider sets of points in the complex plane constructed in the following way. Let $L_\alpha(p)$ be the line in the complex plane through $p$ with angle $\alpha$ (with respect to the real axis). Given…

A creased thin disk is generally bistable since the crease could be pushed through to form a stable cone-like inverted state with an elastic singularity corresponding to the vertex of the conical surface. In a recent study, we found that…

Why is it difficult to refold a previously folded sheet of paper? We show that even crease patterns with only one designed folding motion inevitably contain an exponential number of `distractor' folding branches accessible from a…

Shape-morphing finds widespread utility, from the deployment of small stents and large solar sails to actuation and propulsion in soft robotics. Origami structures provide a template for shape-morphing, but rules for designing and folding…

An origami extrusion is a folding of a 3D object in the middle of a flat piece of paper, using 3D gadgets which create faces with solid angles. In this paper we focus on 3D gadgets which create a top face parallel to the ambient paper and…

This paper gives one set of axioms for origami constructions, and describes the set of constructible points under these axioms. The determination of the set of cunstructible points for this particular set of axioms is related to Hilbert's…

We present an additive approach for the inverse design of kirigami-based mechanical metamaterials by focusing on the empty (negative) spaces instead of the solid tiles. By considering each negative space as a four-bar linkage, we identify a…