Crease Pattern Research Articles

Morphological analysis of crease patterns formed on surface‐attached hydrogel with a gradient in thickness

ABSTRACTThe morphology of crease pattern formed on the surface‐attached hydrogel with a gradient in thickness is analyzed. We label the hydrogel surface at the creased state with fluorescent polyelectrolyte, which enables us to visualize surface morphology of creases using the fluorescent microscopy. Various morphological features of crease patterns are analyzed at different thickness of hydrogel, or characteristic spacing of creases λc,max, to examine the self‐similarity of crease morphology at different length scales. Some morphological features show no λc,max dependence, implying the self‐similarity, while others show weak λc,max dependence with positive values of the exponent of power law fit for the plots. We infer that such nonself‐similarity is originated from the variations in the kinetics of swelling and creasing of hydrogel, the effect of surface tension, or the reduction in the osmotic pressure occurred during the polyelectrolyte labeling step at different λc,max. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40482.

Origami lithium-ion batteries

There are significant challenges in developing deformable devices at the system level that contain integrated, deformable energy storage devices. Here we demonstrate an origami lithium-ion battery that can be deformed at an unprecedented high level, including folding, bending and twisting. Deformability at the system level is enabled using rigid origami, which prescribes a crease pattern such that the materials making the origami pattern do not experience large strain. The origami battery is fabricated through slurry coating of electrodes onto paper current collectors and packaging in standard materials, followed by folding using the Miura pattern. The resulting origami battery achieves significant linear and areal deformability, large twistability and bendability. The strategy described here represents the fusion of the art of origami, materials science and functional energy storage devices, and could provide a paradigm shift for architecture and design of flexible and curvilinear electronics with exceptional mechanical characteristics and functionalities.

Mild dermatoglyphic deviations in adolescents with autism spectrum disorders and average intellectual abilities as compared to typically developing boys.

Dermatoglyphics, ridge constellations on the hands and feet, are permanently formed by the second trimester of pregnancy. Consequently, they are considered “fossilized” evidence of a specific prenatal period. A high frequency of dermatoglyphic anomalies, or a high rate of dermatoglyphic asymmetry (discordance), is an indication of developmental instability (prenatal disturbances) prior to 24-week gestation. Most dermatoglyphic studies in psychiatry focus on adult schizophrenia. Studies on dermatoglyphic deviances and autism are sparse, include severely disturbed and intellectually retarded patients with autism, and are carried out mainly in non-Western European populations. In this study, finger print patterns, atd-angles, and palmar flexion crease patterns (PFCs) are compared between Western European adolescent teenage males, of average intellect, with Autism Spectrum Disorders (ASD; n = 46) and typically developing adolescent teenage males (TD; n = 49). Boys with ASD had a higher rate of discordance in their finger print patterns than TD boys. Thus, the hypothesized prenatal disturbances that play a role in the etiology of schizophrenia and severe autism might not be specific to these severe psychiatric disorders but might also be involved in the etiology of varying degrees of ASD.

Kinetogami: A Reconfigurable, Combinatorial, and Printable Sheet Folding

As an ancient paper craft originating from Japan, origami has been naturally embedded and contextualized in a variety of applications in the fields of mathematics, engineering, food packaging, and biological design. The computational and manufacturing capabilities today urge us to develop significantly new forms of folding as well as different materials for folding. In this paper, by allowing line cuts with crease patterns and creating folded hinges across basic structural units (BSU), typically not done in origami, we achieve a new multiprimitive folding framework such as using tetrahedral, cuboidal, prismatic, and pyramidal components, called “Kinetogami.” “Kinetogami” enables one to fold up closed-loop(s) polyhedral mechanisms (linkages) with multi-degree-of-freedom and self-deployable characteristics in a single build. This paper discusses a set of mathematical and design theories to enable design of 3D structures and mechanisms all folded from preplanned printed sheet materials. We present prototypical exploration of folding polyhedral mechanisms in a hierarchical manner as well as their transformations through reconfiguration that reorients the material and structure. The explicit 2D fabrication layout and construction rules are visually parameterized for geometric properties to ensure a continuous folding motion free of intersection. As a demonstration artifact, a multimaterial sheet is 3D printed with elastomeric flexure hinges connecting the rigid plastic facets.

Reconstructing David Huffman's Origami Tessellations1

David A. Huffman (1925–1999) is best known in computer science for his work in information theory, particularly Huffman codes, and best known in origami as a pioneer of curved-crease folding. But during his early paper folding in the 1970s, he also designed and folded over a 100 different straight-crease origami tessellations. Unlike most origami tessellations designed in the past 20 years, Huffman's straight-crease tessellations are mostly three-dimensional, rigidly foldable, and have no locking mechanism. In collaboration with Huffman's family, our goal is to document all of his designs by reverse-engineering his models into the corresponding crease patterns, or in some cases, matching his models with his sketches of crease patterns. Here, we describe several of Huffman's origami tessellations that are most interesting historically, mathematically, and artistically.

Graph Based Method for the Modelling of Crumpled Structures

This paper proposes the study of innovative packages based on a new folding technique namely crumpling. This technique consists in creating a network of complex 3d crease patterns according to a crumpling process that generates random folds from a single flexible sheet. In order to understand the topological and geometric properties of crumpled structures, a hypergraph method is proposed. The graph gives a trajectory of the geometric and topological changes of the crumpled structure during the folding process and highlights some fundamental crumpling operational sequences.

Designing and programming self-folding sheets

This paper considers a robot in the form of a self-folding sheet that is capable of origami-style autonomous folding. The sheet is composed of triangular tiles, folding actuators and an integrated electronic substrate, and is formed as an n×m box-pleated crease pattern. The design of the sheet is generated by an automated sheet design algorithm. We control the sheet with a programming method including a hardware model and supporting algorithms. In this paper we present the programming method. We describe and analyze the algorithms that generate designs and programs for the sheet. We finally demonstrate and analyze experiments with 4×4 and 8×8 self-folding sheet devices.

Low‐Voltage Switching of Crease Patterns on Hydrogel Surfaces

We report electrically driven creasing of polyelectrolye hydrogel surfaces with low switching voltages (2-4 V). Deep creases (up to 70% of the swelled film thickness) can be reversibly formed and eliminated on time-scales of a few seconds, with control of crease locations by micro-patterning of underlying electrodes.

Curved pleat folding for smooth wrapping

A technique is presented to minimize the packaged size of a flat sheet by folding it into a strip that can be wrapped around a hub. This is difficult to accomplish using regular straight creases, because of the thickness of the sheet. A curved crease pattern is used to address this problem of non-zero thickness. A mathematical formulation is developed in order to compute the required crease pattern for coiling a folded strip to any desired curvature, and specifically for coiling it into a tight spiral around a hub. This method is demonstrated with paper models. The crease computation algorithm is then extended to provide a folding strategy to efficiently package a square sheet around a central hub such that it can easily unfold or deploy. This development has applications particularly for deployable structures on small spacecraft.

ORICRETE: Modeling support for design and manufacturing of folded concrete structures

The paper presents a flexible and efficient modeling approach to the simulation of the folding process of general crease patterns. The development of the model has been motivated by the need to provide support for targeted design and efficient manufacturing of shell structures inspired by the origami technique. This type of structures is becoming increasingly popular in many engineering disciplines and has been referred to as origamics. In the present work the folding technique is used to produce spatial structures from continuously reinforced thin-walled cementitious composite plates without the need to construct curved spatial formworks. In order to support the targetted design and manufacturing of folded concrete (oricrete) structures numerical model has been formulated as an optimization framework with several types of optimality conditions and equality constraints. The model is used both for form-finding of the spatial structure and for the realization of the manufacturing process.

Right Triangular Spherical Dihedral f–Tilings with Two Pairs of Congruent Sides

By a dihedral folding tiling (f-tiling, for short) of the sphere S whose prototiles are spherical right triangles, T1 and T2, we mean a polygonal subdivision τ of S such that each cell (tile) of τ is congruent to T1 or T2 and the vertices of τ satisfy the angle-folding relation, i.e., each vertex of τ is of even valency and the sums of alternating angles around each vertex are π. In fact, the crease pattern associated to the subjacent graph of a spherical f-tiling satisfy the Kawasaki’s condition at any vertex v. In this paper we shall discuss dihedral f-tilings by spherical right triangles, considering two distinct cases of adjacency. We assume that from all the sides of the prototiles involved there are two pairs of congruent sides. The 3-dimensional representations of the obtained f-tilings are presented as well as the combinatorial structure. f-tilings are intrinsically related to the theory of isometric foldings of Riemannian manifolds, introduced by S. A. Robertson [6] in 1977. The classification of f-tilings was initiated by Ana Breda [1], with a complete classification of all spherical monohedral f-tilings. Later on, in 2002, Y. Ueno and Y. Agaoka [10] have established the complete classification of all triangular monohedral tilings (without any restrictions on angles). The study of dihedral f-tilings by spherical right triangles is a very extensive and exhaustive work and some particular cases were recently obtained in papers [4, 5]. A list of all dihedral f-tilings of the sphere by triangles and parallelograms including the combinatorial structure of each tiling can be found in [2]. Robert Dawson has also been interested in special classes of spherical tilings, see [7–9] for instance. We shall denote by Ω (T1, T2) the set, up to an isomorphism, of all dihedral f-tilings of S whose prototiles are T1 and T2. From now on T1 is a spherical right triangle of internal angles π2 , α and β, with edge lengths a (opposite to β), b (opposite to α) and c (opposite to π2 ), and T2 is a spherical right triangle of internal angles π2 , γ and δ, with edge lengths d (opposite to δ), e (opposite to γ) and f (opposite to π2 ) (see Figure 1). We will assume throughout the text that T1 and T2 are distinct triangles, i.e., (α, β) = (γ, δ) and (α, β) = (δ, γ). The case α = β or γ = δ was analyzed in [4], and so we will assume further that α = β and γ = δ.

Group-Separation Effect in Cell-Size Distribution of Origami Crease Patterns

Some statistical properties of origami (the art of paper folding) are investigated. In a crease pattern of an origami work, a paper sheet is divided into many “cells” surrounded by creases. We compute the cell-size distributions of four origami works and find that they are described by the superposition of lognormal distributions with different averages and variances. This lognormal behavior can be explained by a successive-folding process that works as a multiplicative effect. To confirm this idea, we introduce a numerical model by only incorporating a successive-folding process, and discuss its analytical properties. Moreover, we show that a group-separation structure is also essential in origami, which is different from pure crumpling.

3104 ボロノイ図に基づく平坦折り可能な折り線図の設計支援システム

It is known that the crease patterns of origami tessellations based on twist folds are generated by applying a simple geometrical operation, shrink and rotate, to the tiling patterns with polygons which have a geometric property of Maxwell's reciprocal figure. We propose an interactive system for designing the origami tessellations with symmetry by using voronoi diagrams. The system provide an interface for assigning valid and symmetrical mountain and valley flags to foldings.

Lip prints: Role in forensic odontology.

Identification plays a major role in any crime investigation. The pattern of wrinkles on the lips has individual characteristics like fingerprints. Cheiloscopy is a forensic investigation technique that deals with identification of humans based on lips traces. In the past decades, lip-print studies attracted the attention of many scientists as a new tool for human identification in both civil and criminal issues. The lip crease pattern is on the vermilion border of the lip, which is quite mobile and lip prints may vary in appearance according to the pressure, direction and method used in making the print. It concludes by enlightening the readers with the fact that the possibilities to use the red part of lips to identify a human being are wider than it is commonly thought.

Signs of the Times: Structures and signatures

This article explores different ways in which time structures and signatures can be figured both as a means of analysis and as a strategy for creation of performance work. It extends Anne Bogart's description of time signatures as understood within her system of Viewpoints training, specifically how different modalities of time combine in ways that uniquely identify each performance “in a similar way that the palm of every hand has a unique pattern of lines and creases”. Anne Ubersfeld's general observation regarding the lack of critical tools available for semiotic analysis of time compared with space is also discussed. How such time structures and schemas are actually signified to audiences then becomes the central question: each may involve varying levels of framing, foregrounding and bringing into view, with audiences sometimes consciously engaged with the playing out of these as a central thematic concern. The temporal devices and strategies that drive the generation of material may also be identified explicitly by the work as its defining ‘signature’. Noting how frequently a musical vocabulary asserts itself in this cross-disciplinary context, the article addresses examples such as Mike Figgis' ‘real-time’ film Timecode (2000), for which the shooting script was drafted on music paper to capture its four cameras over four staves on the model of a string quartet, as well as the theatre work of composer Mauricio Kagel – especially his dramatic text Sur Scène (1959) - alongside an exploration of “compositional linguistics”, the idea of “speech as music” and the temporal notation systems of Conversation Analysis. Through such examples, the article sketches the outlines of a semiotics of time in performance that may adequately describe the rich diversity of contemporary practices across disciplinary boundaries.

The complexity of the stamp folding problem

There are many folded states consistent with a given mountain–valley pattern of equidistant creases on a long paper strip. We would like to fold a paper strip such that the number of paper layers between each pair of hinged paper segments, called the crease width at the crease point, is minimized. This problem is called the stamp folding problem and there are two variants of this problem: minimization of the maximum crease width, and minimization of the total crease width. This optimization problem was recently introduced and investigated from the viewpoint of the counting problem. However, its computational complexity is not known. In this paper, we first show that the minimization problem of the maximum crease width is strongly NP-complete. Hence we cannot solve the problem in polynomial time unless P=NP. We next propose an algorithm that solves the minimization problem. The algorithm itself is a straightforward one, but its analysis is not trivial. We show that this algorithm runs in O((k+1)kn) time where n is the number of creases and k is the total crease width.

819 Finding a folding sequence for an origami crease pattern using graph pattern matching

Origami crease patterns became one of the most common ways to codify origami. They are easy to draw, easy to share and it shows, in just one picture, the structure of the origami base. But crease patterns do not show the reader how to fold itself, a task that can be very laborious and rely on trial and error. This work describes a system designed to find automatically a folding sequence given a crease pattern, so that beginners would have a more detailed guide to collapse the base and designers would have a base set of drawings to begin diagramming their creations. It uses graph pattern matching to find the occurrence of known folds and undo them, thus finding a sequence to unfold the model. The sequence is then reverted, achieving the desired diagram. By the present time, the proposed system only recognizes simple mountain/valley folds.

Swelling-induced long-range ordered structure formation in polyelectrolyte hydrogel

A millimeter-scale periodic structure is created in a polyelectrolyte hydrogel by the rapid-heterogeneous swelling process, and is frozen by the polyion complexation of the polyelectrolyte network with the oppositely charged, semi-rigid polyelectrolyte. The hydrogel is synthesized from a cationic monomer, N-[3-(N,N-dimethylamino)propyl] acrylamide methyl chloride quaternary (DMAPAA-Q), in the presence of a small amount of the oppositely charged poly(2,2′-disulfonyl-4,4′-benzidine terephthalamide) (PBDT) that has a semi-rigid nature. During the swelling process, surface creasing due to the large mismatching of swelling degree between the surface layer and the inner one of the poly DMAPAA-Q (PDMAPAA-Q) gel occurs, which induces highly oriented semi-rigid PBDT molecules along the tensile direction of the crease pattern. To accompany the evolution of surface creasing, a lattice-like periodic birefringence pattern is formed, which is frozen permanently by the strong polyion complex formation, even after the surface instability pattern of the gel disappears completely throughout the dynamic coalescence. In this work we rationally clarified that formation of such a long-range ordered non-equilibrium structure in the polyelectrolyte hydrogel by the rapid-heterogeneous swelling process requires the following three indispensable conditions: (i) swelling-induced surface creasing; (ii) polyion complex formation; and (iii) a semi-rigid or rigid dopant. This sort of non-equilibrium structure formation mechanism may help understand how biomacromolecules that are rigid polyelectrolytes, such as deoxyribonucleic acid, microtubules and actin filaments, form rich architectures during the growth of biological organs.

Designing crease patterns for polyhedra by composing right frusta

We propose an original and novel algorithm for the automatic development of crease patterns for certain polyhedra with discrete rotational symmetry by composing right frusta. Unlike existing algorithms, the folded product will conform to the surface of the target polyhedron without external flaps. The crease patterns of frusta are drawn first and then composed by the algorithm to draw the crease pattern of the rotationally symmetric polyhedron. The composition is performed by splitting creases that were folded on pleats from frustum crease patterns. A CAD program has been written to implement the algorithm automatically, allowing users to specify a target polyhedron and generate a crease pattern that folds into it.

A solution for folding rigid tall shopping bags

Rigid origami is concerned with the folding of rigid thin-walled structures. The materials from which the structures are made are not allowed to deform or bend, but can rotate freely about pre-arranged creases. One of the challenges in rigid origami is the flat folding of a shopping bag with a rectangular base if the bag is made of rigid materials. The problem is not only mathematically interesting but also has practical implications as many consumer goods are packaged in box-shaped cartons or cardboard boxes. In this paper, a new crease pattern has been proposed that allows a tall box-shaped bag with a rectangular base to be rigidly folded flat. Rigid folding conditions are established, and solutions that meet these conditions are found numerically. Simulations and experiments carried out demonstrate that the solution works. The new pattern represents the first practical solution for tall bags and can lead to direct applications in the packaging industry. Moreover, the folding analysis can be used to design an automated packaging process for folding box-shaped stiff cartons.