Origami Model Research Articles

Folding analysis for thick origami with kinematic frame models concerning gravity

Thickness and gravity are both the significant problems and challenges for origami structures in the field of building construction. This paper described a numerical folding analysis method to investigate the kinematic characteristics of thick origami using movable frame structural models driven by the external forces. The numeric methodology of the folding analysis is based on the generalized inverse theory. Therefore, both the morphing modes and the folding paths can be obtained in the environment of gravity through introducing the nodal forces directly. A general modeling approach is proposed to establish thick origami models using kinematic frames. To demonstrate the proposed method, single-DOF and multi-DOF examples are investigated. The folding procedures are obtained under the external forces, and the rigid motion modes are discussed. The presented method shows feasibility of analyzing the folding process of thick origami, which can help assess the practical rapid construction tasks in the future.

Automated Design and Optimization of Origami Electromagnetic Structures [EM Programmer's Notebook

Origami electromagnetic (EM) structures are promising technologies for deployable and reconfigurable EM structures such as antennas and frequency-selective surfaces (FSSs). However, these structures present CAD modeling difficulties due to their complex geometries. Studying the effects of origami substrate folding on EM performance demands multiple CAD models at different fold angles. Also, optimization of such structures for desired EM performance requires analysis of many CAD models. To enable fast CAD modeling, we introduce a toolset for automated modeling of origami EM structures. The proposed toolset uses origami mathematics for generating thin origami models. The thin models are then converted to thick substrates with conductive regions by implementing additional mathematical algorithms. Automated CAD modeling is achieved using Visual Basic Scripting (VBS) of the entire design and simulation process in Ansys high-frequency structure simulator (HFSS) using MATLAB. This toolset is important for future research of origami EM structures because it enables automated CAD modeling and optimization.

Towards Rapid Prototyping of Foldable Graphical User Interfaces with Flecto

Whilst new patents and announcements advertise the technical availability of foldable displays, which are capable to be folded to some extent, there is still a lack of fundamental and applied understanding of how to model, to design, and to prototype graphical user interfaces for these devices before actually implementing them. Without waiting for their off-the-shelf availability and without being tied to any physical foldable mechanism, Flecto defines a model, an associated notation, and a supporting software for prototyping graphical user interfaces running on foldable displays, such as foldable smartphone or assemblies of foldable surfaces. For this purpose, we use an extended notation of the Yoshizawa-Randlett diagramming system, used to describe the folds of origami models, to characterize a foldable display and define possible interactive actions based on its folding operations. A guiding method for rapidly prototyping foldable user interfaces is devised and supported by Flecto, a design environment where foldable user interfaces are simulated in 3D environment instead of in physical reality. We report on a case study to demonstrate Flecto in action and we gather the feedback from users on Flecto, using Microsoft Product Reaction Cards.

DNA Origami Model for Simple Image Decoding

DNA origami is the application of self-assembly in nanotechnology. The combination of DNA origami and hybridization chain reaction is one of the important application methods of DNA origami. In this paper, DNA origami is used to design the cipher pattern on the base of origami. The cipher chain, which is put into the reaction solution, hybridizes with the molecular beacon and the hairpin structure that form the cipher pattern to build a DNA origami model that can decode the pattern. The cipher chain consists of the starting chain and the intermediate chain. When the cipher is correct, the cipher chain can open the molecular beacon and the hairpin structure to display the cipher pattern on the origami base in the solution.

An Approach to comparing protein structures and origami models - Part 2. Multi-domain proteins

Protein structure is an important field of research, with particular significance in its potential applications in biomedicine and nanotechnology. In a recent study, we presented a general approach for comparing protein structures and origami models and demonstrated it with single-domain proteins. For example, the analysis of the α-helical barrel of the outer membrane protein A (OmpA) suggests that there are similar patterns between its structure and the Kresling origami model, providing insight into structure-activity relationships. Here we demonstrate that our approach can be expanded beyond single-domain proteins to also include multi-domain proteins, and to study dynamic processes of biomolecules. Two examples are given: (1) The eukaryotic chaperonin (TRiC) protein is compared with a newly generated origami model, and with an origami model that is constructed from two copies of the Flasher origami model, and (2) the CorA Magnesium transport system is compared with a newly generated origami model and with an origami model that combines the Kresling and Flasher origami models. Based on the analysis of the analog origami models, it is indicated that it is possible to identify building blocks for constructing assembled origami models that are analogous to protein structures. In addition, it is identified that the expansion/collapse mechanisms of the TRiC and CorA are auxetic. Namely, these proteins require a single motion for synchronized folding along two or three axes.

Earwig fan designing: Biomimetic and evolutionary biology applications

Technologies to fold structures into compact shapes are required in multiple engineering applications. Earwigs (Dermaptera) fold their fanlike hind wings in a unique, highly sophisticated manner, granting them the most compact wing storage among all insects. The structural and material composition, in-flight reinforcement mechanisms, and bistable property of earwig wings have been previously studied. However, the geometrical rules required to reproduce their complex crease patterns have remained uncertain. Here we show the method to design an earwig-inspired fan by considering the flat foldability in the origami model, as informed by X-ray microcomputed tomography imaging. As our dedicated designing software shows, the earwig fan can be customized into artificial deployable structures of different sizes and configurations for use in architecture, aerospace, mechanical engineering, and daily use items. Moreover, the proposed method is able to reconstruct the wing-folding mechanism of an ancient earwig relative, the 280-million-year-old Protelytron permianum This allows us to propose evolutionary patterns that explain how extant earwigs acquired their wing-folding mechanism and to project hypothetical, extinct transitional forms. Our findings can be used as the basic design guidelines in biomimetic research for harnessing the excellent engineering properties of earwig wings, and demonstrate how a geometrical designing method can reveal morphofunctional evolutionary constraints and predict plausible biological disparity in deep time.

Origami spring-inspired metamaterials and robots: An attempt at fully programmable robotics.

Recent advances in three-dimensional printing technologies provide one way not only to speed up freeform fabrication but also to exert programmable control over mechanical properties. Besides, origami-inspired structures, origami-inspired metamaterials, and even origami-inspired robotics primarily demonstrate the promising potential for innovative inspirations of engineering solutions. The motivation of this work is to explore a fully programmable robotic perspective with a fusion of programmable metamaterials, programmable mechanics, and programmable fabrication. First, we proposed an illustrative roadmap for transforming an origami model into a fully programmable robotic system. Then, we introduced an origami spring model and revealed its shape-shifting geometry and intrinsic metamaterial mechanisms, especially the rarely switchable behavior from transverse compression to longitudinal stretchability, and the curvilinear deployment. Furthermore, we addressed the fabrication challenges of three-dimensional printable origami sheets considering three-dimensional printability, foldability with high elasticity, and good damage tolerance. Finally, we developed a fully soft manipulator in terms of the highly reversible compressibility of origami spring metamaterials. And we also devised a peristaltic crawling robot with undulatory movements induced by inclination deployment effect of origami spring metamaterials. Conceivably, the proposed fully programmable robotic system was demonstrated starting from programmable metamaterials, programmable mechanics, and programmable fabrication to programmable robotic behaviors. The contribution of this work also suggested that robotic morphing could be tunable by hierarchical programming from modeling and fabrication to actions.

Origami Reconstruction of the Cortical Shell Structures of Radiolarian genus Pantanellium from Planar Graphs

We describe paper models which represent the cortical shell structures of radiolarian genus Pantanellium using the unit origami method: the construction of a polyhedral frame using origami units. Each unit corresponds to the edge of a polyhedron. The models are constructed based on planar graphs representing the cortical shell structures of real specimens. The resulting models reproduce the cortical shell structures appropriately. This means that the origami model is useful for both naked-eye practical observation of shell structures and group educational/art activities.

The Starry Night among art, maths, and origami

We illustrate a project in art, maths, and origami, in the spirit of STEAM, carried out in an Italian high school. We chose the famous Van Gogh's painting: ‘The Starry Night’ and we invited 16-year-old students to cover some elements on the artwork with origami models. These models were related to engineering, architecture, design and art and, for each of them, we designed a lesson on a precise mathematical subject. In this paper, we give the details of the project and we sketch the mathematical lessons we did, giving also the instructions to fold the models. We have also analysed the answers of a questionnaire filled in by students, to check the adequacy and effectiveness of the experience. The results showed that the students welcomed this project, and improved their maths knowledge.

Using direct and contructive methods for the existence of origami models with given boundary conditions

Whenever a unit square is folded to create an origami model in three-dimensional space, the edge of the paper forms a closed curve in space with a total length equal to four units. In this paper, some of the restrictions applicable to such resulting closed curves are derived in the case of classic origami models, in which none of the sections of the folded paper is curved in any way. This allows us to restrict the methods applied to those of classic euclidean geometry. Noting that it is of interest to determine origami models whose edges coincide with a polyline fulfilling the required conditions, we then proceed to show some methods for reconstructing the origami model if the boundary is known. Finally, some concrete reconstructions are demonstrated.

Design of Regular One-Dimensional, Two-Dimensional, and Three-Dimensional Linkage-Based Tessellations

Abstract Linkage origami is one effective approach for addressing stiffness and accommodating panels of finite size in origami models and tessellations. However, successfully implementing linkage origami in tessellations can be challenging. In this work, multiple theorems are presented that provide criteria for designing origami units or cells that can be assembled into arbitrarily large tessellations. The application of these theorems is demonstrated through examples of tessellations in two and three dimensions.

From Pressure-Volume Relationship to Volume-Energy Relationship: A Thermo-Statistical Model for Alveolar Micromechanics

The connective tissue fiber system and the surfactant system are essential and interdependent components of lung elasticity. Despite considerable efforts over the last decades, we are still far from understanding the quantitative roles of either the connective tissue fiber or the surfactant systems. Through thermo-statistic considerations of alveolar micromechanics, the author introduced a thermo-statistic state function “entropy” to analyze the elastic property of pulmonary parenchyma based on the origami model of alveolar polyhedron. By use of the entropy for alveolar micromechanics, from the logistic equation for the static pressure (P)-volume (V) curves including parameters a, b, c, and k (V - a = b/[1+ exp{-k (P - c)}]), a set of equations was obtained to define the internal energy of lungs (UL) and its corresponding lung volume (VL). Then, by use of parameters a, b, c, and k, an individual volume-internal energy (VL - UL) diagram was constructed from reported data in patients on mechanical ventilation. Each VL - UL diagram constructed was discussed that its minimal value Uo = c (a + b/2) and its shape parameter b/k represent quantitatively the energy of tissue force and the energy of surface force. Furthermore, by use of the VL - UL relationship, the hysteresis of lungs estimated by entropy production was discussed as dependent on the difference in the number of contributing pulmonary lobules. That is, entropy production might be a novel quantitative indicator to estimate the dynamics of the bronchial tree. These values obtained by combinations of parameters of the logistic P-V curve seem useful indicators to optimize setting a mechanical ventilator. Thus, it is necessary to develop easy tools for fitting the individual sigmoid pressure-volume curve measured in the intensive care unit to the logistic equation.

Novel origami-inspired metamaterials: Design, mechanical testing and finite element modelling

Two novel, origami-inspired, metamaterials were designed, mechanically tested, and modelled. One novel origami model was folded using a triangular based crease pattern and the other was folded using a rectangular based crease pattern. The origami-inspired metamaterial sheets were fabricated from polylactic acid using fused deposition additive manufacturing. Several configurations, parameterized by varying the fold angle, were mechanically tested under compression and impact loads. It was found that the specific elastic compression modulus of these novel designs was higher, ranging from 594 MPa/kg to 926 MPa/kg, than existing origami-inspired structures made based on the popular Ron-Resch design, which had specific elastic compression moduli between 15 MPa/kg to 365 MPa/kg. A finite element model further analysed the stress distribution of the core structures under compression loads. The impact testing results showed that the pattern of the tessellated cores affected the amount of impact force transferred through the samples, whereas the fold angle of the origami-inspired design had little impact on the results. The rectangular structure was shown to transfer approximately 50–75% of the force transferred by the triangular structure under impact loads.

Approach for comparing protein structures and origami models

The research fields of proteins and origami have intersected in the study of folding and de-novo design of proteins. However, there is limited knowledge on the analogy between protein structures and origami models. We propose a general approach for comparing protein structures with origami models, and present a test case, comparing transmembrane β-barrel and α-helical barrel with the Yoshimura and Kresling origami models. While both shapes and structures may look similar, we demonstrated that the β-barrel and the α-helical barrel are in agreement only with the shape and structural characteristics of the Kresling model. Through the analogy, it is explained how the structural characteristic can help the β-barrel and α-helical barrel to adjust length and diameter in response to changes in the membrane structure. However, such conformations only apply to the α-helical barrel, and the β-barrel, in spite of resembles to the Kresling model, remains stiff due to hydrogen bonds between the β-strands. Thus, our analysis suggests that there are similar patterns between protein structures and origami models and that the proposed approach may provide important insight on the role that the structure of a protein fulfils, and on the preferred structural design of novel proteins with unique characteristics.

Developing Primary School Students’ Formal Geometric Definitions Knowledge by Connecting Origami and Technology

In this paper, we present opportunities with the uses of origami and technology, in our case GeoGebra, in teaching formal geometric definitions for fifth-grade primary school students (11- 12yrs). Applying origami in mathematical lessons is becoming to be recognized as a valuable tool for improving students’ mathematical knowledge. In previous studies, we developed origami and technology activities for high-school mathematics, but we wanted to explore if such approach would work in primary school as well. For this reason, we chose a flat origami model оf the crane and we used this model to introduce students to basic geometrical notions and definitions, such as points, lines, intersections of lines and angles. To complement mathematical ideas from paper folding we also employed mathematical software GeoGebra, to further ideas and extend students’ mathematical toolkits. However, to be able to use software, students would already need basic conceptions of geometric definitions and then the use of the software clearly add to solidifying their knowledge. We believe that the combination hands-on activities and technology could contribute to discovery learning and enhancing students’ understanding of geometric definitions and operations

Single‐View Modeling of Layered Origami with Plausible Outer Shape

AbstractModeling 3D origami pieces using conventional software is laborious due to the geometric constraints imposed by the complicated layered structure. Targeting origami models used in visual content such as CG illustrations and movies, we propose an interactive system that dramatically simplifies the modeling of 3D origami pieces with plausible outer shapes, while omitting accurate inner structures. By focusing on flat origami models with a front‐and‐back symmetry commonly found in traditional artworks, our system realizes easy and quick modeling via single‐view interface; given a reference image of the target origami piece, the user draws polygons of planar faces onto the image, and assigns annotations indicating the types of folding operations. Our system automatically rectifies the manually‐specified polygons, infers the folded structures that should yield the user‐specified polygons with reference to the depth order of layered polygons, and generates a plausible 3D model while accounting for gaps between layers. Our system is versatile enough for modeling pseudo‐origami models that are not realizable by folding a single sheet of paper. Our user study demonstrates that even novice users without the specialized knowledge and experience on origami and 3D modeling can create plausible origami models quickly.

Lattice models and Monte Carlo methods for simulating DNA origami self-assembly.

The optimal design of DNA origami systems that assemble rapidly and robustly is hampered by the lack of a model for self-assembly that is sufficiently detailed yet computationally tractable. Here, we propose a model for DNA origami that strikes a balance between these two criteria by representing these systems on a lattice at the level of binding domains. The free energy of hybridization between individual binding domains is estimated with a nearest-neighbour model. Double helical segments are treated as being rigid, but we allow flexibility at points where the backbone of one of the strands is interrupted, which provides a reasonably realistic representation of partially and fully assembled states. Particular attention is paid to the constraints imposed by the double helical twist, as they determine where strand crossovers between adjacent helices can occur. To improve the efficiency of sampling configuration space, we develop Monte Carlo methods for sampling scaffold conformations in near-assembled states, and we carry out simulations in the grand canonical ensemble, enabling us to avoid considering states with unbound staples. We demonstrate that our model can quickly sample assembled configurations of a small origami design previously studied with the oxDNA model, as well as a design with staples that span longer segments of the scaffold. The sampling ability of our method should allow for good statistics to be obtained when studying the assembly pathways and is suited to investigating, in particular, the effects of design and assembly conditions on these pathways and their resulting final assembled structures.

A folding analysis method for origami based on the frame with kinematic indeterminacy

The kinematic analysis of the folding process is important in practical engineering applications of the mechanism of origami. This paper proposes an efficient methodology for tracing the folding process of origami in a three-dimensional space. This method directly controls the nodal coordinates in the origami model activated by external force on the vertices. The deforming path is obtained using an algorithm based on the generalized inverse theory. An improved type of origami unit is presented for the computational calculation. The results demonstrate that the computational efficiency is strongly related not only to the number of the unknowns, but also the singular value of the compatibility matrix of the origami model. Furthermore, the validity and versatility of the proposed method are confirmed through numerical examples, including general origami models, origami with gravity, origami with special boundary conditions, and curved-crease origami. The proposed method is validated to be feasible and efficient in analyzing the folding mechanism of origami structures for kinematic design in structural and mechanical applications.

Three-dimensional structural dynamics of DNA origami Bennett linkages using individual-particle electron tomography

Scaffolded DNA origami has proven to be a powerful and efficient technique to fabricate functional nanomachines by programming the folding of a single-stranded DNA template strand into three-dimensional (3D) nanostructures, designed to be precisely motion-controlled. Although two-dimensional (2D) imaging of DNA nanomachines using transmission electron microscopy and atomic force microscopy suggested these nanomachines are dynamic in 3D, geometric analysis based on 2D imaging was insufficient to uncover the exact motion in 3D. Here we use the individual-particle electron tomography method and reconstruct 129 density maps from 129 individual DNA origami Bennett linkage mechanisms at ~ 6–14 nm resolution. The statistical analyses of these conformations lead to understanding the 3D structural dynamics of Bennett linkage mechanisms. Moreover, our effort provides experimental verification of a theoretical kinematics model of DNA origami, which can be used as feedback to improve the design and control of motion via optimized DNA sequences and routing.

A coarse-grained model for DNA origami.

Modeling tools provide a valuable support for DNA origami design. However, current solutions have limited application for conformational analysis of the designs. In this work we present a tool for a thorough study of DNA origami structure and dynamics. The tool is based on a novel coarse-grained model dedicated to geometry optimization and conformational analysis of DNA origami. We explored the ability of the model to predict dynamic behavior, global shapes, and fine details of two single-layer systems designed in hexagonal and square lattices using atomic force microscopy, Förster resonance energy transfer spectroscopy, and all-atom molecular dynamic simulations for validation of the results. We also examined the performance of the model for multilayer systems by simulation of DNA origami with published cryo-electron microscopy and atomic force microscopy structures. A good agreement between the simulated and experimental data makes the model suitable for conformational analysis of DNA origami objects. The tool is available at http://vsb.fbb.msu.ru/cosm as a web-service and as a standalone version.