The paper describes a new method for the control of mechanical manipulators which allows the use of the Exact External Linearization (EEL) technique in cases when actuator limitations cannot be ignored. By introducing an extra degree of freedom in a system's transfer function, the method allows the actuators to work in a saturated mode during the initial gross prepositioning motions and then automatically switches to a fine positioning high-gain linear mode when the tracking (positioning) error becomes small. The technique leads to a much more efficient use of the actuators, which can allow the employment of smaller and lighter motors without an appreciable loss of the system's dynamics characteristics.