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Question: If you have one of those gizmos that transforms rotational
motion to reciprocating motion, what path does the reciprocating part trace?
Answer: As far as I can tell, the path is
cos a + Sqrt(k^2 - sin^2 a)
where k is the length of the connecting rod that is free to pivot. As
you can see, that means that for large k, the path is approximately a
sine wave. However, for small k it deviates significantly from a simple
sine wave...
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