Origami Pattern Research Articles

Folding a single high-genus surface into a repertoire of metamaterial functionalities

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.

Oriblock: The origami-blocks based on hinged dissection

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

Optimal Curve Fitting for Serial Chain in Six-Crease Origami Unit

Abstract Origami-inspired structures have been widely used in aerospace and robotics for three-dimensional (3D) symmetrical configurations using crease-symmetrical origami basic patterns. These patterns offer advantages in repeatable and systematic modeling and mass production. However, few studies have focused on 3D non-symmetrical structures using symmetrical origami basic patterns due to their structure complexity, limiting their application. Therefore, we aim to analyze the folding behavior in 3D non-symmetrical structures using a 6-crease symmetry origami base pattern. To achieve this goal, we first focus on behavior in a two-dimensional (2D) plane. This paper presents a scheme for the behavior of origami units with an optimal curve-fitting algorithm. The curve can be any 2D space curve. The fitting curve, constructed by numerical analysis and an optimal approaching scheme, can satisfy error requirements and retain foldable origami unit features. The paper verifies the feasibility of the curve-fitting scheme by presenting two curve examples, including a quadratic curve and a sin wave function. The results show that the fitting error is reduced by 99% when no boundary conditions are applied. This research provides valuable insights into understanding origami unit kinematic optimization through forward and inverse kinematics. It offers potential applications in the engineering design of foldable structures and precision origami-inspired mechanism, thereby opening avenues for further exploration of complex origami structures and their applications in emerging technologies.

A rigidly foldable and reconfigurable thick origami antenna.

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'.

Programming the mechanical properties of double-corrugated metamaterials by varying mountain-valley assignments.

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'.

Synthesis of a highly programmable multistable Kresling origami-inspired unit cell

Multistable origami structures have been exploited for mechanical property tailoring, deployable robotic arms, wave propagation tuning and others, due to its ability to possess multiple stable states with distinct properties. Traditionally these structures are made by assembling bistable unit cells, which results in a significant increase in the size and weight of the system when larger number of stable states are required. Recently, researchers have uncovered a third stable state in the Kresling origami pattern. Although this is an advancement over the bistable unit cell, there is an unexplored opportunity for more systematically expanding the design space of Kresling unit cells to possess many more stable configurations (>>2) and enhance its programmable multistability. In this research, we seek to develop a methodology for the design of a Kresling origami-inspired unit cell that can be easily programmed to achieve up to 10 stable configurations, with the potential to achieve even more. We exploit the rich kinematics of the Kresling origami-inspired unit cell, that arise from its coupled translational and rotational deployment, and propose the strategic integration of tensile elements to realize multiple stable states. Analytically, we study the unstretched length values (defined to be the precise length between the string “slacked” and “tensioned” configurations) of the strings that yield the distinct number of stable states. We present the potential energy profiles with its corresponding force-displacement plots for the bistable, tristable, quadstable, pentastable and decastable unit cells. Moreover, we show that by simply adjusting the unstretched length of the strings we can program and tune the number of stable states of the unit cell. Tristable and pentastable unit cell prototypes are designed and experimentally tested to validate the proposed methodology. Lastly, a study is performed on the mechanical property tailoring capabilities of two unit cells assembled in series. The results show that the decastable unit cell assembly can achieve up to 55 discrete values of equivalent stiffness, while the bistable one can only achieve 3. For the bistable unit cell assembly to match this number, it will require 54 unit cells in series, which will significantly increase the size and weight of the structural system. These findings show that the modular structure will have more programmable capabilities, while maintaining its size and weight at a minimum, as the number of stable states per unit cell is increased.

Origami folding pattern development for gossamer structures

Gossamer structures for satellites are large, thin deployable structures that are attractive for space applications because they can be stowed compactly for transportation and deployed to have large functional surface areas. Reflectarray antennas, in particular, are candidates for gossamer structures because they can be realized on thin membranes. However, the efficiency of reflectarray antennas decreases with any deviations from a flat plane, including those induced by plastically deformed creases. Rolling membranes can prevent some plastic deformation, but requires relative slipping between layers that are rolled together. In this work, we describe, analyze, and demonstrate two rolled configurations for deployable gossamer structures based on a combination of rolled and folded membranes and surrogate folds that allow for sliding between layers. Cuts and Step Hinges are used as surrogate folds. Step Hinges connect membranes while limiting slipping motion in a single direction and reducing wrinkling in the structure. The combination of folding, rolling, and sliding connections reduces plastic deformation while providing a highly efficient packing of the stowed form.

Mechanical Properties Inside Origami-Inspired Structures: An Overview

Abstract In recent decades, origami has transitioned from a traditional art form into a systematic field of scientific inquiry, characterized by attributes such as high foldability, lightweight frameworks, diverse deformation modes, and limited degrees of freedom. Despite the abundant literature on smart materials, actuation methods, design principles, and manufacturing techniques, comprehensive reviews focusing on the mechanical properties of origami-inspired structures remain rare. This review aims to fill this void by analyzing and summarizing the significant studies conducted on the mechanical properties of origami-inspired structures from 2013 to 2023. We begin with an overview that includes essential definitions of origami, classical origami patterns, and their associated tessellated or stacked structures. Following this, we delve into the principal dynamic modeling method for origami and conduct an in-depth analysis of the key mechanical properties of origami-inspired structures. These properties include tunable stiffness, bistability and multistability, meta-mechanical properties demonstrated by origami-based metamaterials, and bio-inspired mechanical characteristics. Finally, we conclude with a comprehensive summary that discusses the current challenges and future directions in the field of origami-inspired structures. Our review provides a thorough synthesis of both the mechanical properties and practical applications of origami-inspired structures, aiming to serve as a reference and stimulate further research.

Crashworthiness design for novel polygonal asymmetric origami tubes

Origami tubes have attracted widespread attention because it is inclined to deform in the complete diamond mode (DM) with a low initial peak force Fmax and high average crushing force Fave. Although conventional origami tubes can improve crashworthiness, there are still many areas that fail to generate traveling plastic hinge lines, and the crashworthiness can be further improved. This paper presents a novel polygonal asymmetric origami tube (PAT) with origami patterns that can trigger more traveling plastic hinge lines compared to those of conventional origami patterns. The theoretical analysis of the deformation mechanism suggests that the PAT can realize hierarchical deformation and avoid stress concentration at sharp corners. The quasi-static experiments and numerical simulations reveal that the novel origami pattern can successfully trigger up to four times more traveling plastic hinge lines than the conventional square box (CSB) under the premise that each plastic hinge line is similar in length. Compared with the CSB, the PAT can deform in DM with a 56.0 % reduction of Fmax and a 59.1 % increase of Fave. Notably, the stableness of load-carrying capacity SLC is 90.2 %, which is 260.8 % higher than the CSB. A series of parametric studies reveal that the dihedral angle ratio α / β and the width-to-thickness ratio c / t of the PAT have a significant effect on crashworthiness. A smaller ratio of α / β and c / t provides the PAT with superior crashworthiness. Comparing the PAT with other types of origami tubes and multi-cell tubes indicates that the PAT also exhibits outstanding crashworthiness. The impact experiments also unveil a significantly enhanced crashworthiness of the PAT. Compared with the CSB, the Fmax decreases by approximately 46.4 %, while the Fave increases by around 92.7 %. The SLC and SEA values for the PAT surpass those of the CSB by about 260.8 % and 93.1 %, respectively. Furthermore, the theoretical analysis for predicting the Fave of the PAT is developed, with a maximum error not exceeding 8.5 %.

Expandable rotational origami nano-boxes made by giant shape amphiphile

Dynamic cavity is widespread in living matter and supramolecular scaffolds. Generally speaking, flexible building block as a segment is used to realize dynamic cavities building in artificial molecules and materials. However, the incorporation of rigid synthetic supramolecular scaffolds with flexible cavity motion remains rare. Inspired by rotational origami patterns, giant shape amphiphile (GSA), POSS-NDI-POSS (PNP), assembled into an origami nano-box with feature of rotational expansion. The open/close of cavity and size control of PNP host can be adjusted by rotational offset between adjacent PNP in supramolecule entities. The rotational offset of 150°, 130° and 0° were observed when the host nano-box presented close, half-open and fully-open state, respectively. The rotational expansion of PNP trigged by gaseous arenes makes PNP as a novel nonporous crystal. Compared with conformation change in flexible building segment, rotational expansion in acyclic host (PNP) provides a new strategy for the development of rigid segment to build adaptive host-guest recognition.

Derivation of an effective plate theory for parallelogram origami from bar and hinge elasticity

Periodic origami patterns made with repeating unit cells of creases and panels bend and twist in complex ways. In principle, such soft modes of deformation admit a simplified asymptotic description in the limit of a large number of cells. Starting from a bar and hinge model for the elastic energy of a generic four parallelogram panel origami pattern, we derive a complete set of geometric compatibility conditions identifying the pattern’s soft modes in this limit. The compatibility equations form a system of partial differential equations constraining the actuation of the origami’s creases (a scalar angle field) and the relative rotations of its unit cells (a pair of skew tensor fields). We show that every solution of the compatibility equations is the limit of a sequence of soft modes — origami deformations with finite bending energy and negligible stretching. Using these sequences, we derive a plate-like theory for parallelogram origami patterns with an explicit coarse-grained quadratic energy depending on the gradient of the crease-actuation and the relative rotations of the cells. Finally, we illustrate our theory in the context of two well-known origami designs: the Miura and Eggbox patterns. Though these patterns are distinguished in their anticlastic and synclastic bending responses, they show a universal twisting response. General soft modes captured by our theory involve a rich nonlinear interplay between actuation, bending and twisting, determined by the underlying crease geometry.

Design of self-deployable origami utilizing rigid-elastic coupling spherical mechanism

Origami-inspired mechanisms are extensively utilized in aerospace, medical devices, and soft robotics due to their simplicity, reliability, and high fold-to-deploy ratio. However, actuating these structures for deployment remains challenging. This paper presents a design method for self-deployable origami utilizing the rigid-elastic coupling spherical mechanism. Initially, the rigid-elastic coupling spherical mechanism is designed by replacing one revolute joint of the rigid spherical mechanism with a V-shaped elastic nickel–titanium (Ni–Ti) alloy wire. We show that the rigid-elastic coupling spherical mechanism has equivalent kinematics to the associated rigid spherical mechanism, which is also the equivalent mechanism of the rigid-elastic coupling origami unit. By leveraging the elastic deformation of the Ni–Ti alloy wire in conjunction with the motion of the revolute joints, the rigid-elastic coupling mechanism acquires bistable characteristics, thereby enabling shape memory for self-deployment. The typical origami patterns, such as Miura-ori and Yoshimura-ori, are employed as design examples to showcase the performances of the associated self-deployable origami.

Portable Flexible Spherical Origami Joule‐Heaters with Aerogel

AbstractTrending portable smart devices are providing great convenience to the daily life. Thermal conductivity is efficient for contact heat transfer. Unfortunately, existing rigid surfaces can hardly heat objects in arbitrary shapes. Herein, a flexible origami‐structure heater fabricated by scalable laser manufacturing with temperature feedback control is proposed. The thin film origami heater is designed as a pair of semispherical origami patterns, which can conform to the curved surface of food samples more effectively. Therefore, the heat conducting area is increased to generate a fast and even heating profile to the surface of the food samples. The outer aerogel provides high thermal insulation to prevent heat dissipation in the environment. As proof of concept, the heating device can cook quail eggs within 3 minutes at a constant temperature of 100 °C. The power consumption of this heater is as low as 18 W, which standard portable chargers can power. This work significantly promotes the usability of portable heaters for cooking spherical objects, providing more conveniences during outdoor hiking and even in outer space where water‐boiling is impossible without atmosphere and gravity.

Analysis of binding site dependent labelling efficiency for DNA-PAINT using particle fusion

DNA-origami nanostructures have shown promising applications in single molecule localization microscopy. They have become a reference standard for benchmarking and for developing new techniques for nanoscopy. Here, we present a pipeline for quantifying the quality of these nano-structures when imaging multiple instances of them using DNA-PAINT technique. We show on several experimental datasets that these structures can have deformations and that the designed binding sites are not equally accessible for the labelled imager strands during the image acquisition process. These limitations result in non-uniform activation of the sites over the origami pattern when fusing the instances into a single reconstruction.

Kresling origami derived structures and inspired mechanical metamaterial

Origami has attracted more and more attention due to its exotic mechanical properties, and the inspired metamaterials are also popular. However, the main focus of current research is on existing origami patterns and properties, although new origami patterns or results that expand on existing origami patterns are gradually emerging. In this paper, we summarize a series of derived structures of the Kresling origami, demonstrating more stable states and richer structural forms. At the same time, a point-searching method is proposed along the ideas of the truss model, which is effective for irregular stable states of these derived structures. On this basis, we create an origami-inspired mechanical metamaterial with foldable property and high load-bearing capacity, fabricate the prototype, and validate its performance through experiments. These works make important contributions for promoting the Kresling origami and origami-inspired metamaterials.

Analysis of the Rigid Foldability of Origami Patterns Based on Spatial Positions of Creases

Abstract Rigid foldability is a special property of rigid origami patterns, where each origami plane remains undeformed during continuous movement along the predetermined crease. Current research on the rigid foldability of origami patterns mainly focuses on kinematics, while less attention is paid to factors that cause deformation of the folding plane. Whether the relative spatial position of adjacent creases has been changed is a critical factor that influences the state (rigid or deformed) of the folding plane between the two adjacent creases during the folding process. This study considered two factors (linear relationship and Euclidean distance) to measure the changes in the spatial positions of creases, explored the relationship between the two factors and rigid folding, and identified deformation forms that affect rigid foldability. First, the origami pattern was regarded as a linkage mechanism, and the linear relationship between creases was determined from the single-vertex origami unit forming this origami structure. Then, the geometric parameters of the origami pattern were used to calculate the Euclidean distance between two points on adjacent creases during the folding process. If the linear relationship and Euclidean distance always remain the same, the origami pattern has rigid foldability. Based on changes in the Euclidean distance, this method can also help determine the main deformation of non-rigidly foldable origami patterns. In addition, it can be applied to origami patterns with four or five vertices and multiple loops, and it further provides a novel approach for determining the layout of the crease position and the judgment of rigid foldability during origami-inspired mechanism design.

Simulation and design of isostatic thick origami structures

Thick origami structures are considered here as assemblies of polygonal panels hinged to each other along their edges according to a corresponding origami crease pattern. The determination of the internal actions in equilibrium with the external loads in such structures is not an easy task, owing to their high degree of static indeterminacy, and the likelihood of unwanted self-balanced internal actions induced by manufacturing imperfections. Here, we present a method for reducing the degree of static indeterminacy which can be applied to several thick origami structures to make them isostatic. The method utilizes sliding hinges, which allow relative translation along the hinge axis, to replace conventional hinges. After giving the analytical description of both types of hinges and describing a rigid folding simulation procedure based on the integration of the exponential map, we present the static analysis of a series of noteworthy examples based on the Miura-ori pattern, the Yoshimura pattern, and the Kresling pattern. Our method, based on kinematic-static duality, provides a novel design paradigm that can be applied for the design and realization of thick origami structures with adequate strength to resist external actions.

Kinematic modeling and formability analysis of revolved bodies formed by origami waterbomb units based on a chain-like layer-building method

ABSTRACT Origami patterns play a critical role in the field of soft and reconfigurable robotics. The revolved body formed by waterbomb units is also widely used in robot design. The kinematic model plays a key role in understanding motion characteristics and is vital for dynamic modeling and control of robots based on origami. However, while the deformation of origami patterns is well-studied on the finite element level, the assembly of rigid origami patterns is rarely explored on the kinematic level. Therefore, we propose a chain-like assembly method for constructing revolved bodies using rigid waterbomb units, ensuring crease status unalternation, collision avoidance, axis existence, and seamless assembly. We explore the formability of waterbomb units and investigate the resulting revolved body with some layer and column numbers of waterbomb units. Results demonstrate that increasing the number of columns does not necessarily provide more space for building layers. Additionally, they reveal boundaries of the layer and column numbers for constructing the revolved body and highlight the impact of the aspect ratio and configuration of the waterbomb units on the formability of the revolved body. This method can provide insights for origami-based robot research and can be extended to model other origami patterns.

Region crossing change on origami and link

Region Select is a game originally defined on a knot projection. In this paper, Region Select on an origami crease pattern is introduced and investigated. As an application, a new unlinking number associated with region crossing change is defined and discussed.

Energy absorption characteristics of origami-folded thin-walled square tubes internally filled with graded polyurethane foam structures

Rigid polyurethane foam, known for its low density, lightweight, and excellent energy absorption properties, has been effectively employed to enhance the energy absorption capacity of origami-folded thin-walled square tubes filled with graded foam. In this study, quasi-static compression experiments and finite element simulations were conducted on 3D-printed origami-folded thin-walled tubes filled with graded foam. The impact of factors such as the number of folding layers, interlayer dihedral angles, wall thickness, and various foam densities on the energy absorption characteristics of these thin-walled tubes was analyzed. It was found that the incorporation of fold designs significantly improved the energy absorption properties of thin-walled tubes. Notably, origami tubes filled with positively graded foam outperform their negatively graded and single-density foam-filled counterparts in terms of energy absorption capability. The research underscores the excellent energy absorption properties of origami-folded thin-walled square tubes filled with graded foam, offering valuable insights for optimizing structures involving more intricate origami patterns and subsequent graded foam filling.Keywords