The pressure equation at any point on the spur tooth surface of the cylindrical gear α ， The expanded length of point F is recorded as L α， That is, the distance from point e to point F, then L α For:
Where Rb2 — base circle radius of spur gear (mm)
In the figure, the included angle between the normal of any point F on the tooth surface and the positive direction of XG axis is recorded as θ g 。 If the tooth surface rotates from the starting position φ G angle, rotate clockwise and take a negative value, then θ G angle is:
Of which:
Where: inv（ α 0) – involute function, i.e. pressure angle α Function for 0
In the spur gear coordinate system: SG, (OG: XG YG ZG), the coordinate parameter equations of point E and point F are expressed as:
The formula is the tooth surface equation of spur involute cylindrical gear.