基于折纸的圆柱及圆台薄膜折叠设计及分析

Origami-inspired folding analysis on the membrane structure of the cylinder and the circular truncated cone

为减小航天器的遮光罩和热屏蔽的占用体积,基于折纸的基本规则和特点,设计一种圆柱面及圆台面薄膜的折叠方式。对圆柱面折叠过程进行分析及计算,推导出将圆柱面折叠成平面图形的角度约束和高度约束,并建立该折叠方式折痕的数学模型,在该模型下圆柱面折叠后截面为正多边形。在此基础上对圆台面折叠方式进行了类比分析,推导出将圆台面折叠成平面图形的角度约束和高度约束,并建立该折叠方式折痕的数学模型,在该模型下圆台面折叠后截面为正多边形。两个数学模型为航天器的遮光罩和热屏蔽等圆柱面或圆台面结构提供了一种可设计的折叠方式,该方式不同于已有的固定式或者伞形轴向展开式,可以大大减小相关结构所占用的体积,对遮光罩和热屏蔽等薄膜结构的设计具有参考意义。

This article,with a view to small volume occupied by the spacecraft’s lens hood and heat shield,focuses on the origami-inspired folding design of membrane structure of the cylinder and the circular truncated cone. The analysis is conducted on the folding process of the cylindrical surface,in order to identify the conditions of folding the cylindrical surface into a plane with regular polygons,and thus work out the mathematical model of the crease. Accordingly,the analysis is conducted on the folding process of the circular truncated cone,in order to identify the conditions of folding the circular truncated cone into a plane with regular polygons,and thus work out the mathematical model of the crease. These two mathematical models provide a new folding method for membrane structure of the cylinder and the circular truncated cone,such as the spacecraft’s lens hood and heat shield and so on,which greatly ensures small volume occupied by the related systems. Furthermore,it renders reference for the design of membrane structure,for example,the spacecraft’s lens hood and heat shield.