When I was in school we had a program (I think it was this: http://www.dynamicgeometry.com/ http://www.dynamicgeometry.com/) that let you do pretty much exactly

When I was in school we had a program (I think it was this: http://www.dynamicgeometry.com/ http://www.dynamicgeometry.com/) that let you do pretty much exactly that. We were never that ambitious, but it was pretty cool. I remember using it's animation functions to create some limited spirographs by tracing out lines defined by pairs of points moving around circles and things like that.