Definition:Epitrochoid

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Definition

Let a circle $C_1$ of radius $b$ roll around the outside of another circle $C_2$ of radius $a$.

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 epitrochoid.


Curtate

Let $d < b$.

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

Graph

Curtate-Epitrochoid.png


Prolate

Let $d > b$.

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

Graph

Prolate-Epitrochoid.png


Epicycloid

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


Let a circle $C_1$ roll around the outside of another circle $C_2$.

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


Epicycloid.png


Also see

  • Results about epitrochoids can be found here.


Sources