Cue ELO song here...
The brushes are not a part of the armature.
The armature is the complete assembly that turns. This is made up of the wound segments (the poles), the commutator, and the armature shaft with a gear on one end.
The commutator is the part with segments that the brushes rub against. The number of segments is equal to the number of poles on the armature. These are ODD numbers above 2. A commutator can be flat(disk) or a drum.
Each commutator segment connects to a pole in front and a pole behind. Two segments complete a winding to energize a pole. This magnetic force causes the armature to turn.
The three parts of an electric motor are field or magnet, armature, and brushes.
