Rigidly foldable origami gadgets and tessellations

Evans, T. A.; Lang, Robert J.; Magleby, Spencer P.; Howell, Larry L.

doi:10.1098/rsos.150067

Cited by 119 publications

(66 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here, Guest fold is not rigid foldable as Lang et al (2015) showed. Also, Connelly et al proved (1997) that closed structure surrounded by triangulated surfaces cannot rigidly change its internal volume.…”

Section: Methods 21 Methods Of Creating Three Dimensionally Foldable Cmentioning

confidence: 90%

See 1 more Smart Citation

Development of folding method for three dimensionally foldable cylindrical structure with base

Kimachi

Morita

2017

Mechanical Engineering Journal

View full text Add to dashboard Cite

Folding method of structures which are composed of hinges and panels are studied in origami engineering.There is an open issue in the origami engineering that folding method of cylindrical structure with base is unknown. In this study, author had elucidated the folding method of a cylindrical structure with a flat bottom from combination and modification of the folding method proposed in previous research. Two types of foldable cylinder with flat base has developed. One is a combination of the Sogame fold and modified Guest fold (structure A), and the other is a combination of the modified stent fold and Guest fold (structure B). Here, modification has been done in order to coincide their trajectories at their juncture. Then we evaluate the dissimilarity of trajectories at the juncture of base and side, transition of strain value during folding process, and the shrink ratio which is the ratio which is the ratio of deployed volume to folded volume. From evaluation of those element, we clarified that structure A can shrink about twice smaller than structure B in its volume, and the dissimilarity of trajectories and magnitude of strain are smaller for structure A than structure B. So it can be said that structure A has an advantage over practicality. Shape of the base is expandable to dome type by combing the Sogame dome or dome type Guest fold with Sogame fold. In addition, Sogame dome's top flat surface can be replaced by the modified Guest fold. Note that these proposed foldable structures are not rigidly foldable, but elastically foldable. These results will cause the expansion of the application range of origami engineering.

show abstract

Section: Methods 21 Methods Of Creating Three Dimensionally Foldable Cmentioning

confidence: 90%

“…The similar technique can be seen in the corner gadget by Evans (2015). After modification, stent fold and Guest fold can be combined like Fig.…”

Section: Structure B (Combination Of Stent Fold and Guest Fold) 321mentioning

confidence: 99%

Development of folding method for three dimensionally foldable cylindrical structure with base

Kimachi

Morita

2017

Mechanical Engineering Journal

View full text Add to dashboard Cite

show abstract

“…Therefore, since we are interested in changing crease assignments to allow for defects, we must also incorporate the effect of the CP angles on the number of allowed crease assignments around a vertex into our models. Furthermore, aside from the importance of angles in flat-foldability and determining the number of valid crease assignments, flat-foldable CPs with the same connectivity and the same crease asignments but different angles can have very different folding properties, as seen in [23], where the Miura-ori, Barreto's Mars, the quadrilateral mesh, and the dual square twist CPs only differ in their angles, even though their resulting global foldings are quite different. We will not directly consider the resulting folding of the CP.…”

Section: Introductionmentioning

confidence: 99%

Exactly solvable flat-foldable quadrilateral origami tilings

Assis

2018

Phys. Rev. E

View full text Add to dashboard Cite

We consider several quadrilateral origami tilings, including the Miura-ori crease pattern, allowing for crease-reversal defects above the ground state which maintain local flat-foldability. Using exactly solvable models, we show that these origami tilings can have phase transitions as a function of crease state variables, as a function of the arrangement of creases around vertices, and as a function of local layer orderings of neighboring faces. We use the exactly solved cases of the staggered odd 8-vertex model as well as Baxter's exactly solved 3-coloring problem on the square lattice to study these origami tilings. By treating the crease-reversal defects as a lattice gas, we find exact analytic expressions for their density, which is directly related to the origami material's elastic modulus. The density and phase transition analysis has implications for the use of these origami tilings as tunable metamaterials; our analysis shows that Miura-ori's density is more tunable than Barreto's Mars, for example. We also find that there is a broader range of tunability as a function of the density of layering defects compared to as a function of the density of crease order defects before the phase transition point is reached; material and mechanical properties that depend on local layer ordering properties will have a greater amount of tunability. The defect density of Barreto's Mars, on the other hand, can be increased until saturation without passing through a phase transition point. We further consider relaxing the requirement of local flat-foldability by mapping to a solvable case of the 16-vertex model, demonstrating a different phase transition point for this case.

show abstract

“…With the increase in complexity of origami shapes that provide engineering utility, computational methods for the design of origami structures have become essential for developments in this area of study [1,5,23]. As in most kinematic models for origami structures, current methods for origami design consider rigid faces and creased folds [24,25]. For example, one of the most well-known methods for origami design is the tree method [23].…”

Section: Introductionmentioning

confidence: 99%

Design and simulation of origami structures with smooth folds

2017

View full text Add to dashboard Cite

Origami has enabled new approaches to the fabrication and functionality of multiple structures. Current methods for origami design are restricted to the idealization of folds as creases of zerothorder geometric continuity. Such an idealization is not proper for origami structures of non-negligible fold thickness or maximum curvature at the folds restricted by material limitations. For such structures, folds are not properly represented as creases but rather as bent regions of higher-order geometric continuity. Such fold regions of arbitrary order of continuity are termed as smooth folds. This paper presents a method for solving the following origami design problem: given a goal shape represented as a polygonal mesh (termed as the goal mesh), find the geometry of a single planar sheet, its pattern of smooth folds, and the history of folding motion allowing the sheet to approximate the goal mesh. The parametrization of the planar sheet and the constraints that allow for a valid pattern of smooth folds are presented. The method is tested against various goal meshes having diverse geometries. The results show that every determined sheet approximates its corresponding goal mesh in a known folded configuration having fold angles obtained from the geometry of the goal mesh.

show abstract

Rigidly foldable origami gadgets and tessellations

Cited by 119 publications

References 25 publications

Development of folding method for three dimensionally foldable cylindrical structure with base

Development of folding method for three dimensionally foldable cylindrical structure with base

Exactly solvable flat-foldable quadrilateral origami tilings

Design and simulation of origami structures with smooth folds

Contact Info

Product

Resources

About