Abstract In this paper, the operability of the most recent method to design bistable and non-bistable deployable scissors structures (the method of the convergence surface) is extended and this operability will be divided into two types of formulas: The exact formula and the approximate formulas. The exact formula involves the obtaining of the convergence surface using its own equations and this paper will prove that this surface is a triaxial two-leaf hyperboloid (for translational units) and a non-standard surface (for polar units). On the other hand, the approximate formulas are designed due to the need to obtain the convergence surface when the exact formula cannot be used. Finally, this research will demonstrate the potential of these approximate strategies to compete against the exact formulas and to boost an improvement in the mathematical results in terms of precision in the scissor design and speed in the calculation process.

中文翻译：

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可展开剪刀结构设计的收敛面法

摘要 本文扩展了设计双稳态和非双稳态可展开剪刀结构的最新方法（收敛面法）的可操作性，并将这种可操作性分为两类：精确公式和近似公式。公式。确切的公式涉及使用其自己的方程获得收敛面，本文将证明该表面是三轴双叶双曲面（用于平移单元）和非标准表面（用于极轴）。另一方面，由于在无法使用精确公式时需要获得收敛面，因此设计了近似公式。最后，