Fitting method of working surface generatrix for deployable truss antennas

The difference between the shape of the working surface and the spherical truss structure of a deployable truss antenna with hexagonal prism modules causes problems. To resolve them, a fitting method of working surface generatrix based on differential geometry and the least square method was proposed. After analyzing the types of deployable truss antenna, module structures and the relationship between the truss structure and the mesh surface, the working surface was transformed from a space state into a plane state enveloped by a rectangle. The steps for solving the mother paraboloid's generatrix equation were analyzed. Based on offset distances, the endpoint coordinates of a working surface generatrix were obtained. The fitting curve was discretized, and calculation formulas of fitting arc were derived by the least square method. Using this method, three assembled antennas which have the same diameters were calculated. The results were then evaluated. They showed that the maximum fitting error of any curve was less than the allowable error, so it was not necessary to correct the fitting curve. This method proved to be an effective working surface generatrix.