Peritrochoid Curves are produced by a Point on a gear when:

•the rolling gear has more teeth than the fixed gear

•the rolling gear encircles the fixed gear

The shape of the Peritrochoid Curve depends on the ratio of the teeth. With gears, the ratio of the teeth is always a rational number. Therefore the pattern of the curve repeats eventually.

You can easily draw the shape of engine casing with a Trochoid that has two lobes.

The Revolving Gear is OUTSIDE (Internal tooth form)

The Fixed gear is INSIDE (External tooth form)

The ratio of teeth is 2(fixed gear) : :3

There are four separate curves in the image.

You can use this ratio and shape to define the combustion chamber of a Wankel Engine.

The Revolving Gear is OUTSIDE

The Fixed gear is INSIDE

The ratio of teeth is 4:3

There are four curves.

The Revolving Gear is OUTSIDE

The Fixed gear is INSIDE

The ratio of teeth is 11:12

There are four curves.