The fourth order transmission error is applied to improve the transmission stability and tooth strength of circular-arc curvilinear of cylindrical gear.The coefficient of fourth order transmission error curve is determined

the curvilinear shaped imaginary rack cutter is formed by the tilted head cutter

and the imaginary pinion is introduced to establish the tooth surface equation of pinion and gear by the coordinate systems transformation and the mesh equation

respectively.And the tooth contact analysis model which also considered assembly errors is established on the conditions of continuous tangency of two contact surfaces.The computerized simulation of meshing and contact shows that the fourth order transmission error can be achieved by the proposed method

and the stability transmission can be performed by increasing the angle of the transformation point between the adjacent meshing cycles

the tooth fillet strength can be enhanced for decreasing the modification amounts nearby tooth root

finally

the sensitivity of assemble errors of the transmission curve can be reduced.