Final answer:
The Trigeminal nerve is the one that is not associated with eye muscles, unlike the Oculomotor, Trochlear, and Abducens nerves, which all control various extraocular muscles of the eye.
Step-by-step explanation:
The cranial nerve that is NOT associated with eye muscles is the Trigeminal nerve, also known as the fifth cranial nerve. This nerve is primarily responsible for providing cutaneous sensations to the face and for controlling the muscles involved in mastication (chewing), which is unrelated to the movement of the eye muscles. In contrast, the Oculomotor nerve, Trochlear nerve, and Abducens nerve—cranial nerves III, IV, and VI, respectively—are all directly involved in controlling various extraocular muscles that are responsible for different movements of the eyes.