Traditional Origami Research Articles

Oriblock: The origami-blocks based on hinged dissection

Traditional origami, a well-known art of paper-folding, does not account for material thickness. Subsequently, several thickness-accommodation techniques have been developed, considering the non-negligible thickness of materials, which enables the application of origami to a wide range of mechanisms. Although these techniques prevent self-intersections and preserve kinematics after accommodating panel thickness, they are limited by their reliance on initial zero-thickness origami patterns in two dimensions. To address this issue, this study proposes a novel technique, the volume-accommodation technique in three-dimensional space, which allocates non-coplanar origami creases based on solid geometry to allow a greater variety of shape-changing motions. Typical solid geometries, such as a pyramid and a prism, are selected as examples to demonstrate the design procedures. Closure equations of the obtained oriblock are used to analyze the kinematic properties. Additionally, Bennett and Myard Linkages are derived from oriblocks based on their kinematic equivalence to strengthen their connections. As a result, this new type of origami can offer a variety of mechanisms for designers and facilitate potential applications in origami-inspired metamaterials and robotics.

Vibration suppression of a meta-structure with hybridization of Kresling origami and Yoshimura origami

In recent years, the deployment and vibration suppression capabilities of spacecraft have become one of the prominent research topics. Considerable effort has been dedicated to studying the deployability and vibration suppression performance of origami structures. However, traditional origami types severely limit their application in aerospace engineering due to their unique deployment behavior. This study introduces a novel meta-structure with hybridization of Kresling origami and Yoshimura origami (MHKYO), designed to suppress low-frequency vibrations. The band structure and transmission rate of the proposed metastructure were studied to evaluate its vibration suppression performance. The adjustment of the bandgap of the metastructure was achieved through geometric parameter variation. Quasi-static compression experiments and transmission rate experiments were carried out, and the results obtained were almost consistent with those obtained by finite element methods. During the compression process, the origami metastructure exhibited quasi-zero-stiffness (QZS) behavior. The influence of the metastructure’s stiffness on the band structure was analyzed. It is also proved that the hybrid origami metastructure improves the vibration suppression performance of the traditional origami metastructure. This work proposes a new origami-inspired metastructure, providing a certain theoretical basis for the application of origami technology in aerospace engineering.

An Accordion-Folding Series-Fed Patch Array With Finite Thickness: A folding technique for CubeSat arrays

Combining antenna arrays with physical reconfigurability (i.e., origami) allows for additional degrees of freedom in operation and enables larger structures to be folded into smaller volumes. The packaging ability of origami antennas is of great interest for CubeSat applications in particular. However, traditional origami is based on the manipulation of thin sheets, making physical reconfigurability with thick substrates very difficult. In this article, we present a foldable series-fed patch array designed on a strictly rigid printed circuit board (PCB). Notably, the array does not require any external mechanical folding appendages (i.e., brackets, tapes, or offsets), and it can be manufactured using commercially available PCBs and equipment. The PCB itself is strategically cut to form lamina emergent torsion (LET) joints. When fully deployed, the array operates at 5.7 GHz. A significant shift is not seen in the operational frequency until the folding exceeds 60° (5.7–5.61 GHz). This shows that the array, even in a state of near extreme faulty deployment, will operate as intended. An 8 × 6 prototype array was fabricated using a Rogers DiClad 880. When fully deployed, the array is extended in a surface area of 280 × 198 × 1.524 mm and can be folded into a 35.5 × 198 × 12.5-mm compartment. The array held its integrity well after 100 cycles. (One cycle starts at a state of full deployment, moves to a state of being fully packaged, and goes back to a state of full deployment.) Measurements show that the active reflection coefficients are in good agreement with the finite array simulations. The measured realized gains at 5.7 GHz for 0° and 30° folds were 22.4 and 21.4 dBi, respectively. At the 60° fold, a realized gain of 20.6 dBi was achieved at the frequency of 5.61 GHz.

Computational design methods for cylindrical and axisymmetric waterbomb tessellations

Origami has provided a potential way to construct 3D curved structures by folding flat sheet materials without cutting or stretching. As a traditional origami, waterbomb tessellation is widely studied from aspects of science and engineering. However, users cannot easily utilize this kind of origami to fit curved target surfaces because the underlying geometric constraints limit the design space. In this study, we propose computational design methods for approximating cylindrical and axisymmetric curved surfaces based on waterbomb tessellations. With consideration of symmetry and periodic repetition, a single strip of the waterbomb tessellation is first modeled and then longitudinally and circumferentially replicated to construct cylindrical and axisymmetric waterbomb tessellations, respectively. To fulfill flat-foldability, an optimization process is introduced for minimizing flat-foldable residuals iteratively and then a regulation process of the crease pattern is applied for further reducing such residuals. In addition, we demonstrate waterbomb-derivative tessellations with quad-paddings to expand the design variations. Furthermore, rigid-folding sequences and several physically engineered origami pieces are presented. The proposed methods can be utilized to facilitate the design of origami-inspired structures for various engineering design purposes, such as foldable shelters, tubular structures, metamaterials, and so on.

Non-Euclidean origami.

Traditional origami starts from flat surfaces, leading to crease patterns consisting of Euclidean vertices. However, Euclidean vertices are limited in their folding motions, are degenerate, and suffer from misfolding. Here we show how non-Euclidean 4-vertices overcome these limitations by lifting this degeneracy, and that when the elasticity of the hinges is taken into account, non-Euclidean 4-vertices permit higher order multistability. We harness these advantages to design an origami inverter that does not suffer from misfolding and to physically realize a tristable vertex.

Hyperbolic origami-inspired folding of triply periodic minimal surface structures

Origami-inspired folding methods present novel pathways to fabricate three-dimensional (3D) structures from 2D sheets. A key advantage of this approach is that planar printing and patterning processes could be used prior to folding, affording enhanced surface functionality to the folded structures. This is particularly useful for 3D lattices, possessing very large internal surface areas. While folding polyhedral strut-based lattices has already been demonstrated, more complex, curved sheet-based lattices have not yet been folded due to inherent developability constraints of conventional origami. Here, a novel folding strategy is presented to fold flat sheets into topologically complex cellular materials based on triply periodic minimal surfaces (TPMS), which are attractive geometries for many applications. The approach differs from traditional origami by employing material stretching to accommodate non-developability. Our method leverages the inherent hyperbolic symmetries of TPMS to assemble complex 3D structures from a net of self-foldable patches. We also demonstrate that attaching 3D-printed foldable frames to pre-strained elastomer sheets enables self-folding and self-guided minimal surface shape adaption upon release of the pre-strain. This approach effectively bridges the Euclidean nature of origami with the hyperbolic nature of TPMS, offering novel avenues in the 2D-to-3D fabrication paradigm and the design of architected materials with enhanced functionality.

Approximating 3D surfaces using generalized waterbomb tessellations

AbstractOrigami has received much attention in geometry, mathematics, and engineering due to its potential to construct 3D developable shapes from designed crease patterns on a flat sheet. Waterbomb tessellation, which is one type of traditional origami consisting of a set of waterbomb bases, has been used to create geometrically appealing 3D shapes and been widely studied. In this paper, we propose a method for approximating target surfaces, which are parametric surfaces of varying or constant curvatures, using generalized waterbomb tessellations. First, we generate a base mesh by tiling the target surface using waterbomb bases. Then, by applying a simple numerical optimization algorithm to the base mesh, we achieve a developable waterbomb tessellation, which can be developed onto a plane without stretching. We provide a prototype system using which the user can adjust the resolution of the tessellation and modify waterbomb bases. Our work could expand the exploration of building developable 3D structures using origami.Highlights Generalizing waterbomb tessellations to fit target 3D parametric surfaces. Achieving developable tessellations by a simple numerical optimization algorithm. Non-axisymmetric or non-orientable resulting approximations are demonstrated.

Design and Analysis of a Foldable/Unfoldable Corrugated Architectural Curved Envelop

Origami and paperfolding techniques may inspire the design of structures that have the ability to be folded and unfolded: their geometry can be changed from an extended, servicing state to a compact one, and back-forth. In traditional origami, folds are introduced in a sheet of paper (a developable surface) for transforming its shape, with artistic, or decorative intent; in recent times the ideas behind origami techniques were transferred in various design disciplines to build developable foldable/unfoldable structures, mostly in aerospace industry (Miura, 1985, “Method of Packaging and Deployment of Large Membranes in Space,” Inst. Space Astronaut. Sci. Rep., 618, pp. 1–9; Ikema et al., 2009, “Deformation Analysis of a Joint Structure Designed for Space Suit With the Aid of an Origami Technology,” 27th International Symposium on Space Technology and Science (ISTS)). The geometrical arrangement of folds allows a folding mechanism of great efficiency and is often derived from the buckling patterns of simple geometries, like a plane or a cylinder (e.g., Miura-ori and Yoshimura folding pattern) (Wu et al., 2007, “Optimization of Crush Characteristics of the Cylindrical Origami Structure,” Int. J. Veh. Des., 43, pp. 66–81; Hunt and Ario, 2005, “Twist Buckling and the Foldable Cylinder: An Exercise in Origami,” Int. J. Non-Linear Mech., 40(6), pp. 833–843). Here, we interest ourselves to the conception of foldable/unfoldable structures for civil engineering and architecture. In those disciplines, the need for folding efficiency comes along with the need for structural efficiency (stiffness); for this purpose, we will explore nondevelopable foldable/unfoldable structures: those structures exhibit potential stiffness because, when unfolded, they cannot be flattened to a plane (nondevelopability). In this paper, we propose a classification for foldable/unfoldable surfaces that comprehend non fully developable (and also non fully foldable) surfaces and a method for the description of folding motion. Then, we propose innovative geometrical configurations for those structures by generalizing the Miura-ori folding pattern to nondevelopable surfaces that, once unfolded, exhibit curvature.

817 曲線折紙の数理的取扱い

Elegant 3D origami structures from a planar sheet have been presented by incorporating curved folding into the design. Sometimes they look like sculpture, and a new genre called curved origami are now being formed. However, relation between the curved origami and traditional origami using straight creases is not clear in theoretical bases. We construct curved creases consisting of very short (tending to infinitesimal) straight hinge like creases. In the present report, some origami samples for circular tubes surfaces and conical surfaces are introduced. In the second half, a fundamental design method of such forming collar in vertical form-fill-seal machine is presented by using curved folding without elastic strain.

225 曲線折紙とそのものづくりへの応用

The traditional origami crease has been a straight line. In the 1970's, however, David Huffman began to investigate the possibilities of curved crease. The model made with curved crease is called curved origami and recently some origami artists begin to work with curved folds. Though their works are superior in design, relationship between traditional origami and curved origami isn't clear. In this paper we show the curved origami mathematically and application to the manufacturing.

Modelling of Folding Patterns in Flat Membranes and Cylinders by Origami

This paper describes folding methods of thin flat sheets as well as cylindrical shells by modelling folding patterns through Japanese traditional Origami technique. New folding patterns have been devised in thin flat squared or circular membrane by modifying so called Miura-Ori in Japan (one node with 4 folding lines). Some folding patterns in cylindrical shells have newly been developed including spiral configurations. Devised foldable cylindrical shells were made by using polymer sheets, and it has been assured that they can be folded quite well. The devised models will make it possible to construct foldable/deployable space structures as well as to manufacture foldable industrial products and living goods, e. g., bottles for soft drinks.

Modelling of Folding Patterns in Flat Membranes and Cylinders by Using Origami.

This paper describes folding methods of thin flat sheets as well as thin cylinders by modelling folding patterns through Japanese traditional Origami technique. New folding patterns have been deviced in thin flat squared or circular membranes by modifying so called Miura-Ori(one node with 4 folding lines). Some folding patterns in thin cylinders have newly been developed including spiral configurations. Developed foldable cylinders were made by using polymer sheets, and it has been assured that they can be folded very well. The deviced models will make it possible to construct foldable/developable space structures as well as to manufacture foldable bottles for beverages.