According to the cutting method and cutting principle of Orion hypoid gears

the relative positions and movements among cutter head

cradle and work piece were analysis

and the cutting coordinate systems were established.The theoretical tooth surface equations were derived on the basis of space engagement theory.The equations were established after disserting the theoretical tooth surface

and the coordinates of discrete points were solved by the numeric analysis.On the mean time the simulation of theoretical tooth surface was completed

which will provide the theoretical basis for TCA

the measurement of tooth surface deviation and the finite element analysis.