I thought about an alternative chain solution.
I wanted to make sure that the frame is still straight, so you still sit right on top of the axle.
The cranks are split like in dangerdog’s drawing. The frame is suspended between the axle and the cranks.
It may weight even more because you need 4 chains in total.
Just an idea 
Dangerdog - That’s basically a simpler design of this
The closer the cranks are to the hub, the better the control would be, but the shock’s smoothness of action could be worse. A happy medium would have to be found.
Hugo - would probably work, but IMO one of the reasons why larger wheels are harder to balance on is the axle is higher off the ground.
Good ideas. Keep em coming!
Excellent drawing/photo but the challenge is to have the cranks suspended therefore it seems you have to have split cranks and some form of transmission from cranks to wheel so that the seat to cranks relationship remains constant and only the wheel travels up and down.Anyway your drawing/photo thingy looks great.
I just realized the pic I posted is basically a complicated suspended seat post only:(
I think yours is still full suspension though.
you could also stick some gears on that very easily
EDIT: I’m confused as to how the middle hub/axle part stays put, maybe you could draw a wheel around the image
As it is the wheel would not spin in relation to the cranks when the suspension is compressed. If you geared it up the wheel would turn in relation to the pedals when the suspension moves.
How the system would work is basically the gears and suspension make an isometric triangle. When the suspension compresses the part that sticks out has half the vertical movement and moves out a bit in an arc.
Apparently N.A.S.A’s original brief was to build a geared suspension unicycle but they found space exploration much simpler and easier to implement the rest is history.
