Crease Pattern Research Articles

GWAS of the association between infections and mental disorders including heritability estimation and polygenic risk score analysis

In this paper, we focus on some aspects of the finite element simulations of robotic paper folding and the reconstruction of models from the origami crease patterns by the robot arms. The paper highlights the simulation problems, which should be solved in developing our recent study in mechanical and geometrical design of the origami-performing robot. The basic premise underlying the study is that folding operations with the origami crease patterns are considered as the functions of the mechanical systems such as a robot. Manipulations with the foldable objects, such as a sheet of paper (the origami crease pattern), by the robot arms in the simulation environment lead to understanding the design of the origami-performing robot without testing physical prototypes at each design stage. In this case, dynamic and kinematic behavior of the robot arms in forming the 3D origami objects is modelled by using the finite element method (FEM) in LS-DYNA solver. For simulating, two forms of origami are considered: flexible, if bending is used for paper folding, and rigid, if origami patterns are considered as the kinematic systems. Results of the simulation are presented and provided by the illustrations.

Finite element simulation of robotic origami folding

In this paper, we focus on some aspects of the finite element simulations of robotic paper folding and the reconstruction of models from the origami crease patterns by the robot arms. The paper highlights the simulation problems, which should be solved in developing our recent study in mechanical and geometrical design of the origami-performing robot. The basic premise underlying the study is that folding operations with the origami crease patterns are considered as the functions of the mechanical systems such as a robot. Manipulations with the foldable objects, such as a sheet of paper (the origami crease pattern), by the robot arms in the simulation environment lead to understanding the design of the origami-performing robot without testing physical prototypes at each design stage. In this case, dynamic and kinematic behavior of the robot arms in forming the 3D origami objects is modelled by using the finite element method (FEM) in LS-DYNA solver. For simulating, two forms of origami are considered: flexible, if bending is used for paper folding, and rigid, if origami patterns are considered as the kinematic systems. Results of the simulation are presented and provided by the illustrations.

Approximating 3D surfaces using generalized waterbomb tessellations

AbstractOrigami has received much attention in geometry, mathematics, and engineering due to its potential to construct 3D developable shapes from designed crease patterns on a flat sheet. Waterbomb tessellation, which is one type of traditional origami consisting of a set of waterbomb bases, has been used to create geometrically appealing 3D shapes and been widely studied. In this paper, we propose a method for approximating target surfaces, which are parametric surfaces of varying or constant curvatures, using generalized waterbomb tessellations. First, we generate a base mesh by tiling the target surface using waterbomb bases. Then, by applying a simple numerical optimization algorithm to the base mesh, we achieve a developable waterbomb tessellation, which can be developed onto a plane without stretching. We provide a prototype system using which the user can adjust the resolution of the tessellation and modify waterbomb bases. Our work could expand the exploration of building developable 3D structures using origami.Highlights Generalizing waterbomb tessellations to fit target 3D parametric surfaces. Achieving developable tessellations by a simple numerical optimization algorithm. Non-axisymmetric or non-orientable resulting approximations are demonstrated.

Study on the Crease Pattern of 3D shapes for Paper-Folding Robot

Study on the Crease Pattern of 3D shapes for Paper-Folding Robot

Discussion of “A Review of Thickness-Accommodation Techniques in Origami-Inspired Engineering” (Lang, R. J., Tolman, K. A., Crampton, E. B., Magleby, S. P., and Howell, L. L., 2018, ASME Appl. Mech. Rev., 70(1), p. 010805

Origami is a traditional art form that realizes three-dimensional shapes by folding paper sheets. Origami designers use mathematical theorems to support their design efforts. These theorems require a condition of a flat fold on folded sheets. When working with paper, the paper is essentially zero thickness and folds flat. Thus, to access the power of flat-foldability theorems for origami-inspire design, nonzero thickness stiff sheet crease patterns must still be flat foldable. For nonzero thickness sheets as would be used in practical engineering applications, special fold designs are required to allow an effectively flat fold. In this issue of ASME Applied Mechanics Reviews, Lang and co-authors present a review of fold design techniques to enable effectively flat folding of nonzero thickness sheets. In this discussion, the impact of the author's work is highlighted. As well, the contributions of the authors work is situated in the context of origami-inspired systems design. The integration of their work into a systems construct clarifies and motivates the need for further origami-inspired design research.

The Complexity 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.

From flat sheets to curved geometries: Origami and kirigami approaches

Abstract Transforming flat sheets into three-dimensional structures has emerged as an exciting manufacturing paradigm on a broad range of length scales. Among other advantages, this technique permits the use of functionality-inducing planar processes on flat starting materials, which after shape-shifting, result in a unique combination of macro-scale geometry and surface topography. Fabricating arbitrarily complex three-dimensional geometries requires the ability to change the intrinsic curvature of initially flat structures, while simultaneously limiting material distortion to not disturb the surface features. The centuries-old art forms of origami and kirigami could offer elegant solutions, involving only folding and cutting to transform flat papers into complex geometries. Although such techniques are limited by an inherent developability constraint, the rational design of the crease and cut patterns enables the shape-shifting of (nearly) inextensible sheets into geometries with apparent intrinsic curvature. Here, we review recent origami and kirigami techniques that can be used for this purpose, discuss their underlying mechanisms, and create physical models to demonstrate and compare their feasibility. Moreover, we highlight practical aspects that are relevant in the development of advanced materials with these techniques. Finally, we provide an outlook on future applications that could benefit from origami and kirigami to create intrinsically curved surfaces.

Design and motion analysis of axisymmetric 3D origami with generic six-crease bases

Origami, also known as paper folding, has shown its potential to construct 3D structures from designed crease patterns on a flat sheet. This paper proposes a method to design axisymmetric 3D origami with generic six-crease bases. Inspired by the conventional six-crease bases, i.e., waterbomb base or Yoshimura base, where six regular crease lines meet at an interior vertex, we generalize the generic base so that the lengths of the crease lines can be regular or irregular. This method is based on designing the crease patterns. First, we interactively generate a crease pattern consisting of such generic bases. Then, our method analytically calculates the 3D origami shape with an axisymmetric structure. We demonstrate various configurations, i.e., sets of input parameters, to explore the variations of the calculated 3D origami. The 3D origami can have multiple degrees of freedom, but by continually changing one parameter we present a motion that can axisymmetrically deploy or flatten the shape. The method for designing 3D origami has potential applications ranging from self-folding tessellations to deployable architectures.

A crawling robot driven by multi-stable origami

Using origami folding to construct and actuate mechanisms and machines offers attractive opportunities from small, scalable, and cheap robots to deployable adaptive structures. This paper presents the design of a bio-inspired origami crawling robot constructed by folding sheets of paper. The origami building block structure is based on the Kresling crease pattern (CP), a chiral tower with a polygonal base, which expands and contracts through coupled longitudinal and rotational motion similar to a screw. We design the origami to have multi-stable structural equilibria which can be tuned by changing the folding CP. Kinematic analysis of these structures based on rigid-plates and hinges at fold lines precludes the shape transformation associated with the bistability of the physical models. To capture the kinematics of the bi-stable origami, the panels’ deformation behavior is modeled utilizing principles of virtual folds. Virtual folds approximate material bending by hinged, rigid panels, which facilitates the development of a kinematic solution via rigid-plate rotation analysis. As such, the kinetics and stability of folded structures are investigated by assigning suitable torsional spring constants to the fold lines. The results presented demonstrate the effect of fold-pattern geometries on the snapping behavior of the bi-stable origami structure based on the Kresling pattern. The crawling robot is presented as a case study for the use of this origami structure to mimic crawling locomotion. The robot is comprised of two origami towers nested inside a paper bellow, and connected by 3D printed end plates. DC motors are used to actuate the expansion and contraction of the internal origami structures to achieve forward locomotion and steering. Beyond locomotion, this simple design can find applications in manipulators, booms, and active structures.

Finite element analysis of the press forming process

Press forming is one of the most suitable paperboard converting techniques to produce deep trays. However, during the forming, severe deformations occur in the tray corners, which can cause cracks and other defects that deteriorate the tray. Formability can be enhanced with creases which assist the folding of the paperboard blank. In this paper, we study the press forming process with the aid of finite element simulations. We focus especially on the effect of creases on the formability. The effects of different materials are also compared. The finite element model consists of a male die, female die, blank holder and paperboard blank. The paperboard is modeled as an orthotropic elastoplastic material. Hill’s yield criterion with isotropic hardening is used to define the plastic behavior. Hinge connector elements are used to model the creases. The modeling is complemented by experimental studies. The results obtained from the finite element analysis show that high localized strains occur in paperboard tray corners during forming and that the intensity and areal size of the strains can be decreased with creases. It is concluded that the developed model can be used to compare different crease patterns which, in turn, enables better crease pattern design.

String actuated curved folded surfaces

Curved folded surfaces, given their ability to produce elegant freeform shapes by folding flat sheets etched with curved creases, hold a special place in computational Origami. Artists and designers have proposed a wide variety of different fold patterns to create a range of interesting surfaces. The creative process, design, as well as fabrication is usually only concerned with the static surface that emerges once folding has completed. Folding such patterns, however, is difficult as multiple creases have to be folded simultaneously to obtain a properly folded target shape. We introduce string actuated curved folded surfaces that can be shaped by pulling a network of strings, thus, vastly simplifying the process of creating such surfaces and making the folding motion an integral part of the design. Technically, we solve the problem of which surface points to string together and how to actuate them by locally expressing a desired folding path in the space of isometric shape deformations in terms of novel string actuation modes. We demonstrate the validity of our approach by computing string actuation networks for a range of well-known crease patterns and testing their effectiveness on physical prototypes. All the examples in this article can be downloaded for personal use from http://geometry.cs.ucl.ac.uk/projects/2017/string-actuated/.

String Actuated Curved Folded Surfaces

Curved folded surfaces, given their ability to produce elegant freeform shapes by folding flat sheets etched with curved creases, hold a special place in computational Origami. Artists and designers have proposed a wide variety of different fold patterns to create a range of interesting surfaces. The creative process, design, as well as fabrication is usually only concerned with the static surface that emerges once folding has completed. Folding such patterns, however, is difficult as multiple creases have to be folded simultaneously to obtain a properly folded target shape. We introduce string actuated curved folded surfaces that can be shaped by pulling a network of strings, thus, vastly simplifying the process of creating such surfaces and making the folding motion an integral part of the design. Technically, we solve the problem of which surface points to string together and how to actuate them by locally expressing a desired folding path in the space of isometric shape deformations in terms of novel string actuation modes. We demonstrate the validity of our approach by computing string actuation networks for a range of well-known crease patterns and testing their effectiveness on physical prototypes. All the examples in this article can be downloaded for personal use from http://geometry.cs.ucl.ac.uk/projects/2017/string-actuated/.

Newborn and infant discrimination: revisiting footprints

ABSTRACTFormal registration of newborns and infants is a necessity to secure their rights for health care or education and to support law enforcement agencies in the fight against the trafficking of children or their illegal adoption. Ideally, all these requirements can be met using a newborn and infant biometric. Difficulties arise due to the small size and fragility of the infants’ physical structures and the effects of rapid physical growth. We review the literature for suitable biometrics and investigate the footprint; asking (a) if there is a time frame shortly after birth when the friction ridge skin pattern of a newborn can be reliably captured; and (b) if the footprint crease pattern is a suitable newborn and infant biometric. For (a), we were unable to confirm the existence of such a time frame. For (b), we performed automatic verification experiments on a small test set of 20 pairs of crease patterns, and then a larger test set, achieving EERs of 22.22% and 46.39%, respectively. The comparison of two dizygotic twins did not show any noteworthy performance difference. Based on these results we do not recommend the foot crease pattern as a newborn or infant biometric for automatic verification.

String Actuated Curved Folded Surfaces

Curved folded surfaces, given their ability to produce elegant freeform shapes by folding flat sheets etched with curved creases, hold a special place in computational Origami. Artists and designers have proposed a wide variety of different fold patterns to create a range of interesting surfaces. The creative process, design, as well as fabrication is usually only concerned with the static surface that emerges once folding has completed. Folding such patterns, however, is difficult as multiple creases have to be folded simultaneously to obtain a properly folded target shape. We introduce string actuated curved folded surfaces that can be shaped by pulling a network of strings, thus, vastly simplifying the process of creating such surfaces and making the folding motion an integral part of the design. Technically, we solve the problem of which surface points to string together and how to actuate them by locally expressing a desired folding path in the space of isometric shape deformations in terms of novel string actuation modes. We demonstrate the validity of our approach by computing string actuation networks for a range of well-known crease patterns and testing their effectiveness on physical prototypes. All the examples in this article can be downloaded for personal use from http://geometry.cs.ucl.ac.uk/projects/2017/string-actuated/.

Self-folding origami at any energy scale

Programmable stiff sheets with a single low-energy folding motion have been sought in fields ranging from the ancient art of origami to modern meta-materials research. Despite such attention, only two extreme classes of crease patterns are usually studied; special Miura-Ori-based zero-energy patterns, in which crease folding requires no sheet bending, and random patterns with high-energy folding, in which the sheet bends as much as creases fold. We present a physical approach that allows systematic exploration of the entire space of crease patterns as a function of the folding energy. Consequently, we uncover statistical results in origami, finding the entropy of crease patterns of given folding energy. Notably, we identify three classes of Mountain-Valley choices that have widely varying ‘typical’ folding energies. Our work opens up a wealth of experimentally relevant self-folding origami designs not reliant on Miura-Ori, the Kawasaki condition or any special symmetry in space.

Investigation of hindwing folding in ladybird beetles by artificial elytron transplantation and microcomputed tomography

Ladybird beetles are high-mobility insects and explore broad areas by switching between walking and flying. Their excellent wing transformation systems enabling this lifestyle are expected to provide large potential for engineering applications. However, the mechanism behind the folding of their hindwings remains unclear. The reason is that ladybird beetles close the elytra ahead of wing folding, preventing the observation of detailed processes occurring under the elytra. In the present study, artificial transparent elytra were transplanted on living ladybird beetles, thereby enabling us to observe the detailed wing-folding processes. The result revealed that in addition to the abdominal movements mentioned in previous studies, the edge and ventral surface of the elytra, as well as characteristic shaped veins, play important roles in wing folding. The structures of the wing frames enabling this folding process and detailed 3D shape of the hindwing were investigated using microcomputed tomography. The results showed that the tape spring-like elastic frame plays an important role in the wing transformation mechanism. Compared with other beetles, hindwings in ladybird beetles are characterized by two seemingly incompatible properties: (i) the wing rigidity with relatively thick veins and (ii) the compactness in stored shapes with complex crease patterns. The detailed wing-folding process revealed in this study is expected to facilitate understanding of the naturally optimized system in this excellent deployable structure.

Effect of Cyclic Loading on Surface Instability of Silicone Rubber under Compression.

This work combines experiments and finite element simulations to study the effect of pre-imposed cyclic loading on surface instability of silicon rubber under compression. We first fabricate cuboid blocks of silicon rubber and pinch them cyclicly a few times. Then, an in-house apparatus is set to apply uniaxial compression on the silicon rubber under exact plane strain conditions. Surprisingly, we find multiple creases on the surface of silicone rubber, significantly different from what have been observed on the samples without the cyclic pinching. To reveal the underlying physics for these experimentally observed multiple creases, we perform detailed nanoindentation experiments to measure the material properties at different locations of the silicon rubber. The modulus is found to be nonuniform and varies along the thickness direction after the cyclic pinching. According to these experimental results, three-layer and multilayer finite element models are built with different materials properties informed by experiments. The three-layer finite element model can excellently explain the nucleation and pattern of multiple surface creases on the surface of compressed silicone rubber, in good agreement with experiments. Counterintuitively, the multilayer model with gradient modulus cannot be used to explain the multiple creases observed in our experiments. According to these simulations, the experimentally observed multiple creases should be attributed to a thin and stiff layer formed on the surface of silicon rubber after the pre-imposed cyclic loading.

Buckling of an Elastic Ridge: Competition between Wrinkles and Creases.

We investigate the elastic buckling of a triangular prism made of a soft elastomer. A face of the prism is bonded to a stiff slab that imposes an average axial compression. We observe two possible buckling modes which are localized along the free ridge. For ridge angles ϕ below a critical value ϕ^{⋆}≈90°, experiments reveal an extended sinusoidal mode, while for ϕ above ϕ^{⋆}, we observe a series of creases progressively invading the lateral faces starting from the ridge. A numerical linear stability analysis is set up using the finite-element method and correctly predicts the sinusoidal mode for ϕ≤ϕ^{⋆}, as well as the associated critical strain ε_{c}(ϕ). The experimental transition at ϕ^{⋆} is found to occur when this critical strain ε_{c}(ϕ) attains the value ε_{c}(ϕ^{⋆})=0.44 corresponding to the threshold of the subcritical surface creasing instability. Previous analyses have focused on elastic crease patterns appearing on planar surfaces, where the role of scale invariance has been emphasized; our analysis of the elastic ridge provides a different perspective, and reveals that scale invariance is not a sufficient condition for localization.

Design of rigid-foldable doubly curved origami tessellations based on trapezoidal crease patterns.

This paper presents a mathematical framework for the design of rigid-foldable doubly curved origami tessellations based on trapezoidal crease patterns that can simultaneously fit two target surfaces with rotational symmetry about a common axis. The geometric parameters of the crease pattern and the folding angles of the target folded state are determined through a set of combined geometric and constraint equations. An algorithm to simulate the folding motion of the designed crease pattern is provided. Furthermore, the conditions and procedures to design folded ring structures that are both developable and flat-foldable and stacked folded structures consisting of two layers that can fold independently or compatibly are discussed. The proposed framework has potential applications in designing engineering doubly curved structures such as deployable domes and folded cores for doubly curved sandwich structures on the aircraft.

Self-Foldability of Rigid Origami

When actuating a rigid origami mechanism by applying moments at the crease lines, we often confront the bifurcation problem where it is not possible to predict the way the model will fold when it is in a flat state. In this paper, we develop a mathematical model of self-folding and propose the concept of self-foldability of rigid origami when a set of moments, which we call a driving force, are applied. In particular, we desire to design a driving force such that a given crease pattern can uniquely self-fold to a desired mode without getting caught in a bifurcation. We provide necessary conditions for self-foldability that serve as tools to analyze and design self-foldable crease patterns. Using these tools, we analyze the unique self-foldability of several fundamental patterns and demonstrate the usefulness of the proposed model for mechanical design.