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Four rigid panels connected by hinges that meet at a point form a 4-vertex, the fundamental building block of origami metamaterials. Here we show how the geometry of 4-vertices, given by the sector angles of each plate, affects their…

Shell mechanisms are patterned surface-like structures with compliant deformation modes that allow them to change shape drastically. Examples include many origami and kirigami tessellations as well as other periodic truss mechanisms. The…

This article is concerned with an example of complex planar geometry arising from flat origami challenges. The complexity of solution algorithms is illustrated, depending on the depth of the initial analysis of the problem, starting from…

Reconfigurable robots that can change their physical configuration post-fabrication have demonstrate their potential in adapting to different environments or tasks. However, it is challenging to determine how to optimally adjust…

We introduce a compact yet highly expressive design space for shellular metamaterials. By employing only a few dozen degrees of freedom, this design space represents geometries ranging from simple planar configurations to complex triply…

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…

In this century, a square-tiled translation surface (an origami) is intensively studied as an object with special properties of its translation structure and its $SL(2,\mathbb{R})$-orbit embedded in the moduli space. We generalize this…

This work uncovers the tropical analogue for measured laminations of the convex hull construction of decorated Teichmueller theory, namely, it is a study in coordinates of geometric degeneration to a point of Thurston's boundary for…

The use of origami in engineering has significantly expanded in recent years, spanning deployable structures across scales, folding robotics, and mechanical metamaterials. However, finding foldable paths can be a formidable task as the…

We present a facile desktop fabrication method for origami-based nano-gap indium tin oxide (ITO) electrokinetic particle traps, providing a simplified approach compared to traditional lithographic techniques and effectively trapping of…

Origami-inspired mechanisms can transform flat sheets into functional three-dimensional dynamic structures that are lightweight, compact, and capable of complex motion. These properties make origami increasingly valuable in robotic and…

The ability of mechanical systems to perform basic computations has gained traction over recent years, providing an unconventional alternative to digital computing in off grid, low power, and severe environments which render the majority of…

Kirigami metamaterial sheets and tubes, owing to their capacity to undergo large elastic deformations while developing three-dimensional surface textures, have enormous potential as skins for soft robots. Here, we propose to use kirigami…

Reconfigurable mechanical systems enable precise programmable control over structural properties, opening new opportunities in architected materials, adaptive devices, and multifunctional structures. Here, we introduce elastic rod origami…

Extensive experimental studies have shown that numerous ordered phases can be formed via the self-assembly of T-shaped liquid crystalline molecules (TLCMs) composed of a rigid backbone, two flexible end chains and a flexible side chain.…

Origami structures have been proposed as a means of creating three-dimensional structures from the micro- to the macroscale, and as a means of fabricating mechanical metamaterials. The design of such structures requires a deep understanding…

Self-closing assembly is prone to polymorphism due to thermally-excited bending fluctuations, which permit the formation of off-target assemblies at the point of self-closure. One way to overcome this source of polymorphism is to use…

Cellular solids are a class of materials that have many interesting engineering applications, including ultralight structural materials. The traditional method for analyzing these solids uses convex uniform polyhedral honeycombs to…

We present an additive approach for the inverse design of kirigami-based mechanical metamaterials by focusing on the empty (negative) spaces instead of the solid tiles. By considering each negative space as a four-bar linkage, we identify a…

Overlaying two graphene layers with a small twist angle can create a moire superlattice to realize exotic phenomena that are entirely absent in graphene monolayer. A representative example is the predicted formation of localized…