Dimensional Optimization Design of the Four-Cable-Driven Parallel Manipulator in FAST

For the design of the five-hundred-meter aperture spherical radio telescope (FAST), a four-cable-driven parallel manipulator, which is long in span and heavy in weight, is adopted as the first-level adjustable feed-support system. The purpose of this paper is to optimize dimensions of the four-cable-driven parallel manipulator to meet the workspace requirement of constraint condition in terms of cable tension and stiffness. Accordingly, this optimization method adopts catenary simplification in order to set up the cable tension equilibrium equations, preliminarily optimizing three important dimensional parameters. Stiffness of the cable is also taken into consideration because of its effect on work performance of a cable-driven parallel manipulator. However, the stiffness value of a cable-driven parallel manipulator is not totally credible by traditional theoretical analysis. Therefore, an experimental method for stiffness analysis is presented in this paper. It applies Buckingham
$\pi$
theorem to set up an experimental stiffness similarity model to obtain a more credible stiffness value, which is used in the optimization process. In this way, dimensional optimization is realized with a set of optimized dimensions for building the feed-support system in the FAST. More importantly, the stiffness similarity model can be universally adopted in stiffness analysis of other large cable-driven parallel manipulator.