Session: MR-04-03 Origami-Based Engineering Design

Paper Number: 70089

Start Time: August 19, 03:20 PM

70089 - Method for Generating Mechanical Linkages of Polygons That Fold Into a Similar Shape 

 Origami is the traditional Japanese craft of creating shapes by folding paper, and is comprised of folding techniques that have a mathematical foundation. In recent years, there has been a lot of applied research into using these folding techniques in structures that involve a mechanism for shrinking and deploying by folding and unfolding. The origami crease patterns are called rigid foldable when they can be folded without stretching or bending the faces. The rigid foldability is essential for applying origami techniques for mechanical structures.

 Known rigid foldable crease patterns include the Miura-ori, Waterbomb base, and the Yoshimura pattern. A linkage mechanism can be created by replacing the facets of the rigid foldable crease pattern with panel-shaped links and the crease lines with hinge joints. These mechanisms have been used in mechanical structures. Against this background, increasing a wider variety of rigid foldable crease patterns is useful for broadening the range of applications of origami.

 When multiple shrinkable units are combined to make a structure, it is important that the individual units are transformed to a similar shape. There are some known ways of folding a polygon into a similar shape. However, these crease patterns are not all rigid foldable.

 The present paper extends an existed method to make arbitrary polygons to be rigidly flat foldable. Furthermore, how to generate the crease patterns that can be folded as smaller as possible is also discussed.

 The patterns obtained by the proposed method are called shrinkable patterns, and the structures consists of panels and hinges created from the shrinkable patterns are called shrinkable structures. In addition to being rigid foldable, the shrinkable structures proposed in this paper also have the following features.

- They can be generated from any arbitrary polygon, and the shape during the folding process is always similar when viewed from above.

- They can be folded with one degree of freedom (1DOF).

Since the shrinkable structures transform with 1DOF, the folding process of these structures is easy to control. Furthermore, since the shape during folding process is always similar, shrinkable 3D polyhedral structures can be created by connecting them. Although it has been shown by the bellows conjecture that it is impossible to deform a closed polyhedron by rigid folding in such a way as to change the volume, since the proposed three-dimensional structures have slits, volume reduction becomes possible.

 This kind of structure is expected to be employed in various fields including in portable container design and in construction. For such applications, it is generally thought to be desirable to have a feature than can fold up to be as small as possible. In this paper, the design parameters that maximize the shrinkage ratio, the ratio of the area reduced by folding to the original area, is also discussed.

 The procedure proposed in this paper for creating a shrinkable pattern from any arbitrary polygon is as follows.

(1) Divide the polygon into a tiling of inscribed polygons containing their circumcenter on the inside (called modules).

(2) Divide each of the module into a set of right-angle triangles (called unit) by using lines from the circumcenter to each vertex and the center point of each side.

(3) Generate the crease pattern on each unit based on the triangle twist fold which is folded into flat.

(4) The crease pattern of a module is formed by combining units. Then, the overall crease pattern on the target polygon is formed by combining modules.

The presented paper describes details of the above processes, and presents the method for obtaining the design parameters for the largest shrinkage ratio. Further, the creation of shrinkable structures and 3D printing are presented. As a result, the crease patterns, and the structures that have a shrinking mechanism with rigid panels and hinges are obtained.

Presenting Author: Yohei Yamamoto University of Tsukuba

Authors:

Yohei Yamamoto University of Tsukuba
Jun Mitani University of Tsukuba