To grind sculptured surface by swing motion, it’s needed to interpolate the discrete data nodes on the arc-driving surface. To ensure that all the sample points locate on the arc surface, a novel unfolding parameter curve is proposed. Firstly, all the discrete data are stretched onto a plane, inside which the cubic B-spline curves are interpolated. After that, some points are sampled from the spline curves and bended to the arc-driving surface according to the swing radius. To eliminate cutting vibration and chord error exceeds limitation; radial speed is tuned by controlling the chord error. The simulation results are given to prove the proposed algorithm.