Based on the space coordinates transformation principle, the movement rules of the numerical controls spiral bevel gear machine with six axes five linkages were studied, and the machine machining coordinate systems were established. The principle was analyzed from the traditional machine to the numerical controls machine with six axes five linkages and its numerical control mathematical model was proposed. Moreover, according to the gear generating method of traditional machine, the gear generating machining principle of the spiral bevel gear with six axes five linkages was established. Finally, according to the example computation，the instantaneous locations and fourthorder expressions with the time were obtained when five linkage axes machining. 