Don Barnett of Arizona e-mailed a request to draw a spline of an epitrochoid so he can develop a machined part from it. Barnett provided the mathematical representation of the curve in AutoLISP form. The parametric equations for an epitrochoid are shown in the figure below.
An epitrochoid is a roulette traced by a point attached to a circle of radius r rolling around the outside of a fixed circle of radius R, where the point is a distance d from the center of the exterior circle.
The parametric equations for an epitrochoid are
The AutoLISP Solution uses SPLINECURVE.LSP and SPLINECURVE.DCL. The routine automatically draws an epitrochoidal spline using input from a user for the base circle radius, rolling circle radius, eccentricity, and resolution.