This paper presents the process used to generate hyperboloid modules for deployable structures and the general equations for their design. These units are formed by three or more rods connected at a common articulated joint. During the opening process all the rods rotate in the same direction, and at the final unfolded stage each bar sits on its adjacent bar, activating a reciprocal self-locking system. The combination of these modules creates large span structures that can be folded in compact bundles. In this paper, the geometrical relationships between the dimensions of the elements to achieve a specific maximum opening angle is established. The connectivity between units is studied, as well as the requirements to achieve the maximum compactness of the grid at the folded stage.

中文翻译：

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可展开结构的双曲面模块

本文介绍了用于为可展开结构生成双曲面模块的过程及其设计的一般方程。这些单元由三个或更多杆连接在一个共同的铰接接头处形成。在打开过程中，所有杆都向同一方向旋转，在最后展开阶段，每个杆都位于相邻杆上，从而激活相互自锁系统。这些模块的组合创造了可以折叠成紧凑束的大跨度结构。在本文中，建立了实现特定最大张角的单元尺寸之间的几何关系。研究了单元之间的连通性，以及在折叠阶段实现网格最大紧凑性的要求。