Related papers: Rigid Origami Vertices: Conditions and Forcing Set…
Kirigami patterned materials have found several applications in recent years due to their ability to assume complicated shapes and exhibit emergent physical properties when exposed to external forces. Consisting of an array of cuts in a…
"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…
Periodic origami patterns made with repeating unit cells of creases and panels bend and twist in complex ways. In principle, such soft modes of deformation admit a simplified asymptotic description in the limit of a large number of cells.…
A zero forcing set is a set $S$ of vertices of a graph $G$, called forced vertices of $G$, which are able to force the entire graph by applying the following process iteratively: At any particular instance of time, if any forced vertex has…
Self-folding origami has emerged as a tool to make functional objects in material science. The common idea is to pattern a sheet with creases and activate them to have the object fold spontaneously into a desired configuration. This article…
We consider a problem in computational origami. Given a piece of paper as a convex polygon $P$ and a point $f$ located within, fold every point on a boundary of $P$ to $f$ and compute a region that is safe from folding, i.e., the region…
Designing a robot or structure that can fold itself into a target shape is a process that involves challenges originated from multiple sources. For example, the designer of rigid self-folding robots must consider foldability from geometric…
We give a modification of Mitchell's technique for adding objects of size $\omega_2$ with conditions with finite working parts in which the collections of models used as side conditions are very highly structured, arguably making them more…
Controlling the connectivity and rigidity of kirigami, i.e. the process of cutting paper to deploy it into an articulated system, is critical in the manifestations of kirigami in art, science and technology, as it provides the resulting…
Due to its rigid foldability and predictable kinematics, the reverse fold is the fundamental mechanism behind some of the most well known origami kinematic structures, including the Miura Ori, Yoshimura, and waterbomb patterns. However, the…
This study proposes a reconfigurable modular building system that assembles multistable curved-crease origami blocks. Curved-crease origami is designed with even-vertex polygonal trajectories and an elastica curvature profile. We then…
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…
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…
We prove that the pleated hyperbolic paraboloid, a familiar origami model known since 1927, in fact cannot be folded with the standard crease pattern in the standard mathematical model of zero-thickness paper. In contrast, we show that the…
We show that deciding whether a given set of circles can be packed into a rectangle, an equilateral triangle, or a unit square are NP-hard problems, settling the complexity of these natural packing problems. On the positive side, we show…
The geometry of bending-active kirigami arches, decorated by cuts and holes, is strongly influenced by the location and geometry of the perforations. This study demonstrates that, in some instances, the geometric stiffening induced by…
We propose a novel computational framework for modeling and simulating origami structures. In this framework, bilinear solid-shell elements are employed to model the origami panels while crease folding is considered through the angle…
We define a weak compatibility condition for the Newest Vertex Bisection algorithm on simplex grids of any dimension and show that using this condition the iterative algorithm terminates successfully. Additionally we provide an O(n)…
Twisting sheets as a strategy to form functional yarns relies on millennia of human practice in making catguts and fabric wearables, but still lacks overarching principles to guide their intricate architectures. We show that twisted…
Connections between vital linkages and zero forcing are established. Specifically, the notion of a rigid linkage is introduced as a special kind of unique linkage and it is shown that spanning forcing paths of a zero forcing process form a…