In order to fully understand how automatic sliding doors work, you need to know how all these different components function together.
When movement is picked up by the sensors, the motor mechanism is triggered to start moving its belt. This will cause the rollers to move along the tracks and pull the doors open
The operator is placed in the space above the sliding door.
An electric motor, geared down to get a lower speed and a higher torque, drives a pulley at one end of a belt. The door is clamped to the belt. To open the door, the motor turns the pulley, which in turn turns the belt, which in turn drags the door. To close the door, the reverse occurs.
Historically, elevator doors were opened using simple harmonic motion by a set of mechanical linkages; the motor, geared down, would rotate linked arms, which in turn would drive the door.