Shaft-driven bicycle - video and photo

[Frank S]

If the pitch of driven side is equal, the 'pinion' could slide on a splined [square would do, or two flats on a round] axle, indexed for each ratio. A light spring could advance the position for speed, overcome by a lever to downshift.
Interesting what reduced friction vs chain is possible.

Notice one thing as well the teeth on the pinion are actually rollers just like in a chain further reducing the friction. the drive reminds me of an ancient pinion driven planter where the flat gear had a multitude of teeth in a dozen different ratios the pinion couldn't be just slid across the flat gear but had to be raised out of contact then lowered back in place but essentially it was the same concept think of an index wheel with bumps instead of holes