Some AC motors that run on 110 volts can be reversed, like Doc said.
Reversing is accomplished by swapping around the field coils, and which ends of the coils get AC power connnected to them.
These coil connections are normally inside the protective power feed box built on the motor chassis. Some motors use terminal strips, others use bare wires held together with wire nuts, and some use spade lugs.
If you can get a brand name and model number off your motors, it should be possible to find the connection diagram for it on the internet. If you have a motor that is reversible, then a diagram of how to wire the motor to an external reversing circuit should be possible.
Note, I have some AC motors (like the one on my small air compressor) that cannot be reversed, but can be wired to run on either 110 or 220 volts. Connection-wise, it looks about the same as a reversible motor. On the outside of the motor is an information plate, and it has a very-hard-to-understand diagram of how to rewire the connections.
I have an AC motor on my lathe that reverses. It does not have 220 volt capability, but has the same number of wires as my compressor motor, and a really bad wiring diagram.
Maybe this helps?