This section is dedicated to anyone that doesn't want or have the time to learn everything about gear design and is just trying to tinker with them.

The module controls the size of the teeth, and thus, the size of the gear. Overall, the impact of the module on gear design can be summarized as follows:

Larger module -> Larger teeth -> Bigger gear

Gear tooth dimensions in function of the module

In the image above, the black dashed line represents the root circumference of the gear (the one where the teeth start), and the blue dashed line the pitch circle.

Here you can check a table for the DIN modules.

The pressure angle affects the load capacity, the efficiency and the transmission error of a gear system. A higher pressure angle generally results in a stronger, more efficient and more accurate transmission, but also in higher friction and noise. In practice, a pressure angle of 20° to 25° is commonly used for gears

Pressure angle effects on tooth geometry

With an increase in pressure angle, the teeth become sharper. This, in turn, influences the minimum number of teeth required, as a higher pressure angle allows for fewer teeth in the gear.

Two dimensions come into play when manufacturing and using gears, the addendum circle and the pitch circle:

Gear radii

The respective formulas for the addendum and pitch circumferences are:

If you're planning to machine gears, the addendum circle represents the size of your material previous to the cutting. The pitch circle is just a reference for assembling gears together.

When assembling gears, the distance between centers is derived from the position they take when their pitch circles are tangent:

Distance between centers

Meaning that the distance between centers 'C' can be expressed as:

C = \( (PD_{1} + PD_{2})\over 2 \)

Where 'PD' is the pitch diameter of its respective gear.

For gear pairs, the principles of the transmission between them can be expressed as follows:

- Smaller gear drives: Torque increases | Speed decreases.
- Bigger gear drives: Speed increases | Torque decreases.
- The torque ratio is the inverse of the speed ratio.

Gear pair transmission

Transmission of torque and speed between gear pairs is in function of the ratio between their amount of teeth. It can be expressed as follows:

$$ i = {z_{Driven}\over z_{Driving}} $$

Where the general expression involving torque and rotational speed is:

$$i = {\omega_{Driving}\over \omega_{Driven}} = {T_{Driven}\over T_{Driving}} = {z_{Driven}\over z_{Driving}}$$

Where