Analysis and a Simplified Model of the Cable of a Large-Scale Flexible Parallel Manipulator for a Large Radio Telescope

This paper presents the analytical solution of catenary, on the basis of which a parabolic model is derived. To avoid the non-linearity due to the transcendental-function shape of a catenary cable, we introduce a linear simplified model, the Pseudo-Curve model. The Pseudo-Curve model focuses on the cable length and tension, and yields concise expressions for these two aspects. By analyzing the Pseudo-Curve model and the parabolic model, this paper shows that the Pseudo-Curve model is consistent with a type of cases for the parabolic model. A numerical example further shows the accuracy and efficiency of the Pseudo-Curve model.