Study On The Supporting Mechanism Of The Reflection Of The Large Radio Telescope

The large radio telescope is the important tool for people to explore the universe. There are a large number of the designs of the radio telescope, and the cable-net structure as an active reflection of the surface supporting mechanism of the large radio telescope is a novel design scheme. In this paper the cable-net mechanism of the FAST will be study as a multiple-input multiple-output(MIMO) of flexible parallel mechanism. With the principle of minimum potential energy and variational principle the equation of the cable which between any two nodes in cable-net is obtained, and the equation is the catenary equation. The model of the cable-net structure is established with the catenary equation. The main contributions are as follows:1. According to the principle of minimum potential energy and variational principle the catenary equation of the main cable of the cable-net is obtained. The mathematical model of the cable-net structure of the FAST is established with catenary equation.2. The cable-net structure is divided into a large number of layers with the characteristics of it. The mathematical model of the cable-net mechanism will bring a large number of nonlinear equations. In order to find the initial values of the the nonlinear equations the layerwise substitution method is proposed.3. The mathematical model of the cable-net mechanism has been simplified by using the symmetry method. With the rotational symmetry and mirror symmetry the whole cable-net is divided into several parts, some parts of the cable-net is named the original symmetric cablenet, others is the symmetric cable-net. The symmetric cable-net can be solved from the original symmetric cable-net by using the transformation matrix. It also presents the inverse iteration method to deal with of boundary problem of the cable-net.4. The relationship between the rotating paraboloid and spherical surface is obtained. And discussed the relationship between the axis of rotating paraboloid and three axis of the coordinate system when the FAST at working state. Finally, the iterative method is utilized to finding the initial value of the nonlinear equations of the cable-net when it is at the working state. The homotopy method has been introduced to solving the nonlinear equations. With the homotopy method to solving the nonlinear equations is not need to set the initial value of the nonlinear equations. Finally, the reduced model of the FAST has been solved by using the the homotopy method when it is at working state.