Epicycloid type 2D curve



What is the best parameterization of the epicycloid type smooth 2D
curves with curvature = -1/r^2 ? ( r is radius to any point from
origin). Some of these ( maximum radii .2,.4,.6 ) are indicated :

http://img222.imageshack.us/img222/1428/invsqcurv7nj.jpg

.