Pulleys aren't that common on bicycles, pretty much only bikes with external gears have them. They're used in the rear derailer to let the chain change direction so that the derailer can take up the slack that comes from changing gears.
Some ladies/mixte frames use a pulley up by the seatpost to change the pull direction of the brake wire. Yet some bikes use a pulley to get the right pull direction for the front derailer.
The bicycle is not a simple machine, there are too many interacting moving parts.
pulley
lever at crank, connected by chain to lever at rear wheel
pulley
pulley
You can head on down to your local bicycle shop to find a selection of bicycle frames. It might be better to see them in person than to purchase it online.
gears and wheel and axle
Things that might cause a pulley to wobble: The pulley is bent. The shaft the pulley is on is bent. The pulley is mounted crooked.
The rear derailleur pulley in a bicycle's gear shifting system guides the chain to move smoothly between different gears, allowing the rider to change the resistance and speed of pedaling.
The chain is wrapped around a cogwheel, which could be described as a pulley.
Using an oversize derailleur pulley in a bicycle drivetrain system can reduce friction, improve shifting performance, and increase efficiency by allowing for smoother chain movement and better alignment with the cassette cogs.
There are websites that compare prices, for example Nextag, BestCovery and Yahoo! Shopping. On these websites you can look up the bicycle trainer that you want to buy and find the store that has the best deal for it.