# Cogwheel (Gear)

Teeth - set the number of teeth or cogs.

Pitch Radius - set the radius from the centre to the midpoint of the tooth.

Tooth Depth - set values for the Addendum (the top of the tooth) and the Dedendum (the bottom of the tooth)

Tooth Taper - set taper angles for the Addendum and Dedendum.

## Gear Example

In order to create a gear system there are some basic guides to follow:

• The Module of each Cogwheel must match. The module is a ratio which can be easily expressed as:

• pitch diameter / the number of teeth. Or in Cavalry's case:

• 2 * Pitch Radius / Teeth.

• The teeth must be the same shape/size.

• The Pitch Circle of one Cogwheel must 'touch' the other.

In the example below:

• the Medium Cogwheel has a Pitch Radius of 200 and 12 Teeth.

• the Small Cogwheel has a Pitch Radius of 100 and 6 Teeth.

• the Large Cogwheel has a Pitch Radius of 400 and 24 Teeth.

200 / 12, 100 / 6 and 400 / 24 all equal 16.66 so each Cogwheel has the same Module.

The math for the rotation is also quite simple. If:

• r1 = Rotation of the Medium Cogwheel

• t1 = Number of Teeth of the Medium Cogwheel

• r2 = Rotation of the Small Cogwheel

• t2 = Number of Teeth of the Small Cogwheel

$r2 = r1 * t1 / t2$

so in the case of Medium > Small that would be:

$r2 = r1 * 12/6$

You can use a Jsmath Atom to rig this equation up.

1. Create a Jsmath Atom.