How to draw a spur gear involute profile in AutoCAD / GStarCAD / ZwCAD

The tooth form most commonly used today for power transmission gears, is the involute profile.

Check the following video:

The definition of the involute curve is - the curve traced by a point on a straight line, which rolls without slipping the circle. The circle is called the base circle of the involute. Check the RATIONALE here OR here.

With the center of the base circle at the origin of a coordinate system, the involute curve can be expressed by a pair of X and Y formulas, which transcribed into LitioLAB’s format are as follows:

    X = u*cos(r2d(j2))
    Y = u*sin(r2d(j2))


    j1 = d2r(acos(c1/u))
    j2 = tang(r2d(j1))-j1
    c1 = base radius = (base diameter) / 2

    ZwCAD users need to check LitioLAB user manual to review the math functions available and how to adapt the formulas to ZwCAD.

    The R2D (radians-to-degrees) conversion function is not available in ZwCAD. Use 180/PI as a multiplying factor instead.

Gear Profile drafting example:

For the example, I have considered the Gear Specifications as follows:

    Module: 5
    Reference diameter: 150.0
    Base Diameter: 140.95389
    Tip diameter: 160.0
    Pressure Angle: 20°
    Number of teeth: 30

And our calculation parameters are as follows:

    Ui = 70.477 = (base diameter) / 2
    Uf = 80.0 = (Tip diameter) / 2
    dU = 0.05
    c1 = 70.477 = (base diameter) / 2

I enter the formulas and the parameters and we get the involute profile of a spur gear.

And since these graphs are polylines, they can be extruded and used to generate AutoCAD/GStarCAD/ZwCAD solids for further processing and eventually, for CNC machining, laser cutting or 3D printing.

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