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Oil-pump rotors with a trochoidal tooth shape have many advantages compared with others, but the trochoidal tooth shape has not been sufficiently analyzed theoretically. So it is very difficult for the pump designer to decide the specifications for the trochoidal tooth shape, and it is also difficult for the supplier to meet the pump designer's requirements. We have been conducting theoretical analyses of trochoidal gears for several years, and have developed a system for designing the tooth shape. We can rapidly design the tooth shape, which meets the requirements of the pump designer, and develop the market for trochoidal gears by using this system. This paper shows the outline of the theoretical analysis, the outline of oil-pump rotors attached to crank shafts in automobiles as an example of the development of trochoidal gears, and some test results.