The ball screw can be included in steering systems, the brake system, seat moving devices, and transmission systems of vehicles. Performance of the ball screw in these systems plays a key role in delivering agile and accurate power transmission. The purpose of this study is to improve performance by focusing on performance of the ball screw, by applying various conditions based on a design factor in the circulation system. The selected single design factor is to apply the cycloid curve to a circulation area. The circulation part to obtain a cycloid curve with highest performance, can have the smoothest ball flow. In addition, based on results, we intend to reduce failure cost that may be incurred in developing future ball screws for automobiles, and to establish databases that can be applied to developed products by deriving optimal shape.