Electromechanical systems represent a unique blend of electrical and mechanical components that integrate seamlessly.

A DC motor is a unit that transforms voltage into angular displacement, producing a mechanical outcome from an electrical input.

As current flows in the armature circuit placed inside the magnetic field, it experiences a force, leading to torque that rotates the rotor.

Since the armature carries current while rotating in a magnetic field, its voltage becomes proportional to speed.

Applying a loop equation to the Laplace transformed armature circuit reveals a correlation between the armature current, the applied armature voltage, and the back EMF.

The motor's torque is proportional to the armature current, with the proportionality constant depending on the motor and magnetic field characteristics.

The torque is related to the inertia and viscous damping at the armature.

The torque equation is first rewritten to express it in terms of the angular position of the motor shaft.

Following this, it is assumed that the armature inductance is considerably smaller than the armature resistance.

Upon simplification, the transfer function is obtained.