In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point of a circle, (called an epicycle) which rolls without slipping around a fixed circle. It is a particular kind of roulette. The abscissa of a moving point is given in relation to the radii of the two unequal circles, the radian from the tangential point to the moving point and the radian from the starting point to the tangential point.
Formula:
x = ( R + r ) ยท cos ฮธ - r ยท cos โก ( ฮธ + a )
where,x = The abscissa of the point
R = Radius of the larger circle
r = Radius of the smaller circle
ฮธ = Tthe radian from the starting point to the tangential point
a = The radian from the tangential point to the moving point