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Construction of Unknotted and Knotted Symmetric Developable Bands
https://oist.repo.nii.ac.jp/records/1996
https://oist.repo.nii.ac.jp/records/199698ad84df-79db-4557-a012-c8d483fcd30e
名前 / ファイル | ライセンス | アクション |
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Schönke-2021-Construction of Unknotted and Kno (10.7 MB)
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Creative Commons Attribution 4.0 International(https://creativecommons.org/licenses/by/4.0/)
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Item type | 学術雑誌論文 / Journal Article(1) | |||||
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公開日 | 2021-03-23 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | Construction of Unknotted and Knotted Symmetric Developable Bands | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | structural scaffolds | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | orientable and nonorientable surfaces | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | torus knots | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | interior design | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | pure bendings | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | elastic bending energy | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | journal article | |||||
著者(英) |
Schönke, Johannes
× Schönke, Johannes× Grunwald, Michael× Fried, Eliot |
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書誌情報 |
en : Symmetry 巻 13, 号 3, p. 431, 発行日 2021-03-07 |
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抄録 | ||||||
内容記述タイプ | Other | |||||
内容記述 | We describe a method for constructing developable bands with N ≥ 3 half twists. Each band is formed by threading a flat rectangular strip through a scaffold made from identical circular cylinders and smoothly connecting its short ends. The N cylinders in a scaffold are arranged with N-fold rotational symmetry. The number of half twists in a band is equal to the number N of cylinders in its scaffold and each band inherits the symmetry of its scaffold. Each scaffold admits a family of bands of the same length but variable width up to a maximum value determined by the features of the scaffold. Apart from orientable and nonorientable unknots, our method allows for the construction of bands with the topology of torus knots. We detail the geometric properties of the construction, discuss certain fundamental restrictions that must be met to ensure constructability, and calculate the elastic bending energy of each band. The rotational symmetry underlying the construction is essential for obtaining the presented bands, as the general non-symmetric problem is even more complex and has not yet been investigated. The bands and their corresponding scaffolds can be used as structural elements in practical applications, one of which we describe and analyze. The construction serves as a basis for a general framework for building a large variety of scaffolds and the corresponding unstretchable bands. Together, these assemblies can be used in architectural, interior, and machine design. They also open new avenues for the layout of conveyor belts in factories, airports, and other settings. | |||||
出版者 | ||||||
出版者 | MDPI | |||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 2073-8994 | |||||
DOI | ||||||
関連タイプ | isIdenticalTo | |||||
識別子タイプ | DOI | |||||
関連識別子 | info:doi/10.3390/sym13030431 | |||||
権利 | ||||||
権利情報 | © 2021 The Author(s). | |||||
関連サイト | ||||||
識別子タイプ | URI | |||||
関連識別子 | https://www.mdpi.com/2073-8994/13/3/431 | |||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 |