What simple machines are in a bicycle?

Levers: Shifters, crankset (the pedal levers), derailleurs, handlebars, freewheel assembly, brakes.

Wheel and axel: The wheels, pedals, crankset, cassette

Pulleys: Parts of the shifting mechanisms, braking mechanisms, and the drive train (chain on gears).

Screws: (Hold parts together).

Wedges: The teeth on the gears. Not common, but some gooseneck assemblies (where the handlebars attach to the front fork tube) may employ a wedge to tighten the connection. If you have a repair kit on your bike, tire levers are also both levers and wedges.