I can understand how a DC motor works, and keeps rotating in the same direction with the split design of the commutator. The following (simplified) picture nicely explains it:
I know we can use some simple circuits like H-bridges etc. to control the direction of the rotation, but I would like to know if it is possible to modify the existing commutator (like shorting neighbors, or every other, etc.), and make the motor oscillate at half rotations? In real life the commutator is not two-piece only, but quite a large number of slots.