Just done a drawing and model for the Ellipsograph system. With in the model can figure out how this mechanical system work. It is just a sketch model but it produced a ellipsograph which looks pretty close to the drawing.

Note:
I have received an Email from David A. Stevenson who points out the point F in this ellipsograph figure needs to be midway between G and E, so the model in particular will not looked distorted/twisted. Thanks David A. Stevenson.