Trying to create script that drags an object connected by a hinge

So, I am trying to write a script where an object at the end of a chain of hinges follows the mouse. The problem is that when I use seemingly anything that involves "transform.position = ...", the object I am trying to drag completely disconnects from the chain. So is there anything I can do to make this work?

Here is my code:

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 
 public class FollowMouse : MonoBehaviour
 {
     void Update()
     {  
         float xMousePos = Camera.main.ScreenToWorldPoint(Input.mousePosition).x;
         float yMousePos = Camera.main.ScreenToWorldPoint(Input.mousePosition).y;
         new Vector3 mousePos = (xMousePos, yMousePos, 0)
         transform.position = Vector3(xMousePos, yMousePos, 0);
     }
 }

I have tried other things, but this is essentially what I have been doing. Thanks.