Definition:Trochoid

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Definition

Consider a circle $C$ rolling without slipping along a straight line.

Consider a point $P$ on the line of a radius of $C$ at a distance $b$ from the center of $C$.

The curve traced out by $P$ is called a trochoid.


Curtate

Let $b < a$.

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

Graph

Curtate-Trochoid.png


Prolate

Let $b > a$.

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

Graph

Prolate-Trochoid.png


Cycloid

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


Consider a circle rolling without slipping along a straight line.

Consider a point $P$ on the circumference of this circle.

The curve traced out by $P$ is called a cycloid.

Graph

Cycloid.png


Also see


Sources