The Five-hundred-meter Aperture Spherical radio Telescope (FAST) is the largest single-dish aperture telescope with a cable-driven parallel robot introduced to achieve the highest sensitivity in the world. However, to realize the high-precision, mechanical equations of such a robot are always complicated, so that it is difficult to achieve real-time control by the traditional iterative method. In this regard, this paper proposes an approximately analytical solution method, which uses the approximately linear relationship between the main parameters of FAST to bypass some iterations. With the coefficients of the relationship extracted, static or quasi-static mechanical equations can be analytically solved. In this paper’s example, this method saves at least 90% of the calculating time and the calculated values are consistent with the experimental data. With such huge efficiency improvements, real-time and high-precision control of the FAST will no longer be difficult work. Besides, all the work in this paper is expected to be used in the FAST.

五百米口径球面射电望远镜（FAST）是世界上最大的单碟口径射电望远镜，引入了电缆驱动的并联机器人，以达到世界上最高的灵敏度。然而，为了实现高精度，这种机器人的机械方程总是很复杂，传统的迭代方法难以实现实时控制。对此，本文提出了一种近似解析解法，利用FAST的主要参数之间的近似线性关系来绕过一些迭代。通过提取关系系数，可以解析求解静态或准静态力学方程。在本文的例子中，该方法至少节省了90%的计算时间，计算值与实验数据一致。有了如此巨大的效率提升，FAST 的实时高精度控制将不再是困难的工作。此外，本文中的所有工作都有望在 FAST 中使用。