I once had a Yamaha motorcycle with wheel spokes which were curved (made of cast aluminium alloy). There was much tutting at the time, in the technical press, that this was an example of form over function.
In view of the fact that lots of today’s bicycles have several springs, swingarms and dampers embedded in their frames, why not just simplify things and use spokes which are inherently springy? Most conventional thinking about spokes says that they should be as rigid as possible; stiffening the wheel to ensure effective ‘feedback’ from the road surface (and limiting fatigue damage).
But what if you want to be transported on a featherbed and don’t much care about performance? As long as the spokes are stiff in the wheel axle direction, they can stand to be pretty flexible radially. This would probably mean that the hub of the wheel remains slightly eccentric when in motion, but to anyone who has tried to ride over cobbles, springy spokes have got some obvious advantages.
I’d suggest making the spokes C-shaped in the plane of the wheel (allowing alternating tension and compression) and with an oval section with its long axis parallel to the wheel axle (to ensure the rim stays coplanar with the hub).
