The geometrical constraints of hypoid gear with few teeth and large speed ratio is presented
then the design of a pair of hypoid gear with the speed ratio 4 to 41 is designed. Based on the theory of the tooth surface enveloping
the generating coordinate systems of the hypoid gear is established
the tooth surface equation of the gear pair are obtained. The three- dimensional simulation of that hypoid gear are carried out by using MATLAB and UG. Finally
the gear cutting experiment result shows that the proposed hypoid gear with few tooth and large speed ratio is feasibility.