Trochoids
Trochoid is a curve generated by a point fixed to a circle, within or outside its circumference,  as the circle rolls along a straight line.  If the point is outside the rolling circle,  the curve obtained is called an inferior trochoid and when outside the circle is called superior trochoid.  Figure 1 illustrates  an inferior trochoid and a superior trochoid.
Epitrochoid
Epitrochoid is a curve generated by a point fixed to a ircle (within or outside its circumference, which rolls on the outside of another circle. If the point is outside the rolling circle, the curve obtained is called an inferior epitrochoid and when outside the circle, it is called superior epitrochoid.
Hypotrochoid
Hypotroichoid is a curve generated by a point fixed to a ircle (within or outside its circumference, which rolls inside another circle. If the point is outside the rolling circle, the curve obtained is called an inferior hypotrochoid and when outside the circle, it is called superior hypotrochoid.

 

Figure 1 illustrating the superior and inferior trochoids.