The difficulty of folding self-folding origami

Why is it difficult to refold a previously folded sheet of paper? We show that even crease patterns with only one designed folding motion inevitably contain an exponential number of `distractor' folding branches accessible from a bifurcation at the flat state. Consequently, refolding a sheet requires finding the ground state in a glassy energy landscape with an exponential number of other attractors of higher energy, much like in models of protein folding (Levinthal's paradox) and other NP-hard satisfiability (SAT) problems. As in these problems, we find that refolding a sheet requires actuation at multiple carefully chosen creases. We show that seeding successful folding in this way can be understood in terms of sub-patterns that fold when cut out (`folding islands'). Besides providing guidelines for the placement of active hinges in origami applications, our results point to fundamental limits on the programmability of energy landscapes in sheets.Comment: 8 pages, 5 figure

An Overview of Mechanisms and Patterns with Origami

International audienceOrigami (paperfolding) has greatly progressed since its first usage for design of cult objects in Japan, and entertainment in Europe and the USA. It has now entered into artistic areas using many other materials than paper, and has been used as an inspiration for scientific and engineering realizations. This article is intended to illustrate several aspects of origami that are relevant to engineering structures, namely: geometry, pattern generation, strength of material, and mechanisms. It does not provide an exhaustive list of applications nor an in-depth chronology of development of origami patterns, but exemplifies the relationships of origami to other disciplines, with selected examples

Elastically and Plastically Foldable Electrothermal Micro‐Origami for Controllable and Rapid Shape Morphing

Integrating origami principles within traditional microfabrication methods can produce shape morphing microscale metamaterials and 3D systems with complex geometries and programmable mechanical properties. However, available micro‐origami systems usually have slow folding speeds, provide few active degrees of freedom, rely on environmental stimuli for actuation, and allow for either elastic or plastic folding but not both. This work introduces an integrated fabrication–design–actuation methodology of an electrothermal micro‐origami system that addresses the above‐mentioned challenges. Controllable and localized Joule heating from electrothermal actuator arrays enables rapid, large‐angle, and reversible elastic folding, while overheating can achieve plastic folding to reprogram the static 3D geometry. Because the proposed micro‐origami do not rely on an environmental stimulus for actuation, they can function in different atmospheric environments and perform controllable multi‐degrees‐of‐freedom shape morphing, allowing them to achieve complex motions and advanced functions. Combining the elastic and plastic folding enables these micro‐origami to first fold plastically into a desired geometry and then fold elastically to perform a function or for enhanced shape morphing. The proposed origami systems are suitable for creating medical devices, metamaterials, and microrobots, where rapid folding and enhanced control are desired.An elastically and plastically foldable micro‐origami is developed and tested to create controllable and functional 3D shape morphing systems with multiple active degrees of freedom. The work demonstrates a versatile design–fabrication–actuation method to achieve rapid folding, enhanced control, and function in different atmospheric environments, enabling applications in microrobots, medical devices, and metamaterials.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/163442/2/adfm202003741.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163442/1/adfm202003741-sup-0001-SuppMat.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163442/3/adfm202003741_am.pd

Active Polymeric Materials for 3D Shaping and Sensing

Part I: Reprogrammable Chemical 3D Shaping for Origami, Kirigami, and Reconfigurable Molding Origami- and kirigami-based design principles have recently received strong interest from the scientific and engineering communities because they offer fresh approaches to engineering of structural hierarchy and adaptive functions in materials, which could lead to many promising applications. Herein, we present a reprogrammable 3D chemical shaping strategy for creating a wide variety of stable complex origami and kirigami structures autonomously. This strategy relies on a reverse patterning method that encodes prescribed 3D geometric information as a spatial pattern of the unlocked phase (dispersed phase) in the locked phase (matrix phase) in a pre-stretched Nafion sheet. Building upon the unique chemical reprogramming capability of the Nafion shape memory polymer, we have developed a reconfigurable molding technology that can significantly reduce the time, cost, and waste in 3D shaping of various materials with high fidelity. Part II: A Versatile, Multifunctional, Polymer-Based Dynamically Responsive Interference Coloration The bioinspired stimuli-responsive structural coloration offers a wide variety of potential applications, ranging from sensing to camouflage to intelligent textiles. Owing to its design simplicity, which does not require multilayers of materials with alternative refractive indices or micro- and nanostructures, thin film interference represents a promising solution towards scalable and affordable manufacturing of high-quality responsive structural coloration systems. However, thin films of polymers with appropriate thickness generally do not exhibit visible structural colors if they are directly deposited on substrates with relatively low refractive indices such as glass and polydimethylsiloxane (PDMS). Here, a versatile technology that enables polymer-based, stimuli-responsive interference coloration (RIC) on various substrates is presented. Real-time, continuous, colorimetric RIC sensors for humidity, organic vapor, temperature, and mechanical force are demonstrated by using different stimuli-responsive polymers. The transparent RIC film on glass shows strong coupling of constructive interference reflected colors and complementary destructive interference transmitted colors on opposite sides of the film. The ability to use substrates such as glass and PDMS allows for the proof-of-concept demonstration of a humidity-sensing window, and a self-reporting, self-acting sensor that does not consume external power

Origami surfaces for kinetic architecture

This thesis departs from the conviction that spaces that can change their formal configuration through movement may endow buildings of bigger versatility. Through kinetic architecture may be possible to generate adaptable buildings able to respond to different functional solicitations in terms of the used spaces. The research proposes the exploration of rigidly folding origami surfaces as the means to materialize reconfigurable spaces through motion. This specific kind of tessellated surfaces are the result of the transformation of a flat element, without any special structural skill, into a self-supporting element through folds in the material, which gives them the aptitude to undertake various configurations depending on the crease pattern design and welldefined rules for folding according to rigid kinematics. The research follows a methodology based on multidisciplinary, practical experiments supported on digital tools for formal exploration and simulation. The developed experiments allow to propose a workflow, from concept to fabrication, of kinetic structures made through rigidly folding regular origami surfaces. The workflow is a step-by-step process that allows to take a logical path which passes through the main involved areas, namely origami geometry and parameterization, materials and digital fabrication and mechanisms and control. The investigation demonstrates that rigidly folding origami surfaces can be used as dynamic structures to materialize reconfigurable spaces at different scales and also that the use of pantographic systems as a mechanism associated to specific parts of the origami surface permits the achievement of synchronized motion and possibility of locking the structure at specific stages of the folding.A presente tese parte da convicção de que os espaços que são capazes de mudar a sua configuração formal através de movimento podem dotar os edifícios de maior versatilidade. Através da arquitectura cinética pode ser possível a geração de edifícios adaptáveis, capazes de responder a diferentes solicitações funcionais, em termos do espaço utilizado. Esta investigação propõe a exploração de superfícies de origami, dobráveis de forma rígida, como meio de materialização de espaços reconfiguráveis através de movimento. Este tipo de superfícies tesseladas são o resultado da transformação de um elemento plano, sem capacidade estrutural que, através de dobras no material, ganha propriedades de auto-suporte. Dependendo do padrão de dobragem e segundo regras de dobragem bem definidas de acordo com uma cinemática rígida, a superfície ganha a capacidade de assumir diferentes configurações. A investigação segue uma metodologia baseada em experiências práticas e multidisciplinares apoiada em ferramentas digitais para a exploração formal e simulação. Através das experiências desenvolvidas é proposto um processo de trabalho, desde a conceptualização à construção, de estruturas cinéticas baseadas em superfícies dobráveis de origami rígido de padrão regular. O processo de trabalho proposto corresponde a um procedimento passo-apasso que permite seguir um percurso lógico que atravessa as principais áreas envolvidas, nomeadamente geometria do origami e parametrização, materiais e fabricação digital e ainda mecanismos e controle. A dissertação demonstra que as superfícies de origami dobradas de forma rígida podem ser utilizadas como estruturas dinâmicas para materializar espaços reconfiguráveis a diferentes escalas. Demonstra ainda que a utilização de sistemas pantográficos como mecanismos associados a partes específicas da superfície permite atingir um movimento sincronizado e a possibilidade de bloquear o movimento em estados específicos da dobragem

Non-Euclidean Origami

Traditional origami starts from flat surfaces, leading to crease patterns consisting of Euclidean vertices. However, Euclidean vertices are limited in their folding motions, are degenerate, and suffer from misfolding. Here we show how non-Euclidean 4-vertices overcome these limitations by lifting this degeneracy, and that when the elasticity of the hinges is taken into account, non-Euclidean 4-vertices permit higher-order multistability. We harness these advantages to design an origami inverter that does not suffer from misfolding and to physically realize a tristable vertex

Kinetic Solar Skin: A Responsive Folding Technique

The paper focuses on optimized movements analysed by means of Origami, the Japanese traditional art of paper folding. The study is a way to achieve different deployable shading systems categorized by a series of parameters that describe the strengths and weaknesses of each tessellation. Through the kinetic behaviour of Origami geometries the research compares simple folding diagrams with the purpose to understand the deployment at global scale and thus the potential of kinetic patterns’ morphology for application in adaptive facades. The possibilities of using a responsive folding technique to develop a kinetic surface that can change its configuration are here examined through the variation of parameters that influence kinematics’ form. Moreover, in order to perform the shape change without any external mechanical devices, the use of Shape Memory Alloy (SMA) actuators has been tested

Soft Origami: Classification, Constraint, and Actuation of Highly Compliant Origami Structures

Herein, we discuss the folding of highly compliant origami structures—“Soft Origami.” There are benefits to be had in folding compliant sheets (which cannot self-guide their motion) rather than conventional rigid origami. Example applications include scaffolds for artificial tissue generation and foldable substrates for flexible electronic assemblies. Highly compliant origami has not been contemplated by existing theory, which treats origami structures largely as rigid or semirigid mechanisms with compliant hinges—“mechanism-reliant origami.” We present a quantitative metric—the origami compliance metric (OCM)—that aids in identifying proper modeling of a homogeneous origami structure based upon the compliance regime it falls into (soft, hybrid, or mechanism-reliant). We discuss the unique properties, applications, and design drivers for practical implementation of Soft Origami. We detail a theory of proper constraint by which an ideal soft structure's number of degrees-of-freedom may be approximated as 3n, where n is the number of vertices of the fold pattern. Buckling and sagging behaviors in very compliant structures can be counteracted with the application of tension; we present a method for calculating the tension force required to reduce sagging error below a user-prescribed value. Finally, we introduce a concept for a scalable process in which a few actuators and stretching membranes may be used to simultaneously fold many origami substructures that share common degrees-of-freedom.United States. Air Force Office of Scientific Research (Grant 1332249)National Science Foundation (U.S.

Architected Origami Materials: How Folding Creates Sophisticated Mechanical Properties

Origami, the ancient Japanese art of paper folding, is not only an inspiring technique to create sophisticated shapes, but also a surprisingly powerful method to induce nonlinear mechanical properties. Over the last decade, advances in crease design, mechanics modeling, and scalable fabrication have fostered the rapid emergence of architected origami materials. These materials typically consist of folded origami sheets or modules with intricate 3D geometries, and feature many unique and desirable material properties like auxetics, tunable nonlinear stiffness, multistability, and impact absorption. Rich designs in origami offer great freedom to design the performance of such origami materials, and folding offers a unique opportunity to efficiently fabricate these materials at vastly different sizes. Here, recent studies on the different aspects of origami materialsâ geometric design, mechanics analysis, achieved properties, and fabrication techniquesâ are highlighted and the challenges ahead discussed. The synergies between these different aspects will continue to mature and flourish this promising field.Origami, the ancient art of paper folding, has become a framework of designing and constructing architected materials. These materials consist of folded sheets or modules with intricate geometries, and feature many unique and desirable mechanical properties. Recent progress in architected origami materials is highlighted, especially the foldingâ induced mechanics, and the challenges ahead are discussed.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147779/1/adma201805282_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/147779/2/adma201805282.pd