Miura Origami Research Articles

An origami-wheeled robot with variable width and enhanced sand walking versatility

Robots inspired by origami that offer several benefits, including being lightweight, requiring less assembly, and possessing remarkable deformability, have drawn a lot of interest. However, the existing origami-inspired robots are usually of limited functionalities and developing feature-rich robots is very challenging. Here, we report an origami-wheeled robot (OriWheelBot) with exceptional mobility for sand walking and a changing width. Origami wheels created using Miura origami permit the OriWheelBot to alter wheel width over obstacles. We derive the variable-width and diameter analytical models of the origami wheel, assuming rigid-folding, which has been confirmed by testing. An enhanced variant, dubbed iOriWheelBot, is additionally being developed to autonomously determine the obstacle's breadth. Based on the width of the channel between the barriers, three actions will be executed: direct pass, variable width pass, and direct return. Sand-pushing is more suitable for walking on the sand than sand-digging, which is the other of the two motion mechanisms that we have identified. Many aspects of sand walking, including carrying loads, walking on a slope, climbing a slope, and negotiating sand pits, small rocks, and sand traps, have been methodically investigated. The OriWheelBot can climb a 17-degree sand incline, vary its width by 40 %, and have a loading-carrying ratio of 66.7 % on flat sand. Rescue operations in disaster areas and planetary subsurface exploration can benefit from the OriWheelBot.

Modular Flat Structure with Miura Origami for Space Solar Power Station

To address the challenges associated with existing space solar power station (SSPS) concepts, including noncompact structural design, nonuniform solar energy flow density, and orbital deployment complexities, an integrated, highly modular, flat functional structure based on the Miura origami pattern is proposed. The flat functional structure consists of a flat quadrilateral Fresnel concentrator for solar energy collection, a photovoltaic array for photoelectric conversion, and a transmitting array for microwave power transmission. To optimize space utilization and enhance the deployment ratio, the Miura origami pattern is introduced, and the subarray composed of multiple flat functional structures can be packaged in a payload capsule before launch and unfold as a standard rectangle with uniform thickness and a flat surface in orbit, improving the transportability of the launch vehicle. Additionally, to solve the nonuniform solar energy flow density, a Fresnel concentrator was employed to achieve uniform irradiation, while the transmitting array was designed to achieve good electrical performance. Finally, the structural parameters and efficiency of the SSPS system composed of multiple subarrays are presented in detail.

Cushioning performance of origami negative poisson's ratio honeycomb steel structure

The honeycomb structure with a negative Poisson's ratio, inspired by the Miura origami unit, exhibits three-dimensional negative Poisson's ratio characteristics and effective energy dissipation performance. This unique property provides significant potential in the field of protection applications. This study aims to comprehensively understand the impact of auxetic and origami structures on the cushioning performance of honeycomb structures. For this purpose, 316 L stainless steel specimens were fabricated using 3D printing technology and subjected to drop hammer impact tests, and the results were verified by finite element simulation. This paper focuses on assessing the deformation mode and energy dissipation performance of origami auxetic honeycomb structures with varying width-to-thickness ratios and folding angles under different impact energy levels. The results indicate that the negative Poisson's ratio origami specimens exhibit higher plateau stress and specific energy absorption compared to their positive and zero Poisson's ratio origami counterparts with the same geometry. In addition, a smaller width-to-thickness ratio and higher input impact energy enhance the cushioning performance of honeycomb structures.

Origami-Enhanced Mechanical Properties for Worm-Like Robot.

In recent years, the exploration of worm-like robots has garnered much attention for their adaptability in confined environments. However, current designs face challenges in fully utilizing the mechanical properties of structures/materials to replicate the superior performance of real worms. In this article, we propose an approach to address this limitation based on the stacked Miura origami structure, achieving the seamless integration of structural design, mechanical properties, and robotic functionalities, that is, the mechanical properties originate from the geometric design of the origami structure and at the same time serve the locomotion capability of the robot. Three major advantages of our design are: the implementation of origami technology facilitates a more accessible and convenient fabrication process for segmented robotic skin with periodicity and flexibility, as well as robotic bristles with anchoring effect; the utilization of the Poisson's ratio effect for deformation amplification; and the incorporation of localized folding motion for continuous peristaltic locomotion. Utilizing the high geometric designability inherent in origami, our robot demonstrates customizable morphing and quantifiable mechanical properties. Based on the origami worm-like robot prototype, we experimentally verified the effectiveness of the proposed design in realizing the deformation amplification effect and localized folding motion. By comparing this to a conventional worm-like robot with discontinuous deformation, we highlight the merits of these mechanical properties in enhancing the robot's mobility. To sum up, this article showcases a bottom-up approach to robot development, including geometric design, mechanical characterization, and functionality realization, presenting a unique perspective for advancing the development of bioinspired soft robots.

Multi-material optimal design of miura origami folds based on genetic algorithm

Multi-material optimal design of miura origami folds based on genetic algorithm

Miura-ori based reconfigurable multilayer absorber for high-efficiency wide-angle absorption.

Radar stealth structures that can achieve high-efficiency wide-angle absorption are key components of future military equipment. However, it is difficult for both planar and three-dimensional (3D) absorbers to achieve efficient absorption in a large incidence angle range. The multilayer reconfigurable absorber component based on Miura origami provides a unique solution. First, the multilayer origami absorber is parameterized in the simulation software. Each origami structure is covered with resistive films that fit the panels. Geometric constraints are satisfied among the multilayer structures. They support reconfigurability in the range of continuous states (as opposed to discrete states), which is conducive to finding the folded state with a more efficient absorption rate within the frequency band. Secondly, the designed structure does not require a specialized mechanically supported multilayer origami absorber. In addition, the equivalent analogue circuit method is used to analyze the efficient absorption of multilayer origami under oblique incidence. Finally, our proposed absorber satisfies the requirements of multiple absorption metrics: broadband, high efficiency, wide incidence angle, and polarization insensitivity. As the validation, we simulated and fabricated a double-layer origami absorber. Our proposed origami absorber can maintain an absorption rate of more than 90% for both transverse electric (TE) and transverse magnetic (TM) polarizations in the operating frequency band (5-20 GHz) over a wide range of incidence angles (0°-70°). When the incidence angle qinc = 40°, the double-layer origami absorber (q1 = 90°, α1 = 60°, and a2 = 75°) can achieve at least 10 dB reflection reduction of -18 dB and -20 dB in TE and TM modes, respectively. The proposed origami absorber provides a reference for the design of other absorbers.

Miura Origami‐Inspired Reconfigurable Phase Gradient Metasurface for Linearly and Circularly Polarized Differential Modulation

Miura origami's reconfigurable characteristic and structural asymmetry, combined with electromagnetic (EM) wave manipulation, crashed a unique spark. However, the complexity of the three‐dimensional (3D) origami structure after folding makes it challenging to study the phase regulation mechanism. Here, we propose a reconfigurable phase gradient metasurface based on Miura origami and derive the underlying mechanism of phase modulation in detail under linearly and circularly polarized (LP and CP) incidence. We adopt the one‐dimensional (1D) gradient design along the x direction to verify the idea. The phase calculation formulas are given under LP and CP incidence through the Jones matrix's derivation. The beam deflector angles corresponding to LP and CP waves are identical in the planar state. As the folding angle increases, the phase evolution rules corresponding to the LP and CP waves are discrepant, leading to differential beam steering. Finally, the origami sample is processed for verification, and the experimental data are consistent with the simulation and theoretically calculated values. We believe this work can help analyze the EM behavior of complex 3D origami structures and lay a foundation for designing a multifunctional EM origami metasurface.

Miura origami based reconfigurable polarization converter for multifunctional control of electromagnetic waves

Polarization is one of the basic characteristics of electromagnetic (EM) waves, and its flexible control is very important in many practical applications. At present, most of the multifunction polarization metasurfaces are electrically tunable based on PIN and varactor diodes, which are easy to operate and have strong real-time performance. However, there are still some problems in them, such as few degrees of freedom of planar structure control, complex circuit, bulky sample, and high cost. In view of these shortcomings, this paper proposes a Miura origami based reconfigurable polarization conversion metasurface for multifunctional control of EM waves. The interaction between the electric dipoles is changed by adjusting the folding angle θ, thereby tuning the operating frequency of the polarization conversion and the polarization state of the reflected wave. This mechanical control method brings more degrees of freedom to manipulate EM waves. And the processed sample is with lightweight and low cost. To verify the performance of the proposed origami polarization converter, a Miura origami structure loaded with metal split rings is designed and fabricated. The operating frequency of the structure can be tuned in different folding states. In addition, by controlling the folding angle θ, linear-to-linear and linear-to-circular polarization converters can be realized at different folding states. The proposed Miura origami polarization conversion metasurface provides a new idea for reconfigurable linear polarization conversion and multifunctional devices.

Graded in-plane Miura origami as crawling robots and grippers

In this work, we propose a variation of Miura origami which, different from the existing out-of-plane bending Miura origami, has an in-plane bent configuration due to its graded crease pattern. By combining with the one-way shape memory alloy spring, we show that the proposed graded Miura origami can serve as a smart actuator and can be applied to drive crawling robots or grippers. First, we constructed a physical model of the graded Miura origami, from which a curvature-programmable geometric equation is proposed. Then, in addition to providing a mechanical model that can capture the mechanical behavior of the initial force–displacement relationship of the curved beam, we show that the proposed curved origami has a different mechanical behavior compared to the corresponding simple flexible arch, specifically if realized by silicon rubbers. By arranging anisotropic friction to the feet, the origami robot can crawl with an omega-elongation/compression motion like an inchworm. With a closed-loop current source control system using a high-frequency pulse width modulation-based topology, where the strain state of the arched origami is detected by a demodulator-free fiber Bragg grating sensor, the average speed of the origami crawling robot can reach 2.72 mm/s. In addition, by arranging three graded Miura origami, a gripper capable of lifting a weight of 518.5 g can be formed, where the carried load is over 4.5 times its own weight.

Multi-stability of irregular four-fold origami structures

Origami-inspired structures can manifest a range of interesting characteristics such as reconfigurability and multi-stablity. Theoretically, the energy of rigid-foldable origami structures is a result of deformations in their creases. Although the multi-stability of the classic double-corrugated origami (or the Miura-ori) has been studied extensively, the energy variation analysis of its generalized derivatives such as those with less symmetric unit fragments need to be further investigated. Here, we derive the general energy equations and study the multi-stability behavior of certain low-symmetry double-corrugated origami tessellations. In particular, studies on the double-corrugated origami pattern with maximally asymmetric octagonal unit fragments are extended from our previous research on the design of two-dimensional patterns to their deformation and energy analyses in the three-dimensional space. We demonstrate that a reasonable selection of initial design configuration parameters can enable the corresponding origami structure to be multi-stable, on condition that appropriate pre-stresses are introduced to the crease pattern. We also derive the energy equations of non-prestressed origami structures with the abovementioned geometric design specifications. In addition, the obtained theoretical formulas are verified by finite element models, as well as against some previously reported results for the classical Miura-ori. The findings of this study enable the precise customization of multi-stable origami design configurations and facilitate the development of more complex origami structures.

Deployment dynamics of thick panel Miura-origami

Origami and kirigami folding methods applied to deployable structures have been investigated in many studies, and most of them use approximately zero-thickness materials to follow the paper-folding movement. However, the rigidity and thickness of materials cannot be neglected in aerospace engineering applications, resulting in different kinematic and dynamic characteristics of deployment. This work deals with the deployment dynamics of a typical thick panel Miura origami (Miura-ori). The kinematics of the Miura-ori unit and array are discussed considering the tessellated extension of the Miura-ori pattern, which can be described by the recursively relative movement. Based on the Lagrange's equation, the dynamic equation is determined by generalized force and potential energy. Furthermore, prototypes for Miura-ori unit and array are fabricated, respectively. To measure the dynamic behaviours during deployment, a gravity compensation apparatus is designed and constructed, which can effectively reduce the gravity effect of Miura-ori prototypes. The comparison of the numerical and experimental results validates our dynamic model. Our work provides a recursive dynamic modelling method and experiment apparatus for analysing and testing the deploying dynamic behaviours of tessellated thick-panel origami deployable structures, and the findings can be developed in the other thick-panel origami and kirigami concepts of actual engineering applications in the future.

Shape-Morphing Antenna Array by 4D-Printed Multimaterial Miura Origami.

The rapid development of four-dimensional (4D) printing technology has resulted in its application in various fields, including radiofrequency (RF) electronics. Moreover, because origami-inspired RF electronics provide a physically deformable geometry, they are good candidates for reconfigurable RF applications. However, previous origami-inspired RF electronics have generally been fabricated on paper for easy folding and unfolding. Although this facilitates easy fabrication, the resultant structures suffer from a lack of rigidity and stability. In this paper, we propose a 4D-printed multimaterial Miura origami structure for RF spectrum applications. For thermal actuation and robustness, the proposed structure consists of high-temperature durable cores with shape memory polymer (SMP) hinges. The high-temperature durable cores provide rigidity to the desired part and reduce the level of distortion of the conductive pattern, while the SMP hinges enable shape morphing. To demonstrate the feasibility of the technique for RF electronics, a shape-morphing pattern reconfigurable antenna array is designed at 2.4 GHz using the proposed 4D-printed multimaterial structure. Through numerical and experimental demonstrations, the proposed antenna's maximum beam direction is changed from 0° to 50° by thermally morphing the Miura origami. In addition, the antenna successfully recovers to its memorized original state.

Numerical study of the hysteretic behavior of energy dissipation braces based on Miura origami

Miura-ori pattern was adopted to form the tessellation design of slender braces to improve the energy dissipation capacity under the low-cycle repeated loading. The energy dissipation mechanisms of origami energy dissipation braces (OEDBs) and conventional square braces with equal bearing capacity were compared. Finite element models for hysteretic simulation were constructed and analyzed to figure out the influences of various geometrical design parameters on the hysteretic behavior of OEDBs. The results show that the OEDBs have an obvious improvement in the energy dissipation capacity compared to conventional square braces. The influence of parameters on energy dissipation capacity is quite different. The smaller folding angles, smaller aspect ratios, and larger width-to-thickness ratio play positive roles in improving energy dissipation performance rather than elastic stiffness. However, smaller slenderness improves both while the change of in-plane angle is sensitive to the hysteretic performance.

Design and optimization of Miura-Origami-inspired structure for high-performance self-charging hybrid nanogenerator

A hybrid piezoelectric-triboelectric-electromagnetic nanogenerator (HPTENG-EMG) has been designed meticulously by focusing on material selection, structural design, and performance evaluation. The module can operate using three parts; piezoelectric, triboelectric and an electromagnetic mechanism. The hybrid concept of triboelectric and piezoelectric is achieved by fabricating triboelectric-piezoelectric composite materials working through the TENG mechanism. In the material design part, the composite film between bacterial cellulose (BC) and BaTiO3 nanoparticles (BT-NPs) fabricates and optimizes its properties with a suitable number of BT-NPs. The unique Miura-Origami (MO) hexagonal multilayer shape is applied within the structural design to increase the contact surface area, which enhances the electrical output signal. The third part of the hybrid system incorporates an electromagnetic generator (EMG) by designing a structure of compact and lightweight cylindrical tubes with magnetic levitation structures. The hexagonal multilayer shape of MO composite TENG (MO-CTENG) generates an open-circuit output voltage (VOC) of ∼414 V and short-circuit output current (ISC) of ∼48.3 μA with maximum output power (P) of about ∼6.94 mW. The highest ISC value of ∼38 mA can be promoted in the optimized EMG, which is higher than the MO-CTENG by ∼786 times. The practical application of this technology is demonstrated by human shaking motion for battery charging in the wireless Global Positioning System (GPS). The maximum direct current output voltage (VDC) saturation of 30 V can be achieved within 19 s. This work provides a potential methodology for increasing electrical output performance by capturing more mechanical energy through the conjunction of three phenomena into a single device, which exhibits a promising way of addressing an energy crisis.

Folding a flat rectangular plate of uniform-thickness panels using Miura-ori

In the realm of space technology, aerospace solar arrays are conventionally employed as efficient means of energy harvesting. The solar arrays need to be packaged in a payload capsule before launch and unfold as a standard rectangle with uniform thickness and a flat surface in orbit. In this paper, we introduce a novel methodology for folding a standard rectangular plate with uniform thickness and a flat surface based on Miura origami. Importantly, these plates can be unfolded with a single degree of freedom after a special design. The package direction is defined by analyzing the distinct characteristics of wave creases and straight creases. To achieve motion equivalence, different lengths of tape spring hinges are used along the package direction, while door hinges are employed at the wave crease. In order to address the motion interference problem during folding and maintain structural stability, constraints are derived, and a discrete nonlinear optimization model is established. The particle swarm optimization algorithm is used and improved to enhance convergence performance and computational efficiency. According to the calculation results, the corresponding folding plates were made, and the folding process and results are consistent with zero-thickness origami. These findings suggest that the proposed thick-panel origami method not only achieves efficient optimization of the geometric design but also preserves the essential characteristics of traditional zero-thickness origami. To aid designers, some key design recommendations based on the parameter analysis are provided for enhancing the deployment ratio.

Statics of integrated origami and tensegrity systems

This study presents an explicit form of the static equilibrium equations of integrated origami and tensegrity systems. The analytical approach allows one to model and analyze the isolated origami and tensegrity paradigms as a whole system. The tensegrity and origami members are described by the nodal coordinates and hinge angels between the origami panels. The nonlinear static equations of the integrated system are derived by the Lagrangian method. By Taylor’s expansion theory, we also presented its linearized form. The developed approach is capable of conducting the following comprehensive statics studies for any integrated origami and tensegrity systems: (1) Performing loading analysis, where bars and strings can have elastic or plastic deformations. (2) Conducting infinitesimal and large deformation analysis, which is helpful in understanding the stress in structural members and actuation strategies. (3) Dealing with various kinds of boundary conditions, for example, fixing or applying static loads at any nodes in any direction (i.e., gravitational force, some specified forces, or moments). (4) Conducting stiffness analysis, including eigenvalues and their modes. Three examples, a Miura origami unit, an integrated tensegrity origami shelter, and a cable-driven Kresling structure, are carefully selected and studied. This study provides a deep insight into structures, materials, as well as performances. The integration idea also promotes our ability to design and build deployable structures at large.

An ultra-wideband origami microwave absorber

Microwave absorbers have been used to mitigate signal interference, and to shield electromagnetic systems. Two different types of absorbers have been presented: (a) low-cost narrowband absorbers that are simple to manufacture, and (b) expensive wideband microwave absorbers that are based on complex designs. In fact, as designers try to increase the bandwidth of absorbers, they typically increase their complexity with the introduction of several electromagnetic components (e.g., introduction of multi-layer designs, introduction of multiple electromagnetic resonators, etc.,), thereby increasing their fabrication cost. Therefore, it has been a challenge to design wideband absorbers with low cost of fabrication. To address this challenge, we propose a novel design approach that combines origami math with electromagnetics to develop a simple to manufacture ultra-wideband absorber with minimal fabrication and assembly cost. Specifically, we utilize a Tachi–Miura origami pattern in a honeycomb configuration to create the first absorber that can maintain an absorptivity above 90% in a 24.6:1 bandwidth. To explain the ultra-wideband behavior of our absorber, we develop analytical models based on the transmission-reflection theory of electromagnetic waves through a series of inhomogeneous media. The ultra-wideband performance of our absorber is validated and characterized using simulations and measurements.

Deployment Dynamics of Miura Origami Sheets

AbstractOrigami has great potential for creating deployable structures, however, most studies have focused on their static or kinematic features, while the complex and yet important dynamic behaviors of the origami deployment process have remained largely unexplored. In this research, we construct a dynamic model of a Miura origami sheet that captures the combined panel inertial and flexibility effects, which are otherwise ignored in rigid folding kinematic models but are critical in describing the dynamics of origami deployment. Results show that by considering these effects, the dynamic deployment behavior would substantially deviate from a nominal kinematic unfolding path. Additionally, the pattern geometries influence the effective structural stiffness, and it is shown that subtle changes can result in qualitatively different dynamic deployment behaviors. These differences are due to the multistability of the Miura origami sheet, where the structure may snap between its stable equilibria during the transient deployment process. Lastly, we show that varying the deployment rate can affect the dynamic deployment configuration. These observations are original and these phenomena have not and cannot be derived using traditional approaches. The tools and outcomes developed from this research enable a deeper understanding of the physics behind origami deployment that will pave the way for better designs of origami-based deployable structures, as well as extend our fundamental knowledge and expand our comfort zone beyond current practice.

Stacked-origami mechanical metamaterial with tailored multistage stiffness

Origami-based metamaterial has shown remarkable mechanical properties rarely found in natural materials, but achieving tailored multistage stiffness is still challenging. We propose a novel zigzag-base stacked-origami (ZBSO) metamaterial with tailored multistage stiffness based on crease customization and stacking strategies. A high precision finite element (FE) model to identify the stiffness characteristics of the ZBSO metamaterial has been established, and its accuracy is validated by quasi-static compression experiments. Using the verified FE model, we demonstrate that the multistage stiffness of the ZBSO metamaterial can be effectively tailored through two manners, i.e. varying the microstructures (through introducing new creases to the classical Miura origami unit cell) and altering the stacking way. Three strategies are utilized to vary the microstructure, i.e. adding new creases to the right, left, or both sides of the unit cell. We demonstrate that the multistage stiffness is caused by both the self-locking and asymmetrical stiffness distribution of the ZBSO metamaterial. We further reveal that the proposed ZBSO metamaterial has several outstanding advantages compared with traditional mechanical metamaterials, e.g. material independent, scale-invariant, lightweight, and excellent energy absorption capacity. The unraveled superior mechanical properties of the ZBSO metamaterials pave the way for designing the next-generation cellular metamaterials with tailored stiffness properties.

Revealing the Dynamic Characteristics of Composite Material-Based Miura-Origami Tube.

Although Miura origami has excellent planar expansion characteristics and good mechanical properties, its congenital flaws, e.g., open sections leading to weak out-of-plane stiffness and constituting the homogenization of the material, and resulting in limited design freedom, should also be taken seriously. Herein, two identical Miura sheets, made of carbon fiber/epoxy resin composite, were bonded to form a tubular structure with closed sections, i.e., an origami tube. Subsequently, the dynamic performances, including the nature frequency and the dynamic displacement response, of the designed origami tubes were extensively investigated through numerical simulations. The outcomes revealed that the natural frequency and corresponding dynamic displacement response of the structure can be adjusted in a larger range by varying the geometric and material parameters, which is realized by combining origami techniques and the composite structures’ characteristics. This work can provide new ideas for the design of light-weight and high-mechanical-performance structures.