Related papers: Origami Cubes with One-DOF Rigid and Flat Foldabil…
Motivated by a question in origami, we consider sets of points in the complex plane constructed in the following way. Let $L_\alpha(p)$ be the line in the complex plane through $p$ with angle $\alpha$ (with respect to the real axis). Given…
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…
Non-periodic folding of periodic crease patterns paves the way to novel nonlinear phenomena that cannot be feasible through periodic folding. This paper focuses on the non-periodic folding of recursive crease patterns generalized from…
Kirigami, the art of paper cutting, has been widely used in the modern design of mechanical metamaterials. In recent years, many kirigami-based metamaterials have been designed based on different planar tiling patterns and applied to…
We discuss well known geometric constructions via paper-folding. The note is written primary for school students.
Non-Euclidean surfaces are ubiquitous in numerous engineering fields, such as automotive, aerospace, and biomedical engineering domains. Morphing origami has numerous potential engineering applications, including soft robots, mechanical…
When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several…
We offer new insight into the folding kinematics of degree-4 rigid origami vertices by drawing an analogy to spacetime in special relativity. Specifically, folded states of the vertex, described by pairs of fold angles in terms of cotangent…
Thin elastic sheets bend easily and, if they are patterned with cuts, can deform in sophisticated ways. Here we show that carefully tuning the location and arrangement of cuts within thin sheets enables the design of mechanical actuators…
Curve-fold origami, composed of developable panels joined along a curved crease, exhibits rich dynamic behaviors relevant to metamaterials and soft robotic systems. Despite multiple approximated models, a comprehensive and exact dynamical…
Sliced Sudoku-based space-filling designs and, more generally, quasi-sliced orthogonal array-based space-filling designs are useful experimental designs in several contexts, including computer experiments with categorical in addition to…
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 characterize the cut patterns that can be produced by "orthogonal fold & cut": folding an axis-aligned rectangular sheet of paper along horizontal and vertical creases, and then making a single straight cut (at any angle). Along the way,…
Thin-walled structures capable of large, reversible deformation are key to multistable structures, origami, kirigami, and soft robotics. However, conventional fabrication techniques, including 3D printing, casting, and laser cutting, suffer…
Origami design principles are scale invariant and enable direct miniaturization of origami structures provided the sheets used for folding have equal thickness to length ratios. Recently, seminal steps have been taken to fabricate…
Origami metamaterial design enables drastic qualitative changes in the response properties of a thin sheet via the addition of a repeating pattern of folds based around a rigid folding motion. Known also as a mechanism, this folding motion…
Structures like galaxies and filaments of galaxies in the Universe come about from the origami-like folding of an initially flat three-dimensional manifold in 6D phase space. The ORIGAMI method identifies these structures in a cosmological…
Shape-morphing structures, which are able to change their shapes from one state to another, are important in a wide range of engineering applications. A popular scenario is morphing from an initial two-dimensional (2D) shape that is flat to…
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…