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为了满足空间任务对大口径及超大口径可展开天线的要求,根据天线背架与天线工作表面的形状特点,对抛物面型天线工作表面进行了球面拟合,提出了模块分层次拓扑的概念,分析了模块分层次拓扑的性质,给出了拓扑关系下模块数量的计算公式.在对平面进行正六边形模块划分的基础上,得到了平面关键点与其在球面投影的坐标关系,并基于齐次坐标变换方法,建立了单平面模块、多平面模块的正向拓扑几何模型,多平面模块的斜向拓扑几何模型,以及由六棱柱模块组成的构架式空间可展开天线背架的几何模型.通过算例对所建模型的分析及验证表明:该模型可以满足模块任意数量、任意大小的变化要求,能够实现模块间的无缝连接,从而为天线的结构设计以及背架展开状态的精度测量提供了理论参考.
In order to meet the requirements of large-caliber and large-caliber expandable antennas in space missions, the work surface of the parabolic antenna was spherically fitted according to the shape characteristics of the antenna back plane and the antenna working surface. The concept of hierarchical hierarchical topology was proposed and analyzed According to the nature of the hierarchical topology of the module, the formulas for calculating the number of modules under the topological relations are given. Based on the regular hexagonal module partitioning, the coordinate between the planar keypoints and their spherical projections is obtained. Based on the homogeneous Coordinate transformation method, the single-plane module, multi-planar module forward topology geometric model, multi-planar module diagonal topology geometry model, and the hexagonal prism modules can be deployed in the framework of space antenna backplane geometry model by The analysis and verification of the model show that the model can meet the requirements of any number and size of modules and can realize the seamless connection between the modules, so as to provide the structural design of the antenna and the measurement of the accuracy of the deployment state The theoretical reference.