Clamping local position

Hey, I am making a mechanic that basically moves the arms around (2d), I use the arrow keys to move an object, and then both arms are child of a main object, which has the lookAt function to look at the object I move, but that would be problematic, for example if the player got the object too far from the arms, that it would have to go a long way until the arms would actually change the direction they're looking at, so I tried to clamp the position value, but it's happenning in world space and not in local space, how can I fix that? here's my scripts btw:

 using UnityEngine;
 using System.Collections;
 
 public class Pointer : MonoBehaviour {
     
     public float velocity;
     
     void Update () {
         transform.position += new Vector3 (Input.GetAxis("Horizontal") * velocity, Input.GetAxis("Vertical") * velocity,0f);
         transform.position = new Vector3 (Mathf.Clamp(transform.position.x, -1.25f,1.25f), Mathf.Clamp(transform.position.y,1f,3f),transform.position.z);
     }
 }

 using UnityEngine;
 using System.Collections;
 
 public class Arms : MonoBehaviour {
     
     public Transform target;
     
     void Update() {
         transform.LookAt(target);
     }
 }

EDIT: ok maybe this isn't actually the better way to do it, so maybe if you know another possible way of making this pointing arms with arrows mechanic tell me please.