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Ring origami, consisting of closed-loop rods, is a class of shape-morphing structures that undergo shape transformation through folding enabled by snap-buckling instabilities, referred to as snap-folding instabilities. Previous studies have…
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 a novel parabolic reflector system capable of generating a broader class of shapes beyond canonical parabolas. Using a discretized framework, we construct meshes corresponding to key families of developable surfaces, including…
This paper addresses the problem of finding minimum forcing sets in origami. The origami material folds flat along straight lines called creases that can be labeled as mountains or valleys. A forcing set is a subset of creases that force…
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…
Here we describe an ultra-low-cost origami-based approach for large-scale manufacturing of microscopes, specifically demonstrating brightfield, darkfield, and fluorescence microscopes. Merging principles of optical design with origami…
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…
Kirigami tessellations, regular planar patterns formed by cutting flat, thin sheets, have attracted recent scientific interest for their rich geometries, surprising material properties and promise for technologies. Here we pose and solve…
This paper proposes a family of origami tessellations called extruded Miura-Ori, whose folded state lies between two parallel planes with some faces on the planes, potentially useful for folded core materials because of face bonding. An…
Metamaterials with floppy modes called mechanisms are a burgeoning template for shape-morphing systems and structures across scales. Here, we present a design recipe that transforms an arbitrary plane tiling into a 2D kirigami pattern with…
Graphene's exceptional mechanical properties, including its highest-known stiffness (1 TPa) and strength (100 GPa) have been exploited for various structural applications. However, graphene is also known to be quite brittle, with…
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…
A folded disk is bistable, as it can be popped through to an inverted state with elastic energy localized in a small, highly-deformed region on the fold. Cutting out this singularity relaxes the surrounding material and leads to a loss of…
In nature, materials such as ferroelastics and multiferroics can switch their microstructure in response to external stimuli, and this reconfiguration causes a simultaneous modulation of its material properties. Rapid prototyping…
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…
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…
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…
We develop some design examples for approximating a target surface at the final rigidly folded state of a developable quadrilateral creased paper, which is folded with a 1-DOF rigid folding motion from the planar state. The final rigidly…
The construction of atomically-precise carbon nanostructures holds promise for developing novel materials for scientific study and nanotechnology applications. Here we show that graphene origami is an efficient way to convert graphene into…
A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami symplectic manifolds, studied by Cannas da Silva, Guillemin…