Definition:Hypotrochoid

Definition

Let a circle $C_1$ roll around the inside of another (larger) circle $C_2$.

Consider a point $P$ on the line of a radius of $C_1$ at a distance $d$ from the center of $C_1$.

The curve traced out by $P$ is called an hypotrochoid.

Let $d < b$.

The curve traced out by $P$ is called a curtate hypotrochoid.

Let $d > b$.

The curve traced out by $P$ is called a prolate hypotrochoid.

The special case where $d = b$ is usually treated separately:

Let a circle $C_1$ roll around the inside of another (larger) circle $C_2$.

The locus of a given point on the circumference of $C_1$ is known as a hypocycloid.