Abstract : Discussions on topics related to origami engineering will take place at this mini-symposium. Presenters will present their research aimed at applying the technology of origami, the folding of flat materials to create shapes, to engineering, and exploring the geometric properties of origami from a mathematical perspective to explore its range of applications.
Organizer(s) : Jun Mitani, Sachiko Ishida, Kazuya Saito
[01360] Farthest point map on the double cover of a parallelotope
Author(s) :
Yoshikazu Yamagishi (Ryukoku University)
Sayaka Ueda (Ryukoku University)
Abstract : We describe the source unfolding on the double cover of a parallel polytope of dimension n. Suppose two persons p,q play the squash in a parallelotope. Where is the farthest point q from a given point p? What happens if they keep playing the squash by choosing the farthest points? It is shown that the limit set is a union of quadratic curves.
[01518] Deployable earwig fan dome with the algorithmic design tool
Author(s) :
Chisaki KITAJIMA (Kyushu University)
Kazuya Saito (Kyushu University)
Abstract : Earwigs can fold their wing most compactly of all insects, therefore the characteristics have potential for engineering applications. In previous studies, we have already revealed how to design the crease pattern of the earwigs fan. Here we show a method to create three-dimensional forms from the folding simulation of the earwig fan with an algorithmic design tool. Furthermore, we propose to design compactly foldable dome-shape structures based on crease pattern of earwig fan.
[01519] Geometry and mechanics of molting in snakes and caterpillars
Author(s) :
Taiju Yoneda (Kyushu University)
Kazuya Saito ( Kyushu University)
Abstract : Snakes and caterpillars have longer bodies and grow by molting, but the molting process is different.
Snakes molt by reversing the front and back of their skin. In the molting of caterpillars, their skin is folded with buckling.
Which mode is expected to be determined by geometric factors such as thickness and mechanical factors such as friction. We quantify these boundary conditions using a combination of buckling experiments and finite element method with cylindrical shell models.
[01523] Linear transformation of crease pattern boundaries preserving internal graph isomorphisms
Author(s) :
Yohei Yamamoto (University of Tsukuba)
Jun Mitani (University of Tsukuba)
Abstract : A crease pattern whose boundaries are similar before and after flat-folding can be tiled to create larger origami works. In order to increase the variation, linearly transforming the boundary shape is a useful approach, but if the entire crease pattern is transformed, the flat-foldability is not maintained. We propose a method for linear transformation of the boundaries while preserving internal graph isomorphisms. The characteristics of generated crease patterns and the folded states are discussed.
[01536] Refoldability between polyhedra
Author(s) :
Tonan Kamata (Japan Advanced Institute of Science and Technology)
Abstract : Refolding is an operation of reshaping a polyhedron into a polyhedron by cutting open the surface of the original one and folding the resulting unfolding to make the other one. Refolding is a natural subject with applications in space engineering, design engineering, and bioinformatics, but the known result is not so much. In this talk, we will present design methods of refolding for some specific classes of polyhedra and the possibility of reconfiguration by refoldings.
[01559] 3D auxetics made from non-euclidean rigid origami vertex duality
Author(s) :
Thomas C Hull (Western New England University)
Abstract : New equations relating flexible rigid origami folding angles have revealed a duality among non-Euclidean degree-4 vertices. I.e., for every degree-4 vertex that is elliptic, with $<360^\circ$ of paper, there is a corresponding hyperbolic degree-4 vertex, with $>360^\circ$ around it, that has the same kinematics. We will see why this is true and construct new auxetic 3D structures from combined elliptic-hyperbolic vertices.
[01618] Strip folding as Boolean matrix algebra and its Categorical Meanings
Author(s) :
Yiyang Jia (Seikei University)
Jun Mitani (University of Tsukuba)
Abstract : Strip folding, known as map folding in the one-dimensional case, derives from a classical flat-foldability decision problem in the field of computational origami. In this manuscript, different from the existing computational and algorithmic methodology, we investigate strip folding using abstract algebraic language and then characterize it from a categorical viewpoint. We first present a boolean matrix description of strip folding, based on which we then build the category of strip folding. This category gives rise to a natural meet semi-lattice structure. Furthermore, in this category, every product exists. We use the right adjoint functor of the diagonal functor to define these products. Furthermore, the definition of products can be used to build a Grothendieck topology in the space of flatly folded states. Our result shows that the analysis of strip folding can be associated with contemporary mathematical methodologies such as category theory and algebraic geometry.
[02328] Application of the proposed method to a transport origami box
Author(s) :
Toshie Sasaki (Meiji University)
Yang Yang (Meiji University)
Ichiro Hagiwara (Meiji University)
Abstract : Fruits and vegetables are damaged during transportation because there is a mortal frequency band for each transport. We propose a new method named “Energy Density Topology Changing Method” based on the fact that the eigen frequency is determined by equivalent stiffness and equivalent mass. We demonstrate the effectiveness of this method by showing that it can be successfully applied to a transport origami box which cannot be applied by conventional topology optimization method.
[02335] Geometrical Comparison of Two kinds of Pairing Origami Polyhedron and Their Application to Beverage Containers
Author(s) :
Aya Abe (Meiji University)
Yang Yang (Meiji University)
Chie Nara (Meiji University)
Ichiro Hagiwara (Meiji University)
Abstract : Tachi-Miura Polyhedron is gaining attention as a 3-dimensional version of Miura-Ori. Meanwhile, Nojima Polyhedron is similar as TMP in that it can be folded both in the axial and radial direction. In this study, whether both are rigid folding or not is geometrically confirmed, and quantitatively considered how it affects the energy absorption properties. As a result, it effects the deformation modes but does not affect the purpose of investigating the feasibility of industrialization.
[02536] Platonic solids-based optimization for kirigami honeycomb fabrication of complex structures
Author(s) :
Junichi Shinoda (Interlocus CO.LTD)
Keiko Yamazaki (Meiji University)
Ichiro Hagiwara (Meiji University)
Luis Diago (Meiji University)
Abstract : The aerospace, automotive, and marine industries are heavily reliant on sandwich panels with cellular material cores. In this work, a platonic solids-based optimization algorithm has been developed to select the direction of the cells of the kirigami-honeycomb panel with the smallest waste of materials by rotating the 3D solid model of any shape according to the normal vectors in the platonic solids.
[02542] Development of beautifully foldable PET bottles
Author(s) :
Yang Yang (Meiji University)
Chie Nara (Meiji University)
Ichiro Hagiwara (Meiji University)
Abstract : Although many have attempted to develop a PET bottle that is foldable in the axial direction without bending, such bottles are not yet on the market. This is because that although the model with several foldable layers can be folded rather easily without bending, it springs back to almost its original height after compression. Thus, we develop new types of PET bottle with two or three spiral layers to resolve this spring back issue.
[05407] Optimal Simple Fold-and-Cut of a Polygonal Line
Author(s) :
Ryuhei Uehara (Japan Advanced Institute of Science and Technology)
Abstract : We investigate a natural variant of the fold-and-cut problem. We are given a long paper strip P and a polygonal line, which consists of a sequence of line segments, drawn on P. We cut all the line segments by one complete straight cut after overlapping all of them by a sequence of simple foldings. Our goal is to minimize the number of simple foldings to do that. When the polygonal line satisfies some certain geometric conditions, we can find a shortest sequence of simple foldings for the given polygonal line that consists of n line segments in O(n^3) time and O(n^2) space.
