I'm trying to describe the cycloid described by a wheel rolling inside a circle: The (rotor)vector attached to the center of the rolling wheel is described by this equation: r = r cos(w t)e(x') + r sin(w t)e(y') w is the angular velocity of the wheel, e(x') and e(y') are the unit vectors and t is the time This is the relative position vector of the point on the wheel that touches the big circle as the wheel rolls. The origin of the absolute coordinate system x y is the center of the big circle, the origin (the center of the wheel) of the other coordinate system x' y' (where x' always stays parallel to x and y' to y) moves in a smaller circle with radius R - r, R is the radius of the big circle, r is the radius of the wheel. So the position vector of the origin in the absolute coordinate system is given by: p = (R - r) cos( (r/R) w t)e(x) - (R - r) sin( (r/R) w t)e(y) The angular velocity W of the smaller circle is given by (r/R)*w, since r*w = R*W (the wheel doesn't slip). The minus sign is because the wheel rolls clockwise. r + p should describe the curve, now, when R = 4r I should plot an astroid, which is not the case, where have I gone wrong?