Branches of Triangulated Origami Near the Unfolded State
Branches of Triangulated Origami Near the Unfolded State
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DOI：
10.1103/physrevx.8.011034
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发表时间：
2018-02-27
影响因子：
12.5
通讯作者：
Santangelo, Christian D.
中科院分区：
文献类型：
--
作者：
Chen, Bryan Gin-ge;Santangelo, Christian D.
折纸结构的特点是由折叠和顶点连接不可弯曲的板的网络。对于机械设计和自折叠结构的应用，必须了解未折叠折纸中的折叠集和可能的3D折叠配置之间的相互作用。当变形的结构，已被折叠，人们往往可以线性化的几何约束，但退化的展开状态，使线性的方法是不可能的。我们推导出一个理论的二阶无穷小刚度的最初展开的三角形折纸结构，并用它来研究一组几乎展开的配置折纸与四个边界顶点。我们发现，本地，这组由一些不同的“分支”相交的展开状态，这些分支的数量是指数的顶点数。我们发现数值和分析证据表明，分支的特点是选择每个内部顶点要么“弹出”或“弹出”。人们可以折叠最初未折叠的折纸结构的大量路径沿着强烈地表明，通用结构可能陷入“错误折叠”状态。因此，创造自折叠折纸的新技术可能是必要的;控制顶点的弹出状态可能是一种可能性。
Origami structures are characterized by a network of folds and vertices joining unbendable plates. For applications to mechanical design and self-folding structures, it is essential to understand the interplay between the set of folds in the unfolded origami and the possible 3D folded configurations. When deforming a structure that has been folded, one can often linearize the geometric constraints, but the degeneracy of the unfolded state makes a linear approach impossible there. We derive a theory for the second-order infinitesimal rigidity of an initially unfolded triangulated origami structure and use it to study the set of nearly unfolded configurations of origami with four boundary vertices. We find that locally, this set consists of a number of distinct "branches" which intersect at the unfolded state, and that the number of these branches is exponential in the number of vertices. We find numerical and analytical evidence that suggests that the branches are characterized by choosing each internal vertex to either "pop up" or "pop down." The large number of pathways along which one can fold an initially unfolded origami structure strongly indicates that a generic structure is likely to become trapped in a "misfolded" state. Thus, new techniques for creating self-folding origami are likely necessary; controlling the popping state of the vertices may be one possibility.