Looking at it again I think that one of the sliders is superfluous, it could be removed and the machine would still work in the same way.

The only difference between this trammel and the normal two axis one is that the axes do not have a right angle between them and the effect of that (I think) is to move the major and minor axes of the ellipse to a point between the two axes of the trammel.

All of which has nothing at all to do with 3d printing and is probably wrong anyway. I think this needs calculus or some careful drawing to prove. Perhaps the animation software will draw the locus of the handle.