  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 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 FAST will no longer be a difficult
work. Besides, all the work in this paper is expected to be used in the FAST.
