# Cogwheel

## Intro​

Create a Cogwheel (AKA Cog or Gear) primitive as part of a Basic Shape.

## UI​

Teeth - Set the number of teeth or cogs.

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

Tooth Depth - Set a value for the total height of each tooth.

Tooth Width - Set the width of each tooth at its midpoint.

Tooth Taper - Set the inner and outer taper angles for each tooth.

Midpoint Position - Set the midpoint of each tooth where 0 is the base of the tooth and 1 is the tip.

### 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: $Module = 2 * Pitch Radius / Number Of Teeth$
• The teeth must be the same shape/size.
• The Pitch Circle of each Cogwheel must be 'touching'.

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

$r2 = r1 * t1 / t2$

In the case of Medium > Small that would be:

$r2 = r1 * 12/6$

A Jsmath Utility can be used to rig this equation up.

1. Create a Jsmath Utility.
2. Add the expression -n0 * n1/n2