Related papers: Geodesics and isometric immersions in kirigami

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…

We present a simple, accessible method for autonomously transforming flat plastic sheets into intricate three-dimensional structures using only uniform heating and common tools such as household ovens and scissors. Our approach combines…

Origami is the art of folding paper into various patterns without cutting or tearing the paper. By viewing the paper as the complex plane, we iteratively compute and record all intersection points to construct mathematical origami sets.…

Origami is the archetype of a structural material with unusual mechanical properties that arise almost exclusively from the geometry of its constituent folds and forms the basis for mechanical metamaterials with an extreme deformation…

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…

We combine theory and experiments to explore the kinematics and actuation of intrinsically curved folds (ICFs) in otherwise developable shells. Unlike origami folds, ICFs are not bending isometries of flat sheets, but arise via…

Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major…

In this paper we explore and develop a simple set of rules that apply to cutting, pasting, and folding honeycomb lattices. We consider origami-like structures that are extinsically flat away from zero-dimensional sources of Gaussian…

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, the ancient art of folding thin sheets, has attracted increasing attention for its practical value in diverse fields: architectural design, therapeutics, deployable space structures, medical stent design, antenna design and…

This study starts from the counter-intuitive question of how we can render a conventional stiff, non-stretchable and even brittle material conformable so that it can fully wrap around a curved surface, such as a sphere, without failure.…

We introduce a new class of thin flexible structures that morph from a flat shape into prescribed 3D shapes without an external stimulus such as mechanical loads or heat. To achieve control over the target shape, two different concepts are…

Origami is an ancient art that continues to yield both artistic and scientific insights to this day. In 2012, Buhler, Butler, de Launey, and Graham extended these ideas even further by developing a mathematical construction inspired by…

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…

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…

Fold-and-cut theorem claims the possibility to cut out from a sheet a set of straight-line drawing using only one cut of scissors, without producing any other cut in the sheet and separating all the figures at the same time, just by folding…

Shape morphing that transforms morphologies in response to stimuli is crucial for future multifunctional systems. While kirigami holds great promise in enhancing shape-morphing, existing designs primarily focus on kinematics and overlook…

This paper establishes a rigorous geometrical framework for spherical origami, origami using spherical sheets based on spherical geometry. Two settings are treated: origami restricted to the unit sphere ($\mathbb{S}^2$), and…

For centuries, cutting and folding the papers with special patterns have been used to build beautiful, flexible and complex three-dimensional structures. Inspired by the old idea of kirigami (paper cutting), and the outstanding properties…

Origami as a deployable structure offers the unique advantage of achieving compact stowage via flat-folding while forming a well-defined surface composed of rigid panels upon deployment. However, since origami consists of flat facets, it is…