Internal gear transmission with double contact points is consist of the pinion having circular-arc tooth profile and the internal gear having parabola tooth profile. To further improve load capacity and reduce total volume of internal gear drive with double contact points, a multi-objective and multi-parameter optimization mathematical model is established based on genetic algorithm. Through the comparison analysis, contact stress of tooth surfaces after optimization design is reduced by 21.9% and the volume of gear after optimization design is reduced by 3.93%. Furthermore, contact characteristics of tooth surfaces are discussed considering the parameters optimization of contact angles and pressure angles. Based on Hertz contact theory, theoretical calculations of contact stresses under different contact angles and pressure angles are provided. And finite element method is used to analyze the contact conditions of tooth surfaces to verify theoretical calculation results. Research results show that contact angle of the internal gear pair with double contact points should less than 12.5° and pressure angle of the internal gear pair with double contact points should be 20°–30°.
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