When solving the plane coordinate points of the tooth surface of the hypoid gear pinion, because the hypoid gear pinion is wrapped by the big teeth, the tooth surface points of the hypoid gear pinion can be solved simultaneously according to the corresponding relationship between the plane points of the pinion and the three-dimensional coordinates and the meshing equation. Since the equation after simultaneous establishment is a set of nonlinear equations, it is troublesome to solve. After programming with MATLAB software, given the initial values of three unknown parameters, the three-dimensional coordinate points of the small gear tooth surface can be obtained conveniently and quickly. The rotation projection coordinate formula and meshing equation of the small gear tooth surface of hypoid gear are as follows:
The equation contains UG θ G and Φ 2 three parameters, programmed with MATLAB software, when φ When 0 takes a fixed value and UG takes a series of values, a series of data points can be solved, and these data points can be substituted into the tooth surface equation R1 (UG, φ 2) The three-dimensional coordinate points of the tooth surface of the hypoid gear can be obtained.