Research is devoted to the use of energy-efficient hydraulic motors in running modules for mechatronic systems of construction, road, municipal, agricultural, railway and other self-propelled machines; robots are used in various branches of the European economy and can contribute to the practical implementation of the philosophy of the “European Green Deal”. As a result of this research, design schemes and a mathematical apparatus have been developed that allow determining the rational force in the contact zone of the movable and fixed distributors. In order to determine the geometric parameters of the stepped surfaces of the movable and fixed distributors, which ensure the formation of an oil film in the contact zone, a structural-functional diagram of the mathematical model has been developed, which makes it possible to obtain a quantitative estimate of the increase in the productivity of the distribution system. The conducted studies have established that with rational design of the distribution system elements by reducing the clamping force by 3...5% in the distribution system, leakage through the end gap is reduced by 26%. Reduction of leakage in the contact zone allows an increase in productivity of the distribution system of 2.4% by increasing the volumetric efficiency (reducing losses).