Reversing a single phase motor with a drum switch is simple when you understand what you are doing. A drum switch has a number of contacts set up so that some reverse and others just close. Simple inspection will let you determine which ones do what! One set usually does very little and just completes the circuit the same way no matter which way the switch is turned, simple ON/OFF If the terminals were marked ABC and abc the "C" will be connected to "c" in either direction. The other 2 will result in "A" connected to "a" and "B" connected to "b" in one direction of turn and "A" connected to "b" and "B" connected to "a" when turned in the other direction. In the center none are connected.Understand?
A simple description of a reversible single phase motor is there are 2 windings, one is the main winding and the other simply to start the motor spinning in the correct direction. Most use a centrifugal switch to disconnect the start winging when the motor has reached the correct speed. The main winding will run in any direction so it will be connected to the "C" type connection of the drum switch, simply ON/OFF. The start winding is connected to the reversing contacts A and B so that you simply reverse the connection to the start winding and therefore reverse rotation. One thing to remember because of the centrifugal switch a running single phase motor will not reverse like a 3 phase motor when the drum switch is reversed. It will continue running in the same direction! Simply because at run speed the start winding is disconnected by the centrifugal switch so to reverse direction you have to wait until the motor speed drops to below the centrifugal switch "turn on speed"
Help?? I tried to keep it as simple as possible.
Frank