Based on the theory of gearing mesh

a rack-shaped-edge probe was used in the comprehensive on-line measurement for straight generatrix deviation. By measuring the deviation of each straight generatrix on tooth profile to determine the measurement grid

the isolated mathematical models of the tooth profile deviation and the helix deviation are established after obtaining straight generatrix deviation

and then its simulation is carried out. The mathematical models and simulation provide a theoretical basis for the development of the straight generatrix measuring instrument and on-line measurement system.