Oblique cone rolling on surface is it possible to mate?

Hello I am trying to make oblique cone to roll on flat surface or opposite that cone is fixed and planar surface rolls around it. I am stuck with it almost 2 weeks. First what I tried (still thinking it is the way to go) to make path mates with two different points on cones circular base. I managed to make center point path with 3DSketch and equation driven curve. Equation is quite long but it works. But for any other point the equation becomes so long that it is three times the length of my display:) and it wont work. Another approach I found on Internet how mating is done when one right cone rolls inside bigger cone http://kmoddl.library.cornell.edu/download_resource.php?id=1935 it is made using gear mate and fixed angle. But in my case the cone is not right and angle can't be fixed... Is it possible to do this or I am doomed?

SolidworksAssemblies