Related papers: Geometry and design of popup structures
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…
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…
Shape-morphing capabilities are crucial for enabling multifunctionality in both biological and artificial systems. Various strategies for shape morphing have been proposed for applications in metamaterials and robotics. However, few of…
We find a closed-form expression for the Poisson's coefficient of curved-crease variants of the ``Miura ori'' origami tessellation. This is done by explicitly constructing a continuous one-parameter family of isometric piecewise-smooth…
Biology is full of intricate molecular structures whose geometries are inextricably linked to their function. Many of these structures exhibit varying curvature, such as the helical structure of the bacterial flagellum, which is critical…
We introduce a simple and concrete way of visualizing in three dimensions a "flat" Klein bottle -- one whose local intrinsic geometry is the same as that of a flat plane -- which preserves most its topological and geometric structure.…
An origami (also known as square-tiled surface) is a Riemann surface covering a torus with at most one branch point. Lifting two generators of the fundamental group of the punctured torus decomposes the surface into finitely many unit…
Origami, where two-dimensional sheets are folded into complex structures, is proving to be rich with combinatorial and geometric structure, most of which remains to be fully understood. In this paper we consider \emph{flat origami}, where…
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-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…
Orthogonally assembled double-layered corrugated (OADLC) mechanisms are a class of foldable structures that harness origami-inspired methods to enhance the structural stiffness of resulting devices; these mechanisms have extensive…
Origami and crumpling are two extreme tools to shrink a 3-D shell. In the shrink/expand process, the former is reversible due to its topological mechanism, while the latter is irreversible because of its random-generated creases. We observe…
Manipulation of thin sheets by folding and cutting offers opportunity to engineer structures with novel mechanical properties, and to prescribe complex force-displacement relationships via material elasticity in combination with the…
We present a formalization of geometric instruments that considers separately geometric and arithmetic aspects of them. We introduce the concept of tool, which formalizes a physical instrument as a set of axioms representing its geometric…
The study of origami-based mechanical metamaterials usually focuses on the kinematics of deployable structures made of an assembly of rigid flat plates connected by hinges. When the elastic response of each panel is taken into account,…
We are introducing a general framework for the construction of polyhedra and simplicial comlexes that are {\em bifoldable}, i.e. foldable into two two different planes. This vastly generalizes Origami folds known as the Miura pattern, the…
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…
Can folding a piece of paper flat make it larger? We explore whether a shape $S$ must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries $S\rightarrow R^2$).…
Origami offers a promising alternative for designing innovative soft robotic actuators. While features of origami, such as bi-directional motion and structural anisotropy, haven't been extensively explored in the past, this letter presents…
Compacting orthogonal drawings is a challenging task. Usually algorithms try to compute drawings with small area or edge length while preserving the underlying orthogonal shape. We present a one-dimensional compaction algorithm that alters…