What is commutation? How can a commutator convert ac voltages on a machines’ armature to dc voltages at its terminals?

Commutation:

                                        Commutation is the process a coil undergoes after leaving the magnitude field of one pair of poles and just before entering the magnetic field of the next pair poles.

Converting ac voltages on a machines’ armature to dc voltages by commutator:

                           This function is performed by a commutator.

The ends of the coil are connected through the commutator to the brushes which lead to the external circuit.

 An explanation of fig 1 will clarify this process while the coil moves from position 1 to position 2 the brushes remain in contact with the commutator segment and the current direction remain as indicated although the magnitude decreases.  

At position 2 of fig 1 the voltage induced in the coil is zero, and the current in the external circuit is also zero. At this instant segment A leaves brush 1and makes contact with brush 1. As the coil moves from position 2 to position 3, segment a makes contact with brush 2 only, while the current increases from zero and leaves brush 2 of course during this same period current returns to the coil through brush 1and segment B.

Again, when the current in the coil becomes zero, the segment in contact with the brush will change. Thereby, maintaining a unidirectional current in the external circuit.

This follows from the fact that wire 1 is always connecting to the coil side under the North Pole, while wire 2 is always connecting to the coil side under the South Pole. Fig 2 shows the wave form of the output
thus obtained.