hy·po·cy·cloid 
(hī′pō-sīkloid′)
(hī′pō-sīkloid′)n.
The plane locus of a point fixed on a circle that rolls on the inside circumference of a fixed circle.
hypocycloidIf a is the radius of a fixed circle and b is the radius of a smaller rotating circle, the parametric equations of the hypocycloid are x = (a - b) cos θ + b cos [(a - b) θ ]/b
y = (a - b) sin θ - b sin [( a - b) θ ]/b.