Related papers: Origami building blocks: generic and special 4-ver…

Origami principles are used to create strong, lightweight structures with complex mechanical response. However, identifying the fundamental physical principles that determine a sheet's behavior remains a challenge. We introduce a new…

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…

Origami-based mechanical metamaterials have recently received significant scientific interest due to their versatile and reconfigurable architectures. However, it is often challenging to account for all possible geometrical configurations…

The recent development of modular origami structures has ushered in a new era for active metamaterials with multiple degrees of freedom (multi-DOF). Notably, no systematic inverse design approach for volumetric modular origami structures…

This article analyses geometric constructions by origami when up to $n$ simultaneous folds may be done at each step. It shows that any arbitrary angle can be $m$-sected if the largest prime factor of $m$ is $p\le n+2$. Also, the regular…

Thin sheets can be assembled into tubular origami structures that combine deployability with pronounced anisotropic stiffness, enabling applications ranging from robotics to deployable systems. However, most existing tubular origami designs…

Monte Carlo simulations of a Miyazawa-Jernigan lattice-polymer model indicate that, depending on the native's structure geometry, the model exhibits two broad classes of folding mechanisms for two-state folders. Folding to native structures…

Miura-ori is well-known for its capability of flatly folding a sheet of paper through a tessellated crease pattern made of repeating parallelograms. Many potential applications have been based on the Miura-ori and its primary variations.…

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…

Schmith\"usen proved in 2004 that the Veech group of an origami is closely related to a subgroup of the automorphism group of the free group $F_2$. This result is significant in the sense that the framework of approachable Veech groups is…

Three-dimensional shells can be synthesized from the spontaneous self-folding of two-dimensional templates of interconnected panels, called nets. However, some nets are more likely to self-fold into the desired shell under random movements.…

A quad-mesh rigid origami is a continuously deformable panel-hinge structure where planar, rigid, zero-thickness quadrilateral panels are connected by rotational hinges in the combinatorics of a grid. This article provides a comprehensive…

Origami structures have been receiving a lot of attention from engineering and scientific researchers owing to their unique properties such as deployability, multi-stability, negative stiffness, etc. However, dynamic properties of origami…

We present an approach to overcoming challenges in dynamical dexterity for robots through tunable origami structures. Our work leverages a one-parameter family of flat sheet crease patterns that folds into origami bellows, whose axial…

Let $S_{g}$ denote the closed orientable surface of genus $g$. In joint work with Huang, the first author constructed exponentially-many (in $g$) mapping class group orbits of pairs of simple closed curves whose complement is a single…

"Flat origami" refers to the folding of flat, zero-curvature paper such that the finished object lies in a plane. Mathematically, flat origami consists of a continuous, piecewise isometric map $f:P\subseteq\mathbb{R}^2\to\mathbb{R}^2$ along…

Flexible robotics are capable of achieving various functionalities by shape morphing, benefiting from their compliant bodies and reconfigurable structures. Here we construct and study a class of origami springs generalized from the known…

Structures and/or materials with engineered functionality, capable of achieving targeted mechanical responses reacting to changes in external excitation, have various potential engineering applications, e.g. aerospace, oceanographic…

A periodic surface is one that is invariant by a 2D lattice of translations. Deformation modes that stretch the lattice without stretching the surface are effective membrane modes. Deformation modes that bend the lattice without stretching…

In this paper, we show that deciding rigid foldability of a given crease pattern using all creases is weakly NP-hard by a reduction from Partition, and that deciding rigid foldability with optional creases is strongly NP-hard by a reduction…