I'm trying to build a lamp which has about 20 identical layers stacked on top of each other. There is a central spine and, on each level, a pair of arcs attached to the spine that are hinged and which meet each other (this looks like a big rib cage, where the ribs are free to rotate in and out). I'd like to create some gearing such that moving one side of one layer will move the other one symmetrically, keeping each layer symmetrical. I don't need any automation to move them, but I just want them to be constrained to symmetry.
The general gear plan could be something like this: http://www.gearsket.ch/#c74a934963cc29f8
...but I'm not able to attach the outside gears (which would be attached to the ribs) at the rotation axes of the ribs, because of the hinges.
I may be able to get that to work, but I'm getting worried that the gears (to be CNC machined out of wood) are getting to be pretty big (each layer, when closed, is a circle about 8 inches in diameter), and are going to take over the look of the lamp.
Are there any alternate gear or linkage designs that would help to constrain these to symmetrical opening/closing motion?