The stator is the stationary part of the DC machine. It consists of a yoke, which is the outer frame providing mechanical support and carrying the magnetic flux, and field poles mounted on the yoke. These field poles are electromagnets (or permanent magnets in small machines) that produce the main magnetic field. The rotor, or armature, is the rotating part. It consists of a shaft, a laminated core to reduce eddy currents, and armature windings. The armature windings are where the voltage is induced or the torque is developed. A commutator and brushes are also essential components, facilitating the electrical connection between the rotating armature windings and the stationary external circuit.

In a DC motor, the commutator ensures that the torque on the armature is always in the same direction. As the armature rotates, the commutator segments switch contact with the brushes, reversing the current in the armature coil just as it passes the neutral magnetic axis. This reversal maintains the direction of the torque. In a DC generator, the commutator rectifies the alternating voltage induced in the armature windings into a unidirectional (DC) output voltage. Without the commutator, the output would be AC.

The fundamental principle is that a current-carrying conductor placed in a magnetic field experiences a force. The magnitude of this force is given by $F = BIL\sin( heta)$, where B is the magnetic flux density, I is the current in the conductor, L is the length of the conductor, and $heta$ is the angle between the conductor and the magnetic field. In a DC motor, the armature conductors are placed in the magnetic field of the stator. Current is supplied to these conductors through the brushes and commutator. The direction of the force is determined by Fleming's Left-Hand Rule. The forces on opposite sides of the armature create a torque, which causes the armature to rotate. The commutator ensures that the torque is always in the same direction, leading to continuous rotation.

According to Faraday's Law of Electromagnetic Induction, whenever a conductor moves in a magnetic field such that it cuts the magnetic flux, an EMF is induced in the conductor. The magnitude of the induced EMF is proportional to the rate at which the flux is cut. In a DC generator, the armature conductors are rotated mechanically within the magnetic field produced by the stator poles. As the armature rotates, the conductors cut the magnetic flux, and an EMF is induced in them. This induced EMF is alternating in nature within the armature coils. The commutator and brushes then act as a mechanical rectifier, reversing the connections to the external circuit every half rotation, so that the current flows in only one direction in the external circuit, producing a DC output. The direction of the induced EMF is determined by Fleming's Right-Hand Rule.