EpicycloidEEETrochoid



Parametric representation.

x = ( a + b ) cost - c cos (( a + b )/ b ) t
y = ( a + b ) sint - c sin (( a + b )/ b ) t

When one circle rolls (without slipping) on the outside of another fixed circle,a point inside or outside the moving circle describes a curve ,called Trochoid.
aFthe radius of fixed circle, Fthe radius of moving circle, Fdistance of a point from the center of movingcircle


@A point inside the moving circle (if )


Animation


A point outside the moving circle (if )


Animation2

@if a, the locus is Cardioid.

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