7 point hinge system (not a parallelogram)

My problem exists with a hinge system I am trying to devise for a design I am currently working on as part of my final year studying.
The problem is with a 7 point hinge system that folds around an origin point.
Using parallelograms the hinge system works perfectly, but to open the hinges above approx. 90 degrees causes the pivot points to overlap. This is a major problem, which I believe can be avoided (I've seen it done) but don't know how.
I've attached an .pdf file, including drawings, of the hinge system, with as close to the solution I can get with trial and error.
Any help would be much appreciated.