The curve may be regarded as an epitrochoid (see Epicycloid) in which the rolling and fixed circles have equal radii.
The path of a point P in or attached to the rolling cone is a spherical epitrochoid traced on the surface of a sphere of the radius OP. From P draw PQ perpendicular to the instantaneous axis.
The locus of any other carried point is an "epitrochoid" when the circle rolls externally, and a "hypotrochoid" when the circle rolls internally.
It may be shown that if the distance of the carried point from the centre of the rolling circle be mb, the equation to the epitrochoid is x = (a+b) cos 0 - mb cos (a+b/b)0, y = (a +b) sin 9 - mb sin (a +b/b)0.