Related papers: Rigid Origami Vertices: Conditions and Forcing Set…

Thick origami structures are considered here as assemblies of polygonal panels hinged to each other along their edges according to a corresponding origami crease pattern. The determination of the internal actions caused by external loads in…

Inspired by the allure of additive fabrication, we pose the problem of origami design from a new perspective: how can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve…

We study the problem of deciding whether a crease pattern can be folded by simple folds (folding along one line at a time) under the infinite all-layers model introduced by [Akitaya et al., 2017], in which each simple fold is defined by an…

Simple closed curves in the plane can be mapped to nontrivial knots under the action of origami foldings that allow the paper to self-intersect. We show all tame knot types may be produced in this manner, motivating the development of a new…

We introduce a computational origami problem which we call the segment folding problem: given a set of $n$ line-segments in the plane the aim is to make creases along all segments in the minimum number of folding steps. Note that a folding…

The ability to transform a flat sheet into a complex three-dimensional structure is a fundamental test of physical intelligence. Unlike cloth manipulation, origami is governed by strict geometric axioms and hard kinematic constraints, where…

The ancient art of origami, traditionally used to transform simple sheets into intricate objects, also holds potential for diverse engineering applications, such as shape morphing and robotics. In this study, we demonstrate that one of the…

We develop recursion equations to describe the three-dimensional shape of a sheet upon which a series of concentric curved folds have been inscribed. In the case of no stretching outside the fold, the three-dimensional shape of a single…

We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds;…

Four rigid panels connected by hinges that meet at a point form a 4-vertex, the fundamental building block of origami metamaterials. Here we show how the geometry of 4-vertices, given by the sector angles of each plate, affects their…

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…

The geometric, aesthetic, and mathematical elegance of origami is being recognized as a powerful pathway to self-assembly of micro and nano-scale machines with programmable mechanical properties. The typical approach to designing the…

Folding paper along curves leads to spatial structures that have curved surfaces meeting at spatial creases, defined as curve-fold origami. In this work, we provide an Eulerian framework focusing on the mechanics of arbitrary curve-fold…

Soft robots employing compliant materials and deformable structures offer great potential for wearable devices that are comfortable and safe for human interaction. However, achieving both structural integrity and compliance for comfort…

Starting with a flat sheet of paper, points can be constructed as the intersection of two folds. The set of constructible points clearly depends on which folds are admissible. In this paper, we study the situation where a fold is admissible…

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…

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…

Existing Civil Engineering structures have limited capability to adapt their configurations for new functions, non-stationary environments, or future reuse. Although origami principles provide capabilities of dense packaging and…

Non-Euclidean origami is a promising technique for designing multistable deployable structures folded from nonplanar developable surfaces. The impossibility of flat foldability inherent to non-Euclidean origami results in two disconnected…

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…