In this paper, the curvature of pure rolling single arc gear was analyzed according to the principle of differential geometry. The mean curvature and Gaussian curvature of pure rolling single arc gear were deduced systematically, and the relative curvature radius of pure rolling single arc gear was obtained. The influence of different parameters of pure rolling single arc gear on pure rolling single arc gear was analyzed by MATLAB. Based on the elastic contact theory, the tooth contact stress of pure rolling single arc gear transmission was calculated, and the influence of main parameters on the tooth contact stress of pure rolling single arc gear was investigated, which is of great significance for the design and manufacture of the following pure rolling circular arc gear.