Loci in Epicyclic Gearing

R: pitch diameter of the fixed sun gear
r: pitch diameter of the planetary gear
k = R/r = 1.5
Loci of various points on the planetary gear are shown.
The red is for a point on the pitch circle of the planetary gear.
It is a hypocycloid. The two other loci are hypotrochoid.
1 cycle of the mechanism corresponds 2 revolutions of the input crank.

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