Gear and rack meshing index circle and pitch circle are always coincident

gearversusrackThere is also a prerequisite for the constant coincidence of the meshing index circle and pitch circle.
The pressure angle of the indexing circle of the gear is 20 degrees. For a rack with a pressure angle of 20 degrees, their pitch circles coincide with the indexing circles.But if the pressure angle of the index circle of the gear is 20 degrees, but we use a rack with a pressure angle of 15 degrees to match, then the pitch circle of the gear is not coincident with the index circle.At present, the rack design data that ordinary users can find all require that the rack pressure angle is equal to the gear indexing circle pressure angle. Under this premise, your proposition is established.But there are also many occasions where we will use a rack that is not equal to the pressure angle of the gear indexing circle.At this time, the pitch circle of the gear is the diameter of the gear circle corresponding to the pressure angle of the gear and the pressure angle of the rack.