Abstract: The AB positioner of FAST telescope functions as a gimbal with two horizontal orthogonal rotation axes to tune the pointing angle of equipment in a focus cabin. Its outer ring (Ring A) is a large-span curve beam,demanded light weight and high stiffness under heavy loads. Based on the coupled bending and torsion theory of a curve beam,the differential equations are deduced to find analytical solutions directly,which link beam deflections with structural parameters. The objective function is built to minimize the total structural weight under the main restrains of the maximal deflection on the mid-span and the maximal deflection difference caused by the different rotation angles. The trust-region algorithm is successfully employed to search the global function minimum. Two structural concepts,namely a thin-wall box girder and a truss girder,are applied respectively and compared in the optimization. The preliminary computation shows the truss girder concept has lighter optimal structural weight.