Can a bike not have a chain?
Apparently the Ceramic Speed company has made (not for all its models) a gimbal-like bike transmission.
The rotating shaft, coming from the front, can slide back and forth by engaging in the various sprockets.
The rear end is cased to protect it from dirt:
It seems that this type of transmission can transfer 99% of the power impressed on the pedals.
As mentioned by the company itself, the bikes are not designed to carry significant loads. The parts are thinner and many 3D printed. These are just “show-bikes.”
In fact, right now the maximum power applied is about 200–250W, which is little for professional use. During Tour de France sprints it seems that athletes develop 1,200–1,400W of power for 10–15 seconds while “average” cyclists go up to 600–800W.
Who knows if they will be able to increase the transfer capacity of the transmission and if it will be successful.