A

David

Darling

epitrochoid

An epitrochoid is a curve traced out by a point that is a distance c from the center of a circle of radius b, where c < b, that is rolling around the outside of another circle of radius a. It is described by the parametric equations

 

      x = (a + b) cos(t) - c cos[(a/b + 1)t],
      y = (a + b) sin(t) - c sin[(a/b + 1)t].

 

Closely related to the epitrochoid are the epicycloid, hypocycloid, and the hypotrochoid. An example of an epitrochoid appears in Albrecht Dürer's work Instruction in Measurement with Compasses and Straightedge (1525).