While designing hydraulic hypogerotor pumps with internal matched gears based on the given flow, in order to find the set of parameters of the hypocycloidal gears, the equation of work conservation and iterative algoritm are usually used. However, it is still impossible to calculate the dedendum radius of the matching gear with circular profile, which belongs to the specified region (with infinite number of root/solution). To find the solution, the designer need to try in turn with each value of the radius, to measure the areas of the pump chambers using Autocad for each turn, and to compare those values with the areas determined by the work conservation method. This repeating process makes the whole designing work more time-consuming, and also brings a lot of errors. To overcome this problem, in this paper, the authors present the method of establishing formulas for calculation the pump-chamber areas, also programming a software module for automatic calculating and comparing solutions with those achieved by the work conservation method in order to gain the optimal solution. Moreover, this method helps to accurately assess the redundant amount of liquid (which can lead to hardening the shafts), or the shortage of flaw in each pump chamber when designing the hypogerotor pumps
