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Geometry of cycloid and its evolute
Posted:
Feb 6, 2013 4:28 PM


A point C on a cycloid and its corresponding cycloidal evolute point E are made during rolling of its generating circle on xaxis.
If a point P divides CE so that CP/CE = k, find the locus of P.
They appear to be also epi and hypocycloids, but am not sure without some more computation work. Required is the line on which the Pcircle rolls and its crank radius. When k = 1/2, Plocus is a straight line parallel to xaxis.
Please upload its sketch. This is n't a class exercise.
Regards Narasimham



