Cycloidal curves

Cycloidal curves :

Cycloidal curves are generated by a point fixed on the circumference of a rolling circle when it rolls without slipping on a straight line or on  the outside / inside of another circle.

The rolling circle is called the generating circle.

The fixed straight line on which the rolling circle rolls is called the directing line or base line and is equal to the circumference of the rolling circle. (πD)

The circle on which (either outside or inside) the rolling circle rolls is called directing circle or base circle.

Cycloidal curves are three type:

1.Cycloid   

2.Epicycloid 

3.Hypocycloid