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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. [ABSTRACT FROM AUTHOR]

The foldcore of an origami structure made up of rigid triangular units is suggested. This foldcore has two stable states: contraction and expansion. The suggested foldcore's peak stress, average stress, and densification strain were numerically analyzed at different cutting heights and varied parameters n, and the damage modes were analyzed. Finally, the impact of strain rate on the proposed foldcore's structural response and energy absorption capacity is investigated. The contraction stable state foldcore with a cutting 1/5 height was discovered to have the best energy absorption capacity. Increasing n improves its energy absorption performance, but decreases its dense strain. [ABSTRACT FROM AUTHOR]

In this study, the models for the DNA origami lattice will be investigated. Our aim is to theoretically explore the ways of constructing DNA origami. To achieve this goal the DNA origami structure, consisting of nanowires embedded in a host material, will be treated from the perspective of nanowire metamaterial. Surface plasmon polaritons propagating at the interface of air and DNA metamaterial are analyzed. The dispersion relation is attained using the transfer matrix technique and employing continuity conditions of electric fields and their derivatives at the boundary separating two regions. We have concluded that with numerous nanowires into the metamaterial unit, cell frequencies of surface plasmon polaritons are altered to higher frequencies. In this study, we have studied the effect of modifications of the metamaterial, allowing for the shift of the dispersion maps toward higher frequencies. It is possible to obtain the propagation of spoof plasmons mimicking the behavior of surface waves at lower frequencies. All the properties and parameters of the inorganic metamaterials are applicable to study the phenomenon of the organic substances. [ABSTRACT FROM AUTHOR]

Inspired by the origami process, a multicellular tube formed by origami folding based on polygons was designed. First, the accuracy of the finite-element model was verified by experiments; then, under the conditions of the same wall thickness, mass, and energy absorption, comparative studies were carried out between multicellular tubes based on polygonal origami folding (MTPOFs), hollow tubes (HTs), and multicellular tubes (MTs). The results showed that regardless of the same wall thickness or the same mass and energy absorption conditions, MTPOFs have advantages over corresponding MTs and HTs. The crushing force efficiency and specific energy absorption of the square MTPOF were 131.45% and 193.57% higher than those of the square HT with the same wall thickness, respectively. Compared with the hexagonal HT, the crushing force efficiency and specific energy absorption of the hexagonal MTPOF increased by 99.02% and 125.01%, respectively. Under the same energy absorption, the crushing force efficiency of the square MTPOF improved by 78.78% and the specific energy absorption improved by 42.05% compared with the square HT. Ultimately, an investigation was conducted into the energy absorption of the structure concerning variations in wall thickness and the ratio of side length to height H/a. As a result, deformation mode diagrams corresponding to different H/a values were obtained. [ABSTRACT FROM AUTHOR]

The rise of flexible electronics has sparked a demand for components, such as loudspeakers, that seamlessly integrate into various applications while maintaining their performance. However, current loudspeakers typically rely on electromechanical systems, necessitating significant space for components such as coils and magnets. This limits their flexibility and usage in thin, conformable devices. To address this, a paper‐based thermoacoustic (TA) loudspeaker utilizing carbon nanotubes (CNTs) via inkjet printing is introduced. This TA loudspeaker demonstrates exceptional flexibility and durability, maintaining high acoustic performance across human‐audible frequencies up to 20 kHz, even when subjected to extensive mechanical deformation. Additionally, employing inkjet printing technology streamlines their manufacturing processes, offering a cost‐effective solution with scalability for mass production. Furthermore, an origami‐inspired 3D folding architecture enhances the loudspeaker's portability and enables versatile shape configurations, thus broadening its utility across electronic devices. These demonstrations offer a potential solution for next‐generation audio systems in flexible electronics. [ABSTRACT FROM AUTHOR]

Highlights Origami tube (OT) has attracted significant attention in the realm of thin‐walled structures owing to their remarkable energy‐absorption capabilities. Nevertheless, their deformation modes, particularly buckling, present considerable stability challenges. In this research, we introduce a novel corrugated structure to enhance the energy absorption and stabilize the deformation mode of OT. The corrugated origami tube (COT) was manufactured using high‐specific modulus, high‐strength, and lightweight short carbon fiber‐reinforced nylon via 3D printing, followed by axial quasi‐static compression tests. The findings demonstrate that the incorporation of corrugations in COT greatly stabilizes tube deformation, boosting energy absorption by 21.3% compared to OT and reducing the peak crashworthiness force by up to 21.37%. Finite element analysis accurately replicates the experimental performance of the COT, affirming the feasibility of the simulation. Optimization using the Non‐dominated Sorting Genetic Algorithm II (NSGA‐II) produced a Pareto front, revealing trade‐offs among various crashworthiness indicators and offering a flexible design approach to meet diverse requirements. This study provides valuable insights and guidance for the design of lightweight, thin‐walled structures. The corrugated structure effectively stabilizes deformation mode of the OT. COT significantly improves energy absorption and reduces initial peak force compared to OT. The approach of multi‐objective optimization provides a variety of solutions for different needs. [ABSTRACT FROM AUTHOR]

The use of origami in engineering has significantly expanded in recent years, spanning deployable structures across scales, folding robotics and mechanical metamaterials. However, finding foldable paths can be a formidable task as the kinematics are determined by a nonlinear system of equations, often with several degrees of freedom. In this article, we leverage a Lagrangian approach to derive reduced-order compatibility conditions for rigid-facet origami vertices with reflection and rotational symmetries. Then, using the reduced-order conditions, we derive exact, multi-degree of freedom solutions for degree 6 and degree 8 vertices with prescribed symmetries. The exact kinematic solutions allow us to efficiently investigate the topology of allowable kinematics, including the consideration of a self-contact constraint, and then visually interpret the role of geometric design parameters on these admissible fold paths by monitoring the change in the kinematic topology. We then introduce a procedure to construct lower-symmetry kinematic solutions by breaking symmetry of higher-order kinematic solutions in a systematic way that preserves compatibility. The multi-degree of freedom solutions discovered here should assist with building intuition of the kinematic feasibility of higher-degree origami vertices and also facilitate the development of new algorithmic procedures for origami-engineering design. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

With its compactness and foldability, origami has recently been applied to robotic systems to enable versatile robots and mechanisms while maintaining a low weight and compact form. This work investigates how to generate different motions and shapes for origami by tuning its creases' stiffness on the fly. The stiffness tuning is realized by a composite material made by sandwiching a thermoplastic layer between two shape memory polymer layers. This enables the composite to act as a living hinge, whose stiffness can be actively controlled through Joule heating. To demonstrate our concept, we fabricate an origami module with four variable stiffness joints (VSJs), allowing it to have freely controlled crease stiffnesses across its surface. We characterize the origami module's versatile motion when heating different VSJs with different temperatures. We further use two origami modules to build a two-legged robot that can locomote on the ground with different locomotion gaits. The same robot is also used as an adaptive gripper for grasping tasks. Our work can potentially enable more versatile robotic systems made from origami as well as other mechanical systems with programmable properties (e.g. mechanical metamaterials). This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

A periodic surface is one that is invariant by a two-dimensional lattice of translations. Deformation modes that stretch the lattice without stretching the surface are effective membrane modes. Deformation modes that bend the lattice without stretching the surface are effective bending modes. For periodic piecewise smooth simply connected surfaces, it is shown that the effective membrane modes are, in a sense, orthogonal to effective bending modes. This means that if a surface gains a membrane mode, it loses a bending mode, and conversely, in such a way that the total number of modes, membrane and bending combined, can never exceed 3. Various examples, inspired from curved-crease origami tessellations, illustrate the results. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

We present the design and evaluation of a simple, compact and efficient electromagnetic energy harvesting tile that can be used to harness energy from footsteps. The proposed harvester incorporates a translational–rotational origami-inspired coupling mechanism to transform the axial loads exerted by human footsteps into a localized rotation of an electromagnetic generator. The coupling mechanism employs a non-rigid tunable Kresling spring, the restorative behaviour of which is tunable to maximize energy transduction from the applied load to the generator. A computational model is developed to optimize the design parameters of the mechanism, which are then utilized to fabricate a prototype of the energy harvester. The tile is tested under loading conditions that mimic a human step, where it is demonstrated that it is capable of generating 4.18 W of electrical power per step with a surface power density of 2609 μW cm−2. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

Recent advances in origami science and engineering have particularly focused on the challenges of dynamics. While research has primarily focused on statics and kinematics, the need for effective and processable dynamic models has become apparent. This paper evaluates various dynamic modelling techniques for rigid-foldable origami, particularly focusing on their ability to capture nonlinear dynamic behaviours. Two primary methods, the lumped mass–spring–damper approach and the energy-based method, are examined using a bistable stacked Miura-origami (SMO) structure as a case study. Through systematic dynamic experiments, we analyse the effectiveness of these models in predicting bistable dynamic responses, including intra- and interwell oscillations, in different loading conditions. Our findings reveal that the energy-based approach, which considers the structure's inertia and utilizes dynamic experimental data for parameter identification, outperforms other models in terms of validity and accuracy. This model effectively predicts the dynamic response types, the rich and complex nonlinear characteristics and the critical frequency where interwell oscillations occur. Despite its relatively increased complexity in model derivation, it maintains computational efficiency and shows promise for broader applications in origami dynamics. By comparing model predictions with experimental results, this study enhances our understanding of origami dynamics and contributes valuable insights for future research and applications. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

The bar and hinge framework uses truss elements and rotational springs to efficiently model the structural behaviour of origami. The framework is especially useful to investigate origami metamaterials as they have repeating geometry, which makes conventional finite element simulations very expensive due to a large number of degrees of freedom. This work proposes improvements to the parameters of bar and hinge model within the context of structural dynamics, specifically modal analysis under small deformations, which has not been carried out previously in the literature. A range of low-frequency modes involving origami folding and panel bending deformations that can be accurately captured by the bar and hinge framework are identified. Within this range, bar and hinge parameters like the lumped masses and the rotational spring stiffness values are derived using conservation laws and finite element tests. The best among the proposed schemes is found to predict natural frequencies of the considered origami structures to within 10% maximum error, improving the accuracy by more than three times from existing schemes. In most cases, the errors in natural frequencies are less than 5%. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

We explore a new design strategy of leveraging kinematic bifurcation in creating origami/kirigami-based three-dimensional (3D) hierarchical, reconfigurable, mechanical metamaterials with tunable mechanical responses. We start from constructing three basic, thick, panel-based structural units composed of 4, 6 and 8 rigidly rotatable cubes in close-looped connections. They are modelled, respectively, as 4R, 6R and 8R (R stands for revolute joint) spatial looped kinematic mechanisms, and are used to create a library of reconfigurable hierarchical building blocks that exhibit kinematic bifurcations. We analytically investigate their reconfiguration kinematics and predict the occurrence and locations of kinematic bifurcations through a trial-correction modelling method. These building blocks are tessellated in 3D to create various 3D bifurcated hierarchical mechanical metamaterials that preserve the kinematic bifurcations in their building blocks to reconfigure into different 3D architectures. By combining the kinematics and considering the elastic torsional energy stored in the folds, we develop the geometric mechanics to predict their tunable anisotropic Poisson's ratios and stiffnesses. We find that kinematic bifurcation can significantly effect mechanical responses, including changing the sign of Poisson's ratios from negative to positive beyond bifurcation, tuning the anisotropy, and overcoming the polarity of structural stiffness and enhancing the number of deformation paths with more reconfigured shapes. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

Yoshimura origami is a classical folding pattern that has inspired many deployable structure designs. Its applications span from space exploration, kinetic architectures and soft robots to even everyday household items. However, despite its wide usage, Yoshimura has been fixated on a set of design constraints to ensure its flat foldability. Through extensive kinematic analysis and prototype tests, this study presents a new Yoshimura that intentionally defies these constraints. Remarkably, one can impart a unique meta-stability by using the Golden Ratio angle (cot−1⁡1.618≈31.72∘) to define the triangular facets of a generalized Yoshimura (with n=3 , where n is the number of rhombi shapes along its cylindrical circumference). As a result, when its facets are strategically popped out, a 'Golden Ratio Yoshimura' boom with m modules can be theoretically reconfigured into 8m geometrically unique and load-bearing shapes. This result not only challenges the existing design norms but also opens up a new avenue to create deployable and versatile structural systems. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

Origami-inspired mechanisms provide opportunities for deployable systems, including reflectarray antennas. There is a need for approaches to deploy and stabilize such arrays. Magnetic mechanisms show promise for meeting those needs and how methods for modelling their behaviour would facilitate their design and analysis. We demonstrate the existence of bistability in select configurations of magnetically stabilized hinges and characterize their equilibrium positions as a function of parameters estimated from simulation data for these mechanisms. Other relevant information such as potential energy, axial force data, angular position of unstable equilibria and transition values from bistability to monostability are also modelled. The results are verified through experimental torque and stability data for selected configurations of the mechanisms. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

Origami folding structures are vital in shaping programmable mechanical material properties. Of particular note, tunable dynamical properties of elastic wave propagation in origami structures have been reported. Despite the promising features of origami metamaterials, the influence of the kinematics of tessellated origami structures on elastic wave propagation remain unexplored. This study proposes elastic metamaterials using connected Miura-ori tubes, the kinematics of which are coupled by folding and unfolding motions in a tubular axis; achieved by periodically connecting non-rotated and rotated Miura-ori tubes. The kinematics generate wave modes with localized deformations within the unit cell of the metamaterials, affecting the global elastic deformation of Miura-ori tubes via the coupling of wave modes. Dispersion analysis, using the generalized Bloch wave framework based on bar-and-hinge models, verifies the influence of kinematics in the connected tubes on elastic wave propagation. Furthermore, folding the connected tubes changes the coupling strength of wave modes between the kinematics and global elastic deformation of the tubes by breaking the ideal kinematics. The coupling of wave modescontributes to the formation of the band gaps and their tunability. These findings enable adaptive and in situ tunability of band structures to prohibit elastic waves in the desired frequency ranges. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

Origami metamaterials have gained significant attention in recent years, with extensive analysis conducted on their mechanical properties. Previous studies have primarily focused on the effects of design angles, panel side lengths, folding angles or other geometric and material parameters. However, mountain-valley crease assignments of origami patterns, which significantly effect both the geometric and mechanical properties, have yet to be studied in depth. In this article, we create a series of double-corrugated metamaterials with diverse mountain-valley assignments and analyse their Poisson's ratios and mechanical properties under compression loading. The findings of our study demonstrate that varying the mountain-valley assignments allows for the construction of metamaterials with consistent or distinct Poisson's ratios. These assignments have the capability to program the magnitude and to vary the rate of the folding angles. Furthermore, the mechanical properties of the corresponding metamaterials, in particular the specific energy absorption (SEA) and normalized stiffness, exhibit positive correlations with the respective folding angles. Our study highlights the significance of varying mountain-valley assignments as a promising approach for designing origami metamaterials and programming their mechanical properties. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

A rigidly foldable and reconfigurable origami antenna is developed here. This antenna uses thick folding panels thereby providing robust operation and folding/unfolding actuation, which are very important for many applications in extreme environments, such as space. Also, this antenna can be constructed using standard printed circuit boards, which simplifies its manufacturing. For the reconfigurable antenna developed here, the origami flasher pattern is chosen to achieve a spatial transformation of a dipole operating at 0.48 GHz to a conical spiral antenna (CSA) operating from 2.1 to 3.7 GHz. The design equations for the origami CSA are derived. A prototype is built using a 0.81-mm-thick FR4 substrate to validate the proposed methodology. The antenna parameters are investigated in a wide frequency range. Our simulated results agree very well with the measurements. The rigid structure of the proposed design and its reconfigurable nature make it a good candidate for satellite communications. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

The concepts of origami and kirigami have often been presented separately. Here, we put forth a synergistic approach--the folded kirigami--in which kirigami assemblies are complemented by means of folding, typical of origami patterns. Besides the emerging patterns themselves, the synergistic approach also leads to topological mechanical metamaterials. While kirigami metamaterials have been fabricated by various methods, such as 3D printing, cutting, casting, and assemblage of building blocks, the "folded kirigami" claim their distinctive properties from the universal folding protocols. For a target kirigami pattern, we design an extended high-genus pattern with appropriate sets of creases and cuts, and proceed to fold it sequentially to yield the cellular structure of a 2D lattice endowed with finite out-of-plane thickness. The strategy combines two features that are generally mutually exclusive in canonical methods: fabrication involving a single piece of material and realization of nearly ideal intercell hinges. We test the approach against a diverse portfolio of triangular and quadrilateral kirigami configurations. We demonstrate a plethora of emerging metamaterial functionalities, including topological phase-switching reconfigurability between polarized and nonpolarized states in kagome kirigami, and availability of nonreciprocal mechanical response in square-rhombus kirigami. [ABSTRACT FROM AUTHOR]

This commentary explores the structure of Portugali's work, which aims to bridge two urban cultures through a process which we propose to call 'creative folding.' Five key creative folds are identified in the work of Portugali: the origami metaphor, implicate relations, synergetic inter-representation networks, urban regulatory focus, and urban coordination dynamics. At the core of these folds are between-domain transfers, with the Bohm-Haken-Kelso conjunction—an interdisciplinary framework combining ideas from physics, synergetics, and neurodynamics—playing a pivotal role. The commentary also examines several challenges related to creative folding, such as managing cognitive load, developing engaging methods to unify diverse urban theories, and involving people from various backgrounds in collective creative folding. These challenges highlight the need for open dialogues to foster innovation and collaboration in developing unified urban theories. [ABSTRACT FROM AUTHOR]

Translation abstract Nonlinear analysis of the load‐bearing capacity of folded carbon reinforced concrete modulesGiven the increasing demand for low‐carbon construction, the shift from massive to thin‐walled, highly efficient elements are becoming increasingly necessary. The origami‐inspired folded carbon concrete shells are emerging as an alternative to traditional reinforced concrete structures for the development of economical and sustainable structures. However, the field currently lacks any well‐established design and analysis methods that can reliably predict how folded shells will behave structurally when optimal variants, load‐bearing capacity, stress redistribution, and failure mechanisms are considered. Based on this, two FEM modeling approaches to analyze folded waterbomb‐patterned shells were implemented. In these approaches, the carbon reinforcement is modeled in both smeared and resolved forms, whereas a damage plasticity model is applied to the concrete. The testing of the demonstrator elements validates the results of these approaches, which complement the foundation for the design and analysis of folded origami shells. [ABSTRACT FROM AUTHOR]

AbstractThe present work investigates stress, strain and deformation analyses of a shear deformable cylindrical shell manufactures by a Copper (Cu) core reinforced with graphene origami auxetic metamaterial subjected to mechanical and thermal loads. The cylindrical models can be used in sport equipment especially in expander component. The effective material properties of the graphene origami auxetic reinforced Cu matrix are developed using micromechanical models cooperate both material properties of graphene and Cu in terms of local temperature, volume fraction and folding degree. The principle of virtual work is used to derive governing equations with accounting thermal loading. [ABSTRACT FROM AUTHOR]

In order to improve the crashworthiness of traditional Thin-Walled Struct, a new method for designing multicellular tubes is presented in this paper. In this work, multicellular columns based on origami centripetal folding method (MCOCFM) are proposed. The cross section of MCOCFM is designed in the way of origami. The mechanical properties of MCOCFM under uniaxial compression are analyzed by numerical simulation. Studies have shown that increased levels and wall thickness facilitate energy absorption. In addition, the theoretical prediction of MCF is in good agreement with the simulation results. Compared with some existing structures, MCOCFM has better crashworthiness. [ABSTRACT FROM AUTHOR]

In order to address the issue of time-consuming, labor-intensive traditional industrial tomato sorting, this paper proposes a high-precision tomato recognition strategy and fast automatic grasping system. Firstly, the Swin Transformer module is integrated into YOLOv10 to reduce the resolution of each layer by half and double the number of channels, improving recognition accuracy. Then, the Simple Attention Module (SimAM) and the Efficient Multi-Scale Attention (EMA) attention mechanisms are added to achieve complete integration of features, and the Bi-level Routing Attention (BiFormer) is introduced for dynamic sparse attention and resource allocation. Finally, a lightweight detection head is added to YOLOv10 to improve the accuracy of tiny target detection. To complement the recognition system, a single-vertex and multi-crease (SVMC) origami soft gripper is employed for rapid adaptive grasping of identified objects through bistable deformation. This innovative system enables quick and accurate tomato grasping post-identification, showcasing significant potential for application in fruit and vegetable sorting operations. [ABSTRACT FROM AUTHOR]

Origami, the art of paper folding, has emerged as a versatile technique for crafting intricate 3D structures from 2D sheets. Combined with the magnetic actuation, origami paper becomes the building blocks for cost‐effective, wirelessly controllable magnetic robots. Herein, a biodegradable magnetic paper with excellent formability and recyclability is developed, facilitating its convenient utilization and disposal. The programable magnetic paper, fabricated with specific magnetization and crease patterns, enables the transformation of 2D sheets into predetermined 3D structures. Leveraging the lightweight and pliable nature of paper‐based materials, exceptional control of origami robots with fast response is demonstrated, enabling a wide range of locomotion. Furthermore, the paper‐based approach enables the incorporation of electronic functionality into magnetic actuators. By introducing conductive nanoparticles into magnetic paper, an electrically conductive substance is created. Constructing electronic circuits and integrating electronic components onto the paper‐based printed circuit board platform enables the repairing of broken circuits inside complicated equipment and optical sensing of surrounding environments in conjunction with locomotive robots. The origami robots have a huge potential to be facilitated in diverse fields with various functions, demonstrating complex locomotion, and integrating chemical, optical, thermal, and mechanical sensors for monitoring environmental conditions in hard‐to‐reach locations. The array of possibilities holds significant promise for the widespread application of these origami magnetic robots across a diverse spectrum of research fields in soft robotics. [ABSTRACT FROM AUTHOR]

Objective: This study aimed to investigate the clinical efficacy of laparoscopic training using origami, a traditional Japanese papercraft, using laparoscopic forceps to create origami cranes. Methods: In this retrospective study, 4 surgeons were randomly divided into 2 groups: The training group, consisting of surgeons 1 and 2, and the non-training group, consisting of surgeons 3 and 4. Over the course of a one-year study period, the training group regularly underwent laparoscopic surgery training with a dry box, wherein they folded a total of 1000 origami cranes using laparoscopic instruments. The non-training group periodically underwent common laparoscopic surgery training of techniques such as suturing and ligation. Each surgeon regularly performed the transabdominal preperitoneal approach for inguinal hernias. Each training was conducted concurrently with the surgeries. The procedure time (peritoneum detachment, mesh placement, and closure of the peritoneum), total operation time (time from peritoneum detachment to closure of the peritoneum), and surgical outcomes were examined. Results: The training group showed greater improvement in the total operation time and more stable performance than the non-training group. Additionally, the time taken for peritoneum detachment was significantly shorter in the training group. Conclusion: Laparoscopic training using origami has the potential to enhance laparoscopic surgical skills and improve surgical outcomes.

Artificial morphing surfaces, inspired by the high adaptability of biological tissues, have emerged as a significant area of research in recent years. However, the practical applications of these surfaces, constructed from soft materials, are considerably limited due to their low shear stiffness. Rigid‐foldable cylinders are anisotropic structures that exhibit high adaptability and shear stiffness. Thus, they have the potential to address this issue. However, changes in shape and area at both ends during folding can lead to collisions or gaps on the morphing surface. Here, a quasi‐rigid‐foldable (QRF) rate is first introduced to quantify the rigid‐foldability of a foldable structure and validate it through experiments. More importantly, a QRF polyhedron is then proposed, which is not only notably anisotropic, similar to a rigid‐foldable cylinder, but also exhibits a zero‐Poisson's ratio property, making it suitable for arraying as morphing surfaces without any collisions or gaps. Such surfaces have a myriad of applications, including modulating electromagnetic waves, gripping fragile objects, and serving as soles for climbing robots. [ABSTRACT FROM AUTHOR]

Many deployable structures in nature, as well as human-made mechanisms, preserve symmetry as their configurations evolve. Examples in nature include blooming flowers, dilation of the iris within the human eye, viral capsid maturation and molecular and bacterial motors. Engineered examples include opening umbrellas, elongating scissor jacks, variable apertures in cameras, expanding Hoberman spheres and some kinds of morphing origami structures. In these cases, the structures either preserve a discrete symmetry group or are described as an evolution from one discrete symmetry group to another of the same type as the structure deploys. Likewise, elastic metamaterials built from lattice structures can also preserve symmetry type while passively deforming and changing lattice parameters. A mathematical formulation of such transitions/deployments is articulated here. It is shown that if X is Euclidean space, G is a continuous group of motions of Euclidean space and Γ is the type of the discrete subgroup of G describing the symmetries of the deploying structure, then the symmetry of the evolving structure can be described by time-dependent subgroups of G of the form Γαt:=αtΓαt−1 , where αt is a time-dependent affine transformation. Then, instead of considering the whole structure in X , a 'sector' of it that lives in the orbit space Γαt\X can be considered at each instant in time, and instead of considering all motions in G , only representatives from right cosets in the space Γαt\G need to be considered. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'. [ABSTRACT FROM AUTHOR]

This article describes artistic and algorithmic strategies in making fabric origami to create fabric art with tactile sensitivities and expressive shadow effects. [ABSTRACT FROM AUTHOR]

This research aims to explore the use of origami as didactic material to improve the vocabulary acquisition process in children in community service centers in Ecuador. It is subscripted to the postmodern paradigm and the mixed research approach. The participants were 20 students aged from 8 to 10 from two community centers located in Manta and San Mateo, of Manabi province. The instruments used were contextual observation, pre- and post-tests, and a motivation questionnaire. The results showed an increase in participants' vocabulary acquisition in all topics taught. The highest increase in vocabulary was 73.70% in the topic fruits and the least advanced was10.50% in the topic of shapes in English language. The contextual observation revealed an improvement in the children motivation for learning, increment in the participation, and interest of the students. The motivation questionnaire also showed a favorable position towards the use of origami to learn English. It concluded that origami is an art that contributed positively to the improvement of learners' vocabulary acquisition in English language in community service projects. [ABSTRACT FROM AUTHOR]

Spatial skills are crucial to STEM disciplines and involve a variety of cognitive processes and skills related to visualising, reasoning and communicating about spatial relations. Particularly in the primary school years, attaining 'spatial literacy' gives children a valuable set of skills and knowledge that can aid them in successful participation in STEM subjects. However, it is poorly understood what constitutes spatial literacy for primary school age children. Furthermore, research into pedagogy for spatial skills is limited, with training interventions often resembling psychometric tests. Therefore, it is pertinent to explore which spatial skills and knowledge are most important for primary school age children to develop and how pedagogy could look to help children to attain spatial literacy. Maker education provides an integrated and designbased approach to learning in which children could practise spatial skills and knowledge by applying it in a creative way. Origami provides a particularly interesting medium to explore these questions as it has previously been used successfully to train psychometrically assessed spatial skills. This paper details a 'research through design' case study of the development of a theoretically informed origami workshop and its implementation in a makerspace during an after-school makerspace programme. The origami workshop and its pedagogical qualities are described and the implementation of the origami workshop in an after-school makerspace is analysed in light of spatial literacy. These findings are discussed and contextualised with insights from the literature. Finally, several recommendations for further research on spatial literacy for primary school age children, specifically in the context of maker education, are made. [ABSTRACT FROM AUTHOR]

Reconfigurable structures can perform multiple functions and are useful in confined environments with complicated access. To extend the complexity of configurations achievable with reconfigurable mechanisms, remotely reconfigurable mechanisms are explored. Magnetically responsive phase change materials are selected for actuation, and origami backbones as the structure. Modulating the mechanism's coupling and constraints, multiple configurations are achieved. Three functional aspects of in situ reconfiguration are demonstrated. First, selective attachment and actuation enable remote mechanisms to deploy and actuate. Second, reconfiguration that modifies the constraints allows for new kinematics even in confined environments. Third, the actuator can construct and change the configuration of an origami structure, allowing subsequent functions to emerge. Tetherless interface reconfiguration is demonstrated with an in situ needle puncture and escape room puzzle, which can benefit existing robotic applications in confined spaces. [ABSTRACT FROM AUTHOR]

Mechanical metastructures have superior mechanical properties coming from the topology of sperially designed representative elements, and have attracted wide attention due to their mathematical basis, super normal features and broad applications. To optimize the design procedure, grasp the future trends and promote the interdisciplinary innovation, the fundamental design concepts and research advancements of mechanical metastructures were reviewed. First, the design methods for mechanical metastructures were classified based on the forward and inverse design concepts. Second, within the forward design category, the principles, applicable fields, and optimization directions of periodic superstructures, surface defect superstructures, and mathematical model-based superstructures were discussed. For the reverse design category, the progresses and existing problems in the application of optimization algorithms and learning algorithuns in the field of mechanical metastructures were analyzed, with future challenges and open issues concluded. [ABSTRACT FROM AUTHOR]

The research work presents a novel voxel-type soft amphibious robot based on an assembly of origami flexiballs. The geometric and elastic constitutive models of the origami flexiball are theoretically established to elucidate its intricate deformation mechanism. Especially, the zero-energy storage phenomenon and the quasi-zero-stiffness characteristic are revealed to prove that the origami flexiball is suitable for serving as soft robotic components. As a proof of concept, fourteen origami flexiballs are interconnected to form a quadruped robot capable of walking or crawling in both underwater and terrestrial environments, including flat surfaces and sandy terrain. Its adaptability across multiple environments is enhanced by the origami polyhedra-inspired hollow structure, which naturally adjusts to underwater conditions such as hydrostatic pressure and currents, improving stability and performance. Other advantages of the voxel-type soft amphibious quadruped robot include its ease of manufacture using 3D printing with accessible soft elastic materials, ensuring rapid and cost-effective fabrication. We anticipate its potentially versatile applications, including underwater pipeline inspections, offshore maintenance, seabed exploration, ecological monitoring, and marine sample collection. By leveraging metamaterial features embodied in the origami polyhedra, the presented voxel-type soft robot exemplifies an innovative approach to achieving complex functionalities in soft robotics. [ABSTRACT FROM AUTHOR]

Living organisms are constructed from proteins that assemble into biomolecular complexes, each with a unique shape and function. Our knowledge about the structure–activity relationship of these complexes is still limited, mainly because of their small size, complex structure, fast processes, and changing environment. Furthermore, the constraints of current microscopic tools and the difficulty in applying molecular dynamic simulations to capture the dynamic response of biomolecular complexes and long-term phenomena call for new supplementary tools and approaches that can help bridge this gap. In this paper, we present an approach to comparing biomolecular and origami hierarchical structures and apply it to comparing bacterial microcompartments (BMCs) with spiral-based origami models. Our first analysis compares proteins that assemble the BMC with an origami model called "flasher", which is the unit cell of an assembled origami model. Then, the BMC structure is compared with the assembled origami model and based on the similarity, a physical scaled-up origami model, which is analogous to the BMC, is constructed. The origami model is translated into a computer-aided design model and manufactured via 3D-printing technology. Finite element analysis and physical experiments of the origami model and 3D-printed parts reveal trends in the mechanical response of the icosahedron, which is constructed from tiled-chiral elements. The chiral elements rotate as the icosahedron expands and we deduce that it allows the BMC to open gates for transmembrane passage of materials. [ABSTRACT FROM AUTHOR]

Continuum robots, possessing great flexibility, can accomplish tasks in complex work scenes, regarded as an important direction in robotics. However, the current continuum robots are not satisfying enough in terms of fabrication and maintenance, and their workspace is limited by structure and other aspects. In this paper, to address the above problems, a modular deployable robot, which adopts an origami structure instead of a flexible hinge, is proposed. A fabrication method is innovated, the Spherical Linkage Parallel Mechanism (SLPM) unit is optimized, and the installation and fabrication process of the robot is simplified through modularization. The forward kinematics and inverse kinematics of the robot and its workspace are analyzed by using the screw theory. The prototype of the robot is constructed, and its folding performance, bending performance, and motion accuracy are tested, and the error analysis and compensation optimization are carried out. After the optimization, the position error of the robot is reduced by about 65%, and the standard deviation is greatly lowered, which effectively improves the motion accuracy and stability of the robot. [ABSTRACT FROM AUTHOR]

We experimentally study the energy absorption of metallic origami cellular structures additively manufactured from an AlSi10Mg alloy. We fabricate AlSi10Mg origami using the laser powder bed fusion (L-PBF) process. Since the as-fabricated AlSi10Mg has limited elongation at break, we systematically examine the heat treatment conditions and achieve the large deformation (i.e., wide folding range) of AlSi10Mg origami without fracture of origami creases. In addition, we use a drop tower impact system to demonstrate the effectiveness of AlSi10Mg origami's folding behavior for impact energy absorption. Based on our experimental results, AlSi10Mg origami cellular structures could be exploited to develop a highly efficient lightweight impact absorber. [ABSTRACT FROM AUTHOR]

Two of the main challenges in origami antenna designs are creating a reliable hinge and achieving precise actuation for optimal electromagnetic (EM) performance. Herein, a waterbomb origami ring antenna is introduced, integrating the waterbomb origami principle, 3D‐printed liquid metal (LM) hinges, and robotic shape morphing. The approach, combining 3D printing, robotic actuation, and innovative antenna design, enables various origami folding patterns, enhancing both portability and EM performance. This antenna's functionality has been successfully demonstrated, displaying its communication capabilities with another antenna and its ability to navigate narrow spaces on a remote‐controlled wheel robot. The 3D‐printed LM hinge exhibits low DC resistance (200 ± 1.6 mΩ) at both flat and folded state, and, with robotic control, the antenna achieves less than 1° folding angle accuracy and a 66% folding area ratio. The antenna operates in two modes at 2.08 and 2.4 GHz, ideal for fixed mobile use and radiolocation. Through extensive simulations and experiments, the antenna is evaluated in both flat and folded states, focusing on resonant frequency, gain patterns, and hinge connectivity. The findings confirm that the waterbomb origami ring antenna consistently maintains EM performance during folding and unfolding, with stable resonant frequencies and gain patterns, proving the antenna's reliability and adaptability for use in portable and mobile devices. [ABSTRACT FROM AUTHOR]

Inspired by the kirigami and recombination mechanism, a kirigami flexible gripper is presented. The configuration variation behaviors are realized by recombinant kirigami segments, and thus, with only head segment actuation, the gripper slickly deforms among different configurations. Revolutionizing the conventional deployable systems, the proposed design methodology can realize configuration variation‐locking integration, and reusing of multi‐stability property. To realize rapid configuration switching with the lowest energy input, a nested origami actuation, called trigger structure, is given. Furthermore, advanced design for the trigger structure is carried out, broadening the bistable state to four‐stable geometric configurations for enhanced reachable space of the flexible gripper. By combining the design of the advanced trigger structure, the flexible gripper enables an energy‐free switching behavior between deployed and curled configurations in symmetrical and asymmetrical planes. The asymmetrical configurations, induced by the multi‐stability property of the advanced trigger structure, make the flexible gripper appropriate for various moving velocities capture. The proposed kirigami multi‐stable flexible gripper has significant capture capability for moving targets with different types and motion attitudes. Summarily, the proposed kirigami multi‐stable flexible gripper opens a new avenue for flexible robots, with potential applications in space exploration, grippers, and beyond. [ABSTRACT FROM AUTHOR]

Microaerial vehicles (MAVs) have achieved rapid advancement and vast applications. Energy efficiency and friction loss are common problems of MAVs, and exploring novel structural design and enhancing flight performance are critical research directions. Here, a bionic‐inspired single‐rotor MAV with a foldable wing is fabricated by imitating winged achene in nature. The structural design of the wing based on origami principle, overall aerodynamic modeling analysis, kinematic analysis, and control system design is carried out. The prototype weighs 75 g and equipped with only one motor, achieved the desired flight attitude of vertical takeoff and landing, hovering and horizontal flight, and so forth. During nonflight, the wings fold down can reduce 70% storage area for easier transportation. The vehicle combines high flight efficiency with compactness, superior stability, simple structure, economical manufacturing cost, low flight noise, and spin deceleration safety protection, which has good potential for application in the aerial vehicle fields. [ABSTRACT FROM AUTHOR]

In this work, we propose a novel single-end morphing capacitive sensing method for shape tracking, FxC, by combining Folding origami structures and Capacitive sensing to detect the morphing structural motions using state-of-the-art sensing circuits and deep learning. It was observed through embedding areas of origami structures with conductive materials as single-end capacitive sensing patches, that the sensor signals change coherently with the motion of the structure. Different from other origami capacitors where the origami structures are used in adjusting the thickness of the dielectric layer of double-plate capacitors, FxC uses only a single conductive plate per channel, and the origami structure directly changes the geometry of the conductive plate. We examined the operation principle of morphing single-end capacitors through 3D geometry simulation combined with physics theoretical deduction, which deduced similar behavior as observed in experimentation. Then a software pipeline was developed to use the sensor signals to reconstruct the dynamic structural geometry through data-driven deep neural network regression of geometric primitives extracted from vision tracking. We created multiple folding patterns to validate our approach, based on folding patterns including Accordion, Chevron, Sunray and V-Fold patterns with different layouts of capacitive sensors using paper-based and textile-based materials. Experimentation results show that the geometry primitives predicted from the capacitive signals have a strong correlation with the visual ground truth with R-squared value of up to 95% and tracking error of 6.5 mm for patches. The simulation and machine learning constitute two-way information exchange between the sensing signals and structural geometry. By embedding part of the origami surface with morphing single-end capacitive sensors, FxC presents a unique solution that leverages both the mechanical properties of origami and sensing properties of capacitive sensing. [ABSTRACT FROM AUTHOR]

Shape-morphing capabilities are crucial for enabling multifunctionality in both biological and artificial systems. Various strategies for shape morphing have been proposed for applications in metamaterials and robotics. However, few of these approaches have achieved the ability to seamlessly transform into a multitude of volumetric shapes post-fabrication using a relatively simple actuation and control mechanism. Taking inspiration from thick origami and hierarchies in nature, we present a hierarchical construction method based on polyhedrons to create an extensive library of compact origami metastructures. We show that a single hierarchical origami structure can autonomously adapt to over 103 versatile architectural configurations, achieved with the utilization of fewer than 3 actuation degrees of freedom and employing simple transition kinematics. We uncover the fundamental principles governing theses shape transformation through theoretical models. Furthermore, we also demonstrate the wide-ranging potential applications of these transformable hierarchical structures. These include their uses as untethered and autonomous robotic transformers capable of various gait-shifting and multidirectional locomotion, as well as rapidly self-deployable and self-reconfigurable architecture, exemplifying its scalability up to the meter scale. Lastly, we introduce the concept of multitask reconfigurable and deployable space robots and habitats, showcasing the adaptability and versatility of these metastructures. Enabling complex shape morphing in engineering systems remains a significant challenge. In this work, authors demonstrate that a transformer-like hierarchical origami metastructure can self-reconfigure into over 1000 versatile structures with fewer than 3 actuation degrees of freedom and simple control. [ABSTRACT FROM AUTHOR]

Interfacial floater possessing an open surface diversifies the functions of current systems in the field of solar evaporation, micro‐detector, multiphase catalysis, etc. However, most of the current floaters still face challenges such as the anti‐submersion, orientation adjusting, and multifunctional capabilities. Drawing inspiration from water striders and diving bell spiders, here a superhydrophobic cellular origami (SCO) is proposed with reliable stability, submerge resistance, switchable floatability, and multifunctional integration. The remarkable floating ability is achieved through the air storage ability of superhydrophobic air cells. SCO floats stably on the water surface and has a maximum load capacity that is 48% higher than the superhydrophobic sheet. Besides, SCO can resurface rapidly after complete submersion, even using titanium metal as substrate. To further enhance the universality of SCO, the Janus SCO with unbalanced structure can float with a specific orientation facing up and the origami structure is optimized to be switchable with hinge structure for adjustable buoyancy. To prove the concept in 3D structure, a cylindrical SCO is presented for cable locating on the water surface. This study presents an achievable strategy to extend superhydrophobic surfaces into anti‐sinking floaters, offering valuable insights into the development of multifunctional interface carriers. [ABSTRACT FROM AUTHOR]

Origami structures with morphing behaviours and unique mechanical properties are useful in aerospace deployable structures, soft robots and mechanical metamaterials. Curved-crease origami, as one of the variants in the origami family, has a curve that connects two vertices as a crease compared to the straight crease counterpart. This feature couples the crease folding and facet bending during the folding process, providing versatile design space of mechanical metamaterials with tunable stiffness, multi-stability properties and morphing behaviours. However, current design techniques are mostly for simple geometries with intuitive construction, the modelling technique focuses on using the conventional finite element method, and the intrinsically complex geometries make specimens difficult to manufacture, which further hinders the development of curved-crease origami structures. Thus, it is valuable to review the state-of- the-art in curved-crease origami. This paper presents a review on the design methodology, analytical methods, and applications of curved-crease origami over the years, discusses their strengths, identifies future challenges and provides an outlook for the future development of the curved-crease origami concept. [ABSTRACT FROM AUTHOR]

The combined use of origami and dynamic geometry software has recently appeared in mathematics education to enrich students' geometric thinking. The objective of this research is to study the roles played by the interaction of two artifacts, paper folding and GeoGebra, in a construction-proving problem as well as its generalization in the Euclidean geometry context. For this, we designed and implemented two mathematical tasks with 52 secondary education students (15–16 years old, 10th grade) during the COVID-19 emergency lockdown period in Italy. The tasks involved four phases: constructing, exploring, conjecturing, and proving. This article presents an epistemic analysis of the tasks and a cognitive analysis of the answers given by one of the students. The theoretical tools of the onto-semiotic approach supported these analyses. Cognitive analysis allows us to confront the intended meanings of the task and the meanings actually employed by a student, thus drawing specific conclusions about the roles of such artifacts in written arguments and give an interpretation of their combined use in mathematics education. [ABSTRACT FROM AUTHOR]

In this new work, we will investigate the application of a higher-order shear deformable model for elastostatic higher-order displacement, strain, and stress analyses of a shear deformable cylindrical shell. The composite structure is assumed to be composed of a Cu-based matrix reinforced with foldable nanographene, in a thermal environment. The cylindrical shell is reinforced with graphene origami auxetic metamaterial subjected to mechanical and thermal loads. The constitutive relations are extended in thermal environment using three-dimensional Hooke's law where using the mathematical and statistical approach, the effective materials characteristics are experimentally derived as some modification coefficients of foldability, content of reinforcement, and thermal load. The principle of virtual work is used to derive governing equations taking thermal loading into consideration. One can arrive at a parametric analysis and a numerical result investigation through employing an analytical approach to explore elastostatic displacement/strain/stress along the radial coordinate with changes of thermal loads, folding, content characteristics, and other parameters. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Origami exhibits the remarkable ability to transform into diverse shapes, including quadrilaterals, triangles, and more complex polygons. This unique property has inspired the integration of origami principles into engineering design, particularly in the development of foldable mechanisms. In the field of robotics, when combined with actuators, these foldable mechanisms are referred to as active origami. Origami-based mechanisms play a pivotal role as versatile end effectors or grippers, enabling them to accurately trace desired trajectories. The performance of these mechanisms heavily relies on their specific fold patterns. To shed light on their capabilities, this study focuses on five representative structures using spherical mechanisms: oriceps, Miura ori, MACIOR, and two hexagonal structures. To assess their potential, a comparative analysis is conducted, evaluating their kinematic and scaling performances. The analysis employs the "scaling factor" as a metric, which quantifies the mechanical advantage of these mechanisms. This metric aids in the selection of appropriate structures for various applications. [ABSTRACT FROM AUTHOR]

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