Related papers: Rigid foldability of the augmented square twist
It is well-known that a thin sheet held in a rigid circular clamp has a larger flexural strength than when it is flat. Here, we report that the flexural strength of curved sheets is further increased with a softening of the clamping…
We calculate the Gaussian curvature of a curved, twisted crease in terms of the rate of change of solid angle along its length; we find that this depends on the fold angle across the crease and on the curvature along it but is independent…
Origami is the art of paper folding, and it borrows its name from two Japanese words \emph{ori} and \emph{kami}. In Japanese, {ori} means folding, and the paper is called {kami}. While origami is just a hobby to most, there is a lot more to…
Origami and Kirigami, the famous Japanese art forms of paper folding and cutting, have inspired the design of novel materials & structures utilizing their geometry. In this article, we explore the geometry of the lesser known popup art,…
The principles of origami design have proven useful in a number of technological applications. Origami tessellations in particular constitute a class of morphing metamaterials with unusual geometric and elastic properties. Although…
We present an exact formula for the number of distinct crease patterns in a square shaped region of a given size that appear in the 2 dimensional paperfolding structure.
An origami manifold is a manifold equipped with a closed 2-form which is symplectic except on a hypersurface where it is like the pullback of a symplectic form by a folding map and its kernel fibrates with oriented circle fibers over a…
Origami-based design holds promise for developing materials whose mechanical properties are tuned by crease patterns introduced to thin sheets. Although there has been heuristic developments in constructing patterns with desirable…
We consider the zero-energy deformations of periodic origami sheets with generic crease patterns. Using a mapping from the linear folding motions of such sheets to force-bearing modes in conjunction with the Maxwell-Calladine index theorem…
Origami, the traditional paper-folding art, has inspired the modern design of numerous flexible structures in science and engineering. In particular, origami structures with different physical properties have been studied and utilized for…
We show that every polycube tree can be unfolded with a 4x4 refinement of the grid faces. This is the first constant refinement unfolding result for polycube trees that are not required to be well-separated.
We prove that the space of circle packings consistent with a given triangulation on a surface of genus at least two is projectively rigid, so that a packing on a complex projective surface is not deformable within that complex projective…
We introduce an additive approach for the design of a class of transformable structures based on two-bar linkages ("scissor mechanisms") joined at vertices to form a two dimensional lattice. Our discussion traces an underlying mathematical…
Origami folded cylinders (origami bellows) have found increasingly sophisticated applications in space flight and medicine. In spite of this interest, a general understanding of the mechanics of an origami folded cylinder has been elusive.…
Kirigami, art of paper cutting, enables two-dimensional sheets transforming into unique shapes which are also hard to reshape once with prescribed cutting patterns. Rare kirigami designs manipulate cuts on three-dimensional objects to…
We characterize the phase-space of all Helical Miura Origami. These structures are obtained by taking a partially folded Miura parallelogram as the unit cell, applying a generic helical or rod group to the cell, and characterizing all the…
Origami-inspired structures have a rich design space, offering new opportunities for the development of deployable systems that undergo large and complex yet predictable shape transformations. There has been growing interest in such…
This addendum to [O'R17] establishes that a nearly flat acutely triangulated convex cap in the sense of that paper can be edge-unfolded even if closed to a polyhedron by adding the convex polygonal base under the cap.
An embedded twisted paper cylinder of aspect ratio $\lambda$ is a smooth isometric embedding of a flat $\lambda \times 1$ cylinder into $\R^3$ such that the images of the boundary components are linked. We prove that for such an object to…
We characterize the cut patterns that can be produced by "orthogonal fold & cut": folding an axis-aligned rectangular sheet of paper along horizontal and vertical creases, and then making a single straight cut (at any angle). Along the way,…