A hypotrochoid is a curve formed by the path of a point attached to a point c, which is not on the circumference, of circle of radius b that rolls around the inside of a larger circle of radius a. The parametric equations for a hypotrochoid can be written as:
x = (a - b) cos t + c cos(a/b -1)t,
y = (a - b) sin t - c sin(a/b -1)t.
The hypotrochoid is a generalized hypocycloid and comes in two varieties: a prolate hypocycloid if the starting point is outside the circumference of the rolling circle and a curtate hypocycloid if the starting point is inside the rolling circle. In the same family of curves as the hypotrochoid (and hypocycloid) are the epicycloid and epitrochoid.