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Find F of X

I have a large circle and a small circle as shown in the image. The distance between the centers of those circles. The Larger circle is rotating about it's center while traveling in direction D such that it travels its circumference in 1 revolution. There is a point on the smaller circle called X. I need a function that can calculate the path of x (for graphing purposes).

Is there a mathematical formula for this? If not then what group of math formulas could be used to solve this problem?

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up vote 1 down vote accepted

See here for more information (especially look in the Related Curves section). In particular, this appears to be a curtate cycloid, based on my reading of your question.

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Calculate as a Cycloid, many thanks. – user14993 Jul 11 '12 at 19:33

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