I've become bothered by the pulleys on rear derailleurs. They sap your exergy! Here's a more efficient gear system for bikes.

When you change down a gear, the chain would get pushed onto a smaller sprocket at the front, and simultaneously it would get pushed onto a bigger sprocket at the back, and vice versa. The rear derailleur would work like the front derailleur in a conventional system. No pulleys needed, more efficient!

The pulleys on the conventional rear derailleur are there to maintain tension in the chain, because otherwise as you change to a smaller sprocket, the chain would become slack.

In the new system, the chain would always be at the correct tension because as you change to a smaller sprocket at the back, there would be a compensating change to a bigger sprocket at the front.