Based on the index of motion stability for stepping motor systems, according to the module of constant acceleration-deceleration motion planning, a conception of optimal interpolation period was proposed both in single-axis motion and multi-axis motion, and the selection rules were given theoretically. Theoretical analyses and machining experiments have shown that precision, efficiency and stability restrict mutually in CNC machining. To achieve the best motion stability and machining quality, the mentioned parameters should be selected suitably when designing machine tools or selecting machining parameters. The proposed interpolator has already been applied to nonmetal-carving machines with an in-house developed open CNC.