Abstract—This paper introduces a new study on determining optimum partial transmission ratios of mechanical drive systems using a chain drive and two-step bevel helical gearbox. The objective function of the optimum problem was the cross section dimension of the system. In the study, the design equation for pitting resistance of a gear set was investigated and equations on moment equilibrium condition of a mechanic system including a chain drive and a three helical gear units and their regular resistance condition were analyzed for solving the optimum problem. From the results of the problem, effective formula for calculation of the partial ratios of the chain drive and two-step bevel helical gearboxes were proposed. As the formulas are explicit, the partial ratios can be calculated accurately and simply.