In the most general case hypotrochoids are curves generated by rolling a circle of radius b inside a circle of radius a > b. The curve is generated by a point rigidly attached to the inside of the rolling disc. The system below illustrates [Hypotrochoids] resulting when the radii ratio is an integer N = a/b. Given the radii a and b. The shape of the hypotrochoid depends on the distance h of the attached point from the center of the b-circle (h <b). For h=b we get the hypocycloids with N cusps (see Hypocycloid.html ). Thus, varying h in the interval [0,b] we get a deformation of the hypocycloid, via troichoids, to the circle with radius a-b.

To change the shape of the hypotrochoid change N or/and the location of the moving point (red) inside the rolling disc. See the file Roulette.html for a generalization of the hypotrochoids.