基于角接瓷砖的自由形式辅助机构

Kanata Warisaya, Jun Sato, Tomohiro Tachi
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引用次数: 1

摘要

基于角连接多边形瓷砖的辅助机构已用于设计可展开结构,目前应用于可编程表面。然而,现有的表面结构都是通过柔性基利格米实现的,而刚体机构的实现,特别是厚板的实现,由于机构的过度约束性质,仍然局限于具有全局对称性的构型。在本研究中,我们通过在多面体表面上施加局部对称性,将消弱机制推广到自由曲面。从运动学的讨论中,我们证明了边缘与表面上点的Voronoi图重合的多面体表面可以转换为角连接的运动瓦片的运动学系统。我们提出硬约束以保证运动学所需的Voronoi性质,并提出软约束以获得大的扩展比。然后,我们提供了一个基于优化的方案,使用提出的约束来实现给定目标表面的机制。我们还提出了适应瓷砖厚度的方法,并展示了接缝的不同变化。结果,我们得到了正高斯曲率和负高斯曲率的可展开曲面,它们可以通过一自由度机构展开和收缩。如果把这种结构看作是一种细胞物质,它就具有一种泊松比为-1的生性。它也有可能扩展到建筑应用,因为我们的机构是由刚体和铰链组成的。
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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.
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
17
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.
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