Abstract: The kinematics transform model between two machines about tilt generated method is built. Motions of axes when using tilt method are approximately represented with a group of 4th-order Maclaurin formula. To feed the need of real-time for generated simulation, the simplified representations of n-th transform matrix derivatives are achieved through the clear derivation of equations. The assessment of time consumption between the simplified equations and the unhandled ones is made with an example. Based on the reduced equations, a virtual software which can simulating the gear generation process is designed. A set of practical gear parameters is presented as an example. A virtual gear, which is made by the simulation software with the given parameters, is compared to the real gear. Errors of the approximate formula are presented with the several figures. Based on the correct building of virtual software, precise gear solid model can be got for the tooth contact analysis (TCA), virtual machining experiment, and other deep researches. The reduced matrix derivative equations and its methodology could be spread to the whole spatial kinematics.

Key words: Five-axis machining, Kinematics, Spiral bevel and hypoid gears, Tilt method