What restraint device is designed to restrict an animal's side-to-side head movement?

The correct answer is the cross tie. This device is specifically designed to limit an animal's side-to-side movement, particularly of the head and neck. It consists of two straps or ropes that are secured to a stationary object, typically at a height that allows the horse or other large animal to move forward and backward but prevents it from turning its head too far to either side. Cross ties are commonly used in veterinary settings or during grooming and training to keep the animal stable and safe while allowing handlers to work effectively.

While other devices have distinct purposes—like hobbles which restrict leg movements, casting ropes that immobilize an animal for medical procedures, and nose leads that help control the head but do not prevent lateral movement—they do not serve the specific function of restricting side-to-side head movement as effectively as cross ties.