How to rotate part of an object so that it watches another object?

Questions & Answers
1

Created an object consisting of many parts, how to correctly rotate one of the parts of an object so that it tracks another object using LookAt if possible? When I use LookAt, part of the first object is rotated sideways, not front.

And also how to rotate an object so that it tracks another object along one axis?

2

The script below will handle horizontal head movement. Also added a bit where it turns the body if the head reaches its limit. You can remove that.

public float maxAngle = 75; 
public Transform target;
public Transform head;

void FixedUpdate {
	// Handle the head look rotation
	HandleHoodRotation ();
}

void HandleHoodRotation () {
	if (CanLook())
		head.LookAt(target);
	
	// If you want body movement once you reach the end of neck angle
	else
		transform.LookAt(new Vector3(target.position.x, transform.position.y, target.position.z));
}

// Checks if we can look at the object
bool CanLook () {
	// Get the direction vector for the looked at object
	var objectDir = target.position - transform.position;
	
	// Remove the vertical component 
	var objectDir = new Vector3 (objectDir.x, 0, objectDir.z);
	
	// Get the angle
	var angle = Vector3.Angle(objectDir, transform.forward);
	
	// Now do the check
	return angle < maxAngle;
}