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Epicycloid


epicycloid.png

Epicycloid is a parametric curve that is obtained by rolling a smaller circle (r) around a larger one (R). It shows the trace of a point P, fixed on the circumference of the smaller circle.

General equation:

x(θ) = (k + 1)·cos(θ) – cos((k + 1)·θ)

y(θ) = (k + 1)·sin(θ) – sin((k + 1)·θ)

Larger radius: R =

Smaller radius: r =

Ratio: k = R/r

 

Tip: Click "Calculate" to see the respective plot.


Substitute