In the most general case hypocycloids 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 rolling circle. The system below illustrates [Hypocycloids with N cusps] resulting when the radii ratio is an integer N = a/b. The hypocycloids for the lower values of N have been extensively studied. For N =2 the curve is a diameter of circle (a). For N =3 the curve is a [Deltoid]. For N = 4 the curve is an [Astroid].

To get the hypocycloid with N cusps set the value of N. To see the rolling motion press the driver button. See the file Hypotrochoid.html for the generation of related curves.