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,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.
Related category PLANE CURVES
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