The designs and deformations of rigidly and flat-foldable quadrilateral mesh origami

Feng, Fan; Dang, Xiangxin; James, Richard D.; Plucinsky, Paul

doi:10.1016/j.jmps.2020.104018

Cited by 60 publications

(48 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, the entire fourfold tiling is determined by all the centers and by the left and bottom boundary offsets. The result is parallel with previous work [33] of one of us for the design of rigidly and flat-foldable quadrilateral mesh origami, in which the geometrical data on the left and bottom boundaries determine the entire origami pattern.…”

Section: Complex Topographies and The Inverse Design Of Pixelssupporting

confidence: 84%

“…A tiling usually differs from a single intersection in that it requires more global restrictions-we have to arrange different unit cells in a compatible way. In an origami community, the global restriction, called global compatibility, is the key idea to design tilings like rigidly and flat-foldable origami [32,33]. The global compatibility is automatically satisfied for symmetric patterns in Fig.…”

Section: Complex Topographies and The Inverse Design Of Pixelsmentioning

confidence: 99%

See 1 more Smart Citation

Evolving, complex topography from combining centers of Gaussian curvature

2020

Self Cite

View full text Add to dashboard Cite

Liquid crystal elastomers and glasses can have significant shape change determined by their director patterns. Cones deformed from circular director patterns have nontrivial Gaussian curvature localized at tips, curved interfaces, and intersections of interfaces. We employ a generalized metric compatibility condition to characterize two families of interfaces between circular director patterns, hyperbolic and elliptical interfaces, and find that the deformed interfaces are geometrically compatible. We focus on hyperbolic interfaces to design complex topographies and nonisometric origami, including n-fold intersections, symmetric and irregular tilings. The large design space of threefold and fourfold tiling is utilized to quantitatively inverse design an array of pixels to display target images. Taken together, our findings provide comprehensive design principles for the design of actuators, displays, and soft robotics in liquid crystal elastomers and glasses.

show abstract

Section: Complex Topographies and The Inverse Design Of Pixelssupporting

confidence: 84%

Section: Complex Topographies and The Inverse Design Of Pixelsmentioning

confidence: 99%

Evolving, complex topography from combining centers of Gaussian curvature

2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…On the topic of degeneracies, we build on ideas from [14]: As derived there, the question of whether or not a flat crease pattern, like the one shown in figure 3 a , is rigidly and flat-foldable can be addressed succinctly in terms of products of so-called fold angle multipliers . Fold angle multipliers are the functions μ2false(α,β,σfalse):=−σ+cos⁡αcos⁡β+sin⁡αsin⁡βcos⁡β−σcos⁡α,1emμ1false(α,β,−σfalse):=μ2false(α,π−β,−σfalse) defined for sector angles α, β ∈ (0, π ), ( α, β ) ≠ ( π /2, π /2) and mountain-valley assignment σ∈MVfalse(α,βfalse) indicated by MVfalse(α,βfalse):={−11em if α=β≠π/2+11em if α=π−β≠π/2±11em if α≠β≠π−β}. The crease pattern figure 3 a is parameterized by seven sector angles αa,β<...>…”

Section: Two-dimensional Materials Two-dimensional Origamimentioning

confidence: 99%

Origami and materials science

Liu

Plucinsky

Feng

et al. 2021

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

Origami, the ancient art of folding thin sheets, has attracted increasing attention for its practical value in diverse fields: architectural design, therapeutics, deployable space structures, medical stent design, antenna design and robotics. In this survey article, we highlight its suggestive value for the design of materials. At continuum level, the rules for constructing origami have direct analogues in the analysis of the microstructure of materials. At atomistic level, the structure of crystals, nanostructures, viruses and quasi-crystals all link to simplified methods of constructing origami. Underlying these linkages are basic physical scaling laws, the role of isometries, and the simplifying role of group theory. Non-discrete isometry groups suggest an unexpected framework for the design of novel materials. This article is part of the theme issue ‘Topics in mathematical design of complex materials’.

show abstract

“…Pereza-Hernandez et al [21] offers a method to achieve a specified 3D form through the use of smooth folds. Other approaches include a flat foldable 3D polygon design method by Kase et al [22], a flat foldable quadrilateral mesh design method by Feng et al [23], a prism synthesis method by Abdul-Sater [24], and an inverse design method for deployable origami structures by Dang et al [25]. In this study, we develop a design optimization framework to capture both mechanical and electromagnetic (EM) functionality from the robust reconfiguration capability of origami.…”

Section: Mechanical Variablesmentioning

confidence: 99%