The following online calculator computes
the basic dimensions and tooth profiles
of a meshing rack and pinion based on the pinion's module,
number of teeth, pressure angle (usually 20°) and profile shift.
The rack's teeth are trapezoidal, while the pinion has an involute tooth profile.
The profiles of the rack and pinion can be fully defined by the number of teeth on the pinion,
module, profile shift and pressure angle. A positive profile shift is required
for the pinions with 18 teeth or fewer to avoid a collision with the teeth of the rack.
If the specified profile shift is insufficient, the calculator displays a warning.
The rack tooth profile is a trapezoid which dimensions are provided by the calculator.
The base angles of the trapezoid are the same as the overall pressure angle (usually 20°).
The calculator also provides the parameters for the rounded area between the rack teeth, known as fillet.
Related: How to Model a Rack-and-Pinion in Blender