Crease Pattern Research Articles

Inverse Origami Design Model for Soft Robotic Development.

Origami provides an opportunity to construct a wide range of 3D functional structures by folding a flat sheet. It can be used to develop various soft functional robots by combining soft smart actuators. However, a simple and an effective model that can address the challenging problem of designing origami patterns to connect origami design with robotics is lacking, thereby greatly increasing the threshold of soft origami robots and hindering its development. This study proposes an easy-to-use inverse origami design model to generate the flat crease pattern from the desired folded shape automatically while simulating origami morphing by simply providing the shape parameters or 2D shape graphics. This method overcomes the difficulty of origami design and enables a close connection between origami and robotics. Through this method, various soft origami robots can be developed with low design complexity and time cost to achieve different functions, thereby promoting the development of soft origami robots.

A modular continuous robot constructed by Miura-derived origami tubes

Folding a flat sheet under a specific crease pattern can form a three-dimensional origami tube, which has been proven to exhibit unique mechanical properties and has wide engineering applications. In this study, a novel Miura-derived origami tube is designed, and its precise circular closing condition and mechanical properties are systematically analyzed, revealing that the proposed origami tube has programmable stiffness characteristics. Polyvinyl chloride (PVC) sheet enables the origami tube to have the characteristics of flexibility, bending, compression, and torsion resistance. Then, a modular design strategy for the novel continuous robot constructed with the Miura-derived origami tube as the backbone is proposed. A continuous robot with three origami tube modules in series is designed and fabricated as a representative case. Three steel wires drive each module to achieve independent contraction or bending movement. The unified installation of steel wire-driven motors on the base endows the robot with a lightweight, interconnected inner space, high scalability, and flexibility backbone. The kinematic relationships among the driving space, configuration space, and task space are investigated by geometric model and constant curvature assumption, with the circular trajectory tracking and reachable workspace revealed by numerical simulations. Further, the kinematic decoupling or the multi-driving model based on the stiffness difference of the origami tube between multi-segments is discussed. Finally, three prototype experiments demonstrate both the rationality of introducing origami tubes to design the continuous robot and the application potential.

Undulations in tubular origami tessellations: A connection to area-preserving maps

Origami tessellations, whose crease pattern has translational symmetries, have attracted significant attention in designing the mechanical properties of objects. Previous origami-based engineering applications have been designed based on the “uniform-folding” of origami tessellations, where the folding of each unit cell is identical. Although “nonuniform-folding” allows for nonlinear phenomena that are impossible through uniform-folding, there is no universal model for nonuniform-folding, and the underlying mathematics for some observed phenomena remains unclear. Wavy folded states that can be achieved through nonuniform-folding of the tubular origami tessellation called a waterbomb tube are an example. Recently, the authors formulated the kinematic coupled motion of unit cells within a waterbomb tube as the discrete dynamical system and identified a correspondence between its quasiperiodic solutions and wavy folded states. Here, we show that the wavy folded state is a universal phenomenon that can occur in the family of rotationally symmetric tubular origami tessellations. We represent their dynamical system as the composition of the two 2D mappings: taking the intersection of three spheres and crease pattern transformation. We show the universality of the wavy folded state through numerical calculations of phase diagrams and a geometric proof of the system’s conservativeness. Additionally, we present a non-conservative tubular origami tessellation, whose crease pattern includes scaling. The result demonstrates the potential of the dynamical system model as a universal model for nonuniform-folding or a tool for designing metamaterials.

Harnessing a paper-folding mechanism for reconfigurable DNA origami.

The paper-folding mechanism has been widely adopted in building of reconfigurable macroscale systems because of its unique capabilities and advantages in programming variable shapes and stiffness into a structure1-5. However, it has barely been exploited in the construction of molecular-level systems owing to the lack of a suitable design principle, even though various dynamic structures based on DNA self-assembly6-9 have been developed10-23. Here we propose a method to harness the paper-folding mechanism to create reconfigurable DNA origami structures. The main idea is to build a reference, planar wireframe structure24 whose edges follow a crease pattern in paper folding so that it can be folded into various target shapes. We realized several paper-like folding and unfolding patterns using DNA strand displacement25 with high yield. Orthogonal folding, repeatable folding and unfolding, folding-based microRNA detection and fluorescence signal control were demonstrated. Stimuli-responsive folding and unfolding triggered by pH or light-source change were also possible. Moreover, by employing hierarchical assembly26 we could expand the design space and complexity of the paper-folding mechanism in a highly programmable manner. Because of its high programmability and scalability, we expect that the proposed paper-folding-based reconfiguration method will advance the development of complex molecular systems.

Instability-Induced Origami Design by Topology Optimization

Instability-induced wrinkle patterns of thin sheets are ubiquitous in nature, which often result in origami-like patterns that provide inspiration for the engineering of origami designs. Inspired by instability-induced origami patterns, we propose a computational origami design method based on the nonlinear analysis of loaded thin sheets and topology optimization. The bar-and-hinge model is employed for the nonlinear structural analysis, added with a displacement perturbation strategy to initiate out-of-plane buckling. Borrowing ideas from topology optimization, a continuous crease indicator is introduced as the design variable to indicate the state of a crease, which is penalized by power functions to establish the mapping relationships between the crease indicator and hinge properties. Minimizing the structural strain energy with a crease length constraint, we are able to evolve a thin sheet into an origami structure with an optimized crease pattern. Two examples with different initial setups are illustrated, demonstrating the effectiveness and feasibility of the method.

Experimental Demonstration of Low‐Energy First‐Order Hybridized Plasmon Resonances in Origami Metashells

AbstractMetallic nanoshells have emerged as promising optical cavities to steer hybridized plasmonic resonances that show the high spectral tunability and a large surface area of localized fields. Despite various optical and photochemical applications, plasmonic resonances in shells have rarely been explored at low frequencies due to a nonlinear increase in particle size and a rapid degeneration in field localization. Here, this work reports the experimental realization of hybridized plasmon resonances in origami metashells that can be excited by low‐energy photons ≈7 GHz, corresponding to a level below 10−4 eV. Metasurfaces built of interconnected meshes act as thin Drude metallic films that support symmetric spoof surface plasmons. Rigid folding of the metasurface leads to diverse 3D hollow cavities that exhibit strong plasmonic responses, large surface areas, and low relative densities. Experimental measurements demonstrate three typical behaviors in Drude metallic shells: shielding to quasi‐static fields, strong scattering at first‐order hybridized plasmon resonances, and transparency to high frequency radiation. The relative density is remarkably reduced owing to the void cavity enabled by 3D folding, and an extra degree of freedom in anisotropic load capacity is provided by customizing crease patterns. These results open a door for extremely low‐energy plasmons with low‐density mechanics.

Shearigami: Self‐Folding via Shear Deformation

Origami and kirigami have become foundations for programmable sheet materials that fold along flexible creases. However, since they are originated from folded paper that allows no in‐plane sheet deformation, they suffer from limited folding energy arising from narrow creases, and large varieties of crease patterns are completely non‐foldable due to over‐constraint. Herein, a new strategy that breaks the limitations of the conventional crease‐induced folding kinematics by leveraging a folding effect from in‐plane shear deformation of the sheet is reported, and it is referred to as shearigami. It is shown that shearigami extends the realm of foldable structures to include the strictly non‐foldable origami patterns such as degree‐3 vertices, and the sheet‐stored self‐folding energy outperforms the crease‐stored energy by a potentially two orders of magnitude. Shearigami also inherits the mathematical framework of paper folding and provides a unified view that regards origami and kirigami as two special cases. Herein, self‐folding shearigami models are experimentally demonstrated based on previously non‐foldable patterns, including artificial muscles with rapid shear‐induced extension. The way is paved toward active structures and architectured materials with design freedom and self‐folding capabilities beyond origami and kirigami.

Continuous deformation of flat-foldable crease patterns via interpretation as set of twist-patterns

Abstract In the study of origami, various parametric methods have been proposed to design crease patterns under geometric conditions for flat-folding. Each design method contributes to finding a desirable crease pattern, e.g., one with superior engineering properties, by manipulating parameters. On the other hand, to continuously deform other crease patterns, it is necessary to recreate it once with such a parametric method; however, this inverse problem is less studied. This paper is basic research to solve this problem and to allow parametric deformation of flat-foldable crease patterns. Given crease patterns are interpreted as networks consisting of twist-folding patterns that can be generated by an existing parametric method named twist-based design method. Then, by manipulating the parameters, the crease pattern is deformed. Importantly, any flat-foldable crease pattern having no crease line connecting two points on the boundary can be targeted, and it is locally guaranteed that deformed crease patterns have non-intersecting crease lines and are flat-foldable. The proposed method contributes to increased origami variations by deformations of existing crease patterns.

Kinegami: Algorithmic Design of Compliant Kinematic Chains From Tubular Origami

Origami processes can generate both rigid and compliant structures from the same homogeneous sheet material. In this article, we advance the origami robotics literature by showing that it is possible to construct an arbitrary rigid kinematic chain with prescribed joint compliance from a single tubular sheet. Our “Kinegami” algorithm converts a Denavit–Hartenberg specification into a single-sheet crease pattern for an equivalent serial robot mechanism by composing origami modules from a catalogue. The algorithm arises from the key observation that tubular origami linkage design reduces to a Dubins path planning problem. The automatically generated structural connections and movable joints that realize the specified design can also be endowed with independent user-specified compliance. We apply the Kinegami algorithm to a number of common robot mechanisms and hand-fold their algorithmically generated single-sheet crease patterns into functioning kinematic chains. We believe this is the first completely automated end-to-end system for converting an abstract manipulator specification into a physically realizable origami design that requires no additional human input.

Algorithmic Spatial Form-Finding of Four-Fold Origami Structures Based on Mountain-Valley Assignments

AbstractOrigami has attracted tremendous attention in recent years owing to its capability of inspiring and enabling the design and development of reconfigurable structures and mechanisms for applications in various fields such as robotics and biomedical engineering. The vast majority of origami structures are folded starting from an initial two-dimensional crease pattern. However, in general, the planar configuration of such a crease pattern is in a singular state when the origami starts to fold. Such a singular state results in different motion possibilities of rigid or non-rigid folding. Thus, planar origami patterns cannot act as reliable initial configurations for further kinematic or structural analyses. To avoid the singularities of planar states and achieve reliable structural configurations during folding, we introduce a nonlinear prediction–correction method and present a spatial form-finding algorithm for four-fold origami. In this approach, first, initial nodal displacements are predicted based on the mountain-valley assignments of the given origami pattern, which are applied to vertices to form an initial spatial and defective origami model. Subsequently, corrections of nodal displacements are iteratively performed on the defective model until a satisfactory nonplanar configuration is obtained. Numerical experiments demonstrate the performance of the proposed algorithm in the form-finding of both trivial and non-trivial four-fold origami tessellations. The obtained configurations can be effectively utilized for further kinematic and structural analyses. Additionally, it has been verified that corrected and nonplanar configurations are superior to initial configurations in terms of matrix distribution and structural stiffness.

An origami shield with supporting frame structures optimized by a feature-driven topology optimization method

In this paper, the design, manufacture and testing of an origami protective shield with a supporting frame structure are presented. It consists of an origami shield surface and a deployable supporting frame structure that needs to be portable and sufficiently stiff. First, for the design of the shield surface, a three-stage origami crease pattern is developed to reduce the shield size in the folded state. The shield surface consists of several stiff modular panels and layered with flexible fabric. The modular panels are made of a multi-layer composite where a ceramic layer is made of small pieces to improve durability as those small pieces enable restriction of crack propagation. Then, the supporting frame structure is designed as a chain-of-bars structure in order to fold into a highly compact state as a bundle of bars and deploy in sequence. Thus, a feature-driven topology structural optimization method preserving component sequence is developed where the inter-dependence of sub-structures is taken into account. A bar with semi-circular ends is used as a basic design feature. The positions of the bar’s end points are treated as design variables and the width of the bars is kept constant. Then, a constraint on the total length of the chain of bars is introduced. Finally, the modular panels made of multi-layer composite and the full-scale prototype of the origami shield are fabricated and tested to verify the bullet-proof performance.

Data-driven design and morphological analysis of conical six-fold origami structures

In engineering design, origami structures are frequently characterized by their geometry-shifting behavior, mechanical properties, lightness, and appealing aesthetic qualities. In particular, conical origami structures have attracted increasing attention in recent years owing to their excellent energy absorption performance. However, designing conical structures with customizable geometry and folding morphology has remained a less explored research area. In this paper, an artificial intelligence (AI)-based framework is proposed for the customizable design of conical origami structures. To this end, first, the geometric relationships between the 2D crease patterns and 3D structures have been derived to determine the critical parameters. Subsequently, a data-driven method based on a deep neural network (DNN) is developed to train and predict the relationship among these critical parameters to facilitate the parametric design of conical origami structures. Importantly, although the DNN model is trained based on a limited set of data, error analyses demonstrate that the predicted crease patterns are in satisfactory agreement with analytical solutions, verified by physical models. Moreover, numerical simulations are performed to reveal the folding morphology and ensure the smooth deployment of the origami structures. Finally, the findings of this study indicate that conical origami structures are promising choices for further research and development in the area of lightweight energy-absorption structures.

Continuous modeling of creased annuli with tunable bistable and looping behaviors

Creases are purposely introduced to thin structures for designing deployable origami, artistic geometries, and functional structures with tunable nonlinear mechanics. Modeling the mechanics of creased structures is challenging because creases introduce geometric discontinuity and often have complex mechanical responses due to local material damage. In this work, we propose a continuous description of the sharp geometry of creases and apply it to the study of creased annuli, made by introducing radial creases to annular strips with the creases annealed to behave elastically. We find that creased annuli have generic bistability and can be folded into various compact shapes, depending on the crease pattern and the overcurvature of the flat annulus. We use a regularized Dirac delta function (RDDF) to describe the geometry of a crease, with the finite spike of the RDDF capturing the localized curvature. Together with anisotropic rod theory, we solve the nonlinear mechanics of creased annuli, with its stability determined by the standard conjugate point test. We find excellent agreement between precision tabletop models, numerical predictions from our analytical framework, and modeling results from finite element simulations. We further show that by varying the rest curvature of the thin strip, dynamic switches between different states of creased annuli can be achieved, which could inspire the design of deployable and morphable structures. We believe that our smooth description of discontinuous geometries will benefit the mechanical modeling and design of a wide spectrum of engineering structures that embrace geometric and material discontinuities.

Constructing Three-Dimensional Honeycomb Structures Based on Origami Geometry

Abstract Origami has shown the potential to design unique mechanical properties and complex three-dimensional shapes by folding through designed crease patterns on flat materials. The authors investigated a new honeycomb-based origami metamaterial called “kirigami honeycomb.” Resembling origami, kirigami honeycomb allows a single flat sheet of material with periodic slits to be folded into a honeycomb shape. Previous studies have reported successful use of this method to create various honeycomb shapes, changing only the folding line diagrams (FLDs). These previous studies have, however, considered only one-directional cross-sectional modifications; the core thickness and curvature changed only in the W-direction. This study proposes a new method that will support complex 3D honeycomb designs made from single flat sheets. A newly defined crease pattern conversion method provides arbitrary scaling of the honeycomb shape in the L-direction. The combined FLD and pattern conversion design methods encourage the cost-effective manufacture of 3D shaped honeycombs from single flat paper sheets. The proposed method is implemented to the design software, enabling to design arbitrary cross-sectional honeycomb cores with optional L-directional scaling.

Shape reconfiguration through origami folding sets an upper limit on drag

Mechanisms of drag reduction through shape reconfiguration have been extensively studied on model geometries of plates and beams that deform primarily in bending. Adding an origami crease pattern to such plates produces a distinct class of deformation modes, with large shape changes along selected degrees of freedom. Here, we investigate the impact of those creases on reconfiguration processes and on drag, focusing on the waterbomb base as a generic case. When placed in a uniform airflow, this origami unit folds into a compact structure, whose frontal area collapses with increasing flow velocity. It enhances drag reduction to the point that fluid loading eventually ceases to increase with flow speed, reaching an upper limit. We further show that this limit is adjustable through the origami structural parameters: the stiffness and rest angle of the folds, and their pattern. Experimental results, corroborated by a fluid–elastic theoretical model, point to a scenario consistent with the previous literature: reconfiguration is governed by a dimensionless Cauchy number that measures the competition between fluid loading and elastic resistance to deformation, here embodied in creases. This foldable system yet stands out through the rare passive drag-capping lever it provides, a valuable asset for self-protection in strong wind.

Multistable bioinspired origami with reprogrammable self-folding

Origami has emerged as a design paradigm to realize morphing structures with rich kinematic and mechanical properties. Biological examples augment the potential design space by suggesting intriguing routes for achieving self-folding from architected materials. We introduce a class of multistable self-folding origami adaptable after fabrication inspired by the earwig wing. This is achieved by designing bilayer creases that display anisotropic shrinkage in response to external stimulation, enabling a mechanism for prestrain adaptation. We establish a bilayer model for stretchable straight and trapezoidal (β) creases to generate bistable origami structures. We adapt the topology of the structure’s energy landscapes by tuning the fold prestrain level as a function of the stimulation time. The proposed method and model allows for converting flat sheets with arranged facets and prestrained mountain-valley creases into self-folding multistable structures. Introducing multistability from self-folding avoids ambiguous folding branches present in the rich configuration space at the flat state. The obtained crease prestrain programming is leveraged to manufacture a biomimetic earwig wing featuring the complex crease pattern, structural stability and rapid closure of the biological counterpart. The presented method provides a route for encoding prestrain in self-folding origami, the multistability of which is adaptable after fabrication.

Biomimetic folding of triangular deployable membranes

Deployable membranes are being increasingly applied in numerous space projects owing to their light weight, small stowage volume and capacity for use at large scales. The geometric design of biomimetic folding is studied to design crease patterns for triangular deployable membranes applied in space. Various crease designs for triangular membranes based on leaf-in, leaf-out and orthogonal patterns are put forward, especially patterns composed of triangular and hexagonal units. In order to analyse the membrane folding method based on biomimetic folding, a set of evaluation indices, including linear dimension ratio, deployment ratio, crease length and junction number, are established. The indices for various membrane folding patterns are calculated according to the crease distributions and geometric relations. Furthermore, a parametric study of crease parameters is performed to determine how the parameters affect folding behaviour and deployment efficiency. These indices can provide an indication to help with the selection of crease patterns and folding parameters for triangular deployable membranes according to the required performance and space mission requirements.

A Novel Radially Closable Tubular Origami Structure (RC-ori) for Valves

Cylindrical Kresling origami structures are often used in engineering fields due to their axial stretchability, tunable stiffness, and bistability, while their radial closability is rarely mentioned to date. This feature enables a valvelike function, which inspired this study to develop a new origami-based valve. With the unique one-piece structure of origami, the valve requires fewer parts, which can improve its tightness and reduce the cleaning process. These advantages meet the requirements of sanitary valves used in industries such as the pharmaceutical industry. This paper summarizes the geometric definition of the Kresling pattern as developed in previous studies and reveals the similarity of its twisting motion to the widely utilized iris valves. Through this analogy, the Kresling structure’s closability and geometric conditions are characterized. To facilitate the operation of the valve, we optimize the existing structure and create a new crease pattern, RC-ori. This novel design enables an entirely closed state without twisting. In addition, a simplified modeling method is proposed in this paper for the non-rigid foldable cylindrical origami. The relationship between the open area and the unfolded length of the RC-ori structure is explored based on the modeling method with a comparison with nonlinear FEA simulations. Not only limited to valves, the new crease pattern could also be applied to microreactors, drug carriers, samplers, and foldable furniture.

From rigid to amorphous folding behavior in origami-inspired metamaterials with bistable hinges

The folding behavior of origami-inspired metamaterials is often described by linear rotational springs and rigid faces. However, other folding modes and multistability appears when assuming elastic faces, specially when assuming (non-euclidean) crease patterns in 2D or 3D where a high number of hinges meet at their vertices. Instead, here we study multistability by exploring the use of non-linear material behavior implemented as bistable hinges. By drawing a similitude to atomic crystals, we are able to classify the complex folding behavior that non-linear elastic origami metamaterials undergo, where we identify transitions from rigid to elastic to amorphous behavior upon increasing the strength of the bistability. As a result, our study gives a better understanding and provides a tool to control multistable metamaterials for future applications.

Deployment kinematics of axisymmetric Miura origami: Unit cells, tessellations, and stacked metamaterials

Origami is emerging as a promising paradigm for deployable structures. The theoretical analysis on the relationship between geometry of the crease patterns and the induced deployment mechanisms is the key to the rational design of origami-inspired deployable structures. In this paper, we systematically investigate the deployment kinematics of axisymmetric Miura origami from unit cells to single-layer tessellations and multi-layer stacked metamaterials. We show that the axisymmetric Miura cells can be classified into two categories according to the monotonicity of the angular motion, and the axisymmetric Miura origami tessellations can be classified into seven categories based on the developability, flat-deployability, and the ability to form closed-ring shapes. We also derive the conditions for the deployability of the multi-layer metamaterials constructed by stacking axisymmetric Miura origami tessellations. Both the singly and doubly curved cases are studied for the tessellations and metamaterials. Additionally, based on the kinematic formulations, we develop an easy-to-implement optimization framework for the design of doubly curved axisymmetric Miura origami tessellations that approximate surfaces of revolution. The optimized shape-morphing tessellations can also be used to assemble multi-layer stacked metamaterials. Taken together, these results provide a comprehensive guidance to design axisymmetric deployable structures based on origami principles.