{"title":"基于角接瓷砖的自由形式辅助机构","authors":"Kanata Warisaya, Jun Sato, Tomohiro Tachi","doi":"10.20898/j.iass.2022.020","DOIUrl":null,"url":null,"abstract":"Auxetic mechanisms based on corner-connected polygonal tiles have been used to design deployable structures and are currently applied to programmable surfaces. However, existing surface structures are realized by compliant kirigami, and the realization with rigid-body mechanism, in\n particular with thick panels, is still limited to configurations with global symmetries due to the mechanism's overconstraining nature. In this study, we generalize the auxetic mechanisms into freeform surfaces by imposing local symmetries on polyhedral surfaces. From the discussion of kinematics,\n we show that polyhedral surfaces whose edges coincide with a Voronoi diagram of points on the surface can be converted to kinematics systems of corner-connected kinematic tiles. We propose hard constraints to ensure the Voronoi property required for the kinematics and soft constraints to attain\n a large expansion ratio. Then, we provide an optimization-based scheme using the proposed constraints to achieve a mechanism from a given target surface. We also propose methods for accommodating the thickness of the tiles and show different variations of joints. As a result, we obtained deployable\n surfaces of positive and negative Gaussian curvature that can deploy and contract with a one-DOF mechanism. If the structure is viewed as a cellular material, it has an auxetic property with Poisson's ratio of -1. It is also potentially scalable to architectural applications because our mechanism\n is composed of rigid bodies and hinges.","PeriodicalId":42855,"journal":{"name":"Journal of the International Association for Shell and Spatial Structures","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Freeform Auxetic Mechanisms Based on Corner-Connected Tiles\",\"authors\":\"Kanata Warisaya, Jun Sato, Tomohiro Tachi\",\"doi\":\"10.20898/j.iass.2022.020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Auxetic mechanisms based on corner-connected polygonal tiles have been used to design deployable structures and are currently applied to programmable surfaces. However, existing surface structures are realized by compliant kirigami, and the realization with rigid-body mechanism, in\\n particular with thick panels, is still limited to configurations with global symmetries due to the mechanism's overconstraining nature. In this study, we generalize the auxetic mechanisms into freeform surfaces by imposing local symmetries on polyhedral surfaces. From the discussion of kinematics,\\n we show that polyhedral surfaces whose edges coincide with a Voronoi diagram of points on the surface can be converted to kinematics systems of corner-connected kinematic tiles. We propose hard constraints to ensure the Voronoi property required for the kinematics and soft constraints to attain\\n a large expansion ratio. Then, we provide an optimization-based scheme using the proposed constraints to achieve a mechanism from a given target surface. We also propose methods for accommodating the thickness of the tiles and show different variations of joints. As a result, we obtained deployable\\n surfaces of positive and negative Gaussian curvature that can deploy and contract with a one-DOF mechanism. If the structure is viewed as a cellular material, it has an auxetic property with Poisson's ratio of -1. It is also potentially scalable to architectural applications because our mechanism\\n is composed of rigid bodies and hinges.\",\"PeriodicalId\":42855,\"journal\":{\"name\":\"Journal of the International Association for Shell and Spatial Structures\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2022-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the International Association for Shell and Spatial Structures\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.20898/j.iass.2022.020\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, CIVIL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the International Association for Shell and Spatial Structures","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.20898/j.iass.2022.020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, CIVIL","Score":null,"Total":0}
Freeform Auxetic Mechanisms Based on Corner-Connected Tiles
Auxetic mechanisms based on corner-connected polygonal tiles have been used to design deployable structures and are currently applied to programmable surfaces. However, existing surface structures are realized by compliant kirigami, and the realization with rigid-body mechanism, in
particular with thick panels, is still limited to configurations with global symmetries due to the mechanism's overconstraining nature. In this study, we generalize the auxetic mechanisms into freeform surfaces by imposing local symmetries on polyhedral surfaces. From the discussion of kinematics,
we show that polyhedral surfaces whose edges coincide with a Voronoi diagram of points on the surface can be converted to kinematics systems of corner-connected kinematic tiles. We propose hard constraints to ensure the Voronoi property required for the kinematics and soft constraints to attain
a large expansion ratio. Then, we provide an optimization-based scheme using the proposed constraints to achieve a mechanism from a given target surface. We also propose methods for accommodating the thickness of the tiles and show different variations of joints. As a result, we obtained deployable
surfaces of positive and negative Gaussian curvature that can deploy and contract with a one-DOF mechanism. If the structure is viewed as a cellular material, it has an auxetic property with Poisson's ratio of -1. It is also potentially scalable to architectural applications because our mechanism
is composed of rigid bodies and hinges.
期刊介绍:
The Association publishes an international journal, the Journal of the IASS, four times yearly, in print (ISSN 1028-365X) and on-line (ISSN 1996-9015). The months of publication are March, June, September and December. Occasional extra electronic-only issues are included in the on-line version. From this page you can access one or more issues -- a sample issue if you are not logged into the members-only portion of the site, or the current issue and several back issues if you are logged in as a member. For any issue that you can view, you can download articles as .pdf files.