Method for Generating Mechanical Linkages of Polygons that Fold into a Similar Shape

Abstract

Origami techniques, as folding and unfolding, can be utilized in shrinkable structures. Especially when the crease pattern is rigid foldable, it can be treated as a mechanical linkage of rigid panels connected by hinges. Since rigid foldable crease patterns have the strong geometrical constraint of the facets not being able to stretch or bend, it is difficult to design new crease patterns, and variations of existing patterns are limited. However, it is known that there are cases where crease patterns can be made rigid foldable by adding some slits. This paper proposes a mechanical linkage that folds into a similar flat shape by adding slits. A method is presented of generating rigid foldable crease patterns in arbitrary polygons that fold smaller, and it is confirmed that structures that have a mechanism for shrinking can be generated from these crease patterns by using rigid thick panels and hinges.

概要

折り紙の技術は，折りたたみと展開による伸縮機構を持つ構造物に活用できる．特に，折りたたむ過程で折り線に囲まれた領域を伸縮・湾曲させない折り線の集合（展開図）は，剛体のパネルをヒンジで接続したリンク機構として扱える．こうした制約は，剛体可折と呼ばれ，幾何的に厳しい制約であることが知られている．そのため，剛体可折な展開図は，新しいものを設計することが難しく，既存のパターンのバリエーションも限られている．本研究では，展開図にスリットを追加することで剛体可折できる場合があることに着目し，スリットを有し，境界を相似な形に折りたためる剛体可折な展開図のパターンを提案した．任意の多角形を，提案するパターンでできるだけ小さく折りたたむ方法を提案する他，同パターンを活用することで，剛体の素材をヒンジで接続したリンク機構が生成できることを確認した．

Proposed Mechanical Linkages

overview

Purpose

Enrich the shrinkable mechanical linkage

Features

  1. Mechanical linkage of rigid panels connected by hinges
    • Generatable from any arbitrary polygon
  2. During the folding process, the shape seen from above is similars
    • The shape is similar to the original polygon
  3. Foldable with one degree of freedoms
=> The linkage is called shrinkable structure.

Steps to generate a shrinkable structure

overview overview
  1. Divide the polygon into a tiling of modules
    • A module is an inscribed polygon containing its circumcenter on inside
  2. Generate the crease pattern on each module and combine them
    • The crease pattern is the pattern that allows to fold a given polygon as small as possible
  3. Generate the parts with thickness from each facet and connect them to each other

Contributions

overview overview
  • A shrinkable Polyhedron can be designed by replacing each facet of a polygon with a shrinkable structure.

overview
  • Connected rigid panels of existing mechanical linkage, like Miura-Ori, can be replaced with the shrinkable structures.

Video of 3D Printed Structures

Publications

国際会議

  • Yohei Yamamoto, Jun Mitani, "Method for Generating Mechanical Linkages of Polygons that Fold into a Similar Shape", ASME 2022 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Online, August, 2021.