Definition:Trochoid/Curtate

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 $C$. Let $b < a$.

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

Also known as
A curtate trochoid can also be seen referred to as an contracted cycloid.

According to and  in their  of $1989$, the literature is inconsistent as to whether the term prolate or curtate is used to denote this object.

's usage of these terms will be consistent.

Also see

 * Definition:Trochoid
 * Definition:Prolate Trochoid
 * Definition:Cycloid