Flattening surfaces of polyhedral solids and continuous flat foldings
Project/Area Number |
16K05258
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Foundations of mathematics/Applied mathematics
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Research Institution | Meiji University |
Principal Investigator |
Nara Chie 明治大学, 研究・知財戦略機構, 客員教授 (40147898)
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Co-Investigator(Kenkyū-buntansha) |
伊藤 仁一 椙山女学園大学, 教育学部, 教授 (20193493)
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Project Period (FY) |
2016-04-01 – 2019-03-31
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Project Status |
Completed (Fiscal Year 2018)
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Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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Keywords | 多面体 / 折り目 / 平坦化 / 折り畳み / 多胞体 / 剛体折り / 連続的折り畳み / 高次元正多面体 / 剛体折 / ヒンジ / 厚板パネル / 連続変形 / 剛性 |
Outline of Final Research Achievements |
The mission of developping foldable products is increasing not only in daily necessities but also the space and medical engeneering. We worked for the problem on continuous flattening of polyhedra and focused on showing mathematical expression of such motions. In this research we could show continuous flattening motion for many types of polyhedra and moreover, gave such motion under the assumption that some faces and edges of a given polyhedron are rigid. In the case of orthogonal polyhedra we studied to flatten them when their faces are made of thick panels. Moreover, we extended some results in three-dimesional polyhedra to high-dimensional polytopes and gave some results for hypercubes and others.
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Academic Significance and Societal Importance of the Research Achievements |
折り畳み式製品の開発には数理的構造の解明が重要である。もし,多面体のすべての面を剛性素材にすると,2面の交角を変化させただけでは体積が変化しないことが知られている。そこで,本研究では,一部の面の形状を折り目によって変形させるという方法によって,連続的平坦化の過程を種々の多面体について明らかにした。 しかし,一般的な多面体について,どのようにして連続的に平坦折り畳み状態に到達できるかを示すことは困難で未解決である。そこで,応用上有用と思われる条件を設定して,種々の多面体について平坦折り畳みの具体的な連続的変形過程を明らかにした。また,高次元多胞体についてこの問題を拡張する一つの手がかりを与えた。
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Report
(4 results)
Research Products
(90 results)
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[Journal Article] Continuous flattening of orthogonal polyhedra2016
Author(s)
Erik Demaine, Martin Demaine, Jin-ichi Itoh, Chie Nara
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Journal Title
Revised Selected Papers of JCDCGG 2015, J. Akiyama et al. (eds.) LNCS, vol. 9943, Springer-Heidelberg
Volume: LNCS, vol. 9943
Pages: 85-93
DOI
ISBN
9783319485317, 9783319485324
Related Report
Peer Reviewed / Open Access / Int'l Joint Research
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[Journal Article] Norigami folding machines for complex 3D shapes2016
Author(s)
J. Romelo, L. A. Diago, J. Shinoda, C. Nara, I. Hagiwara
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Journal Title
Proceedings of the ASME 2016 International Design Engineering Technical Conferences &Computers and Information in Engineering Conference
Volume: 5B: 40th Mec. & Robotics Conf.
DOI
Related Report
Peer Reviewed / Open Access / Int'l Joint Research
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[Journal Article] Thread construction revisited2016
Author(s)
Jin-ichi Itoh, Kazuyoshi Kiyohara
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Journal Title
Journal of the Mathematical Society of Japan
Volume: 68
Issue: 3
Pages: 917-938
DOI
NAID
ISSN
0025-5645, 1881-1167, 1881-2333
Related Report
Peer Reviewed / Open Access
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[Presentation] 最小跡と直観幾何学2017
Author(s)
伊藤仁一
Organizer
研究集会「測地線および関連する諸問題」
Place of Presentation
熊本大学(熊本県・熊本市)
Year and Date
2017-01-07
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