Moving a set of objects does not work

I am currently working on medical research room in virtual reality. I imported a model of a head and its slices into Unity.

I orded it like this in the hierachy:

 -tissue(2)                                <--- Headmodel
 -Slices
      -X                                   <---Slice (X-Axis)
           -Handle                         <---Handle (where to grab)
      -Y                                   <---Slice (Y-Axis)
           -Handle                        
      -Z                                    <---Slice (Z-Axis)
           -Handle

I created this simple code that moves the Coordinate system of the slices according to the headmodel:

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 
 public class SlicesFolloeModel : MonoBehaviour {
 
     public GameObject headmodel;
 
     // Use this for initialization
     void Start () {
         transform.position = headmodel.transform.position;
     }
     
     // Update is called once per frame
     void Update () {
         transform.position = headmodel.transform.position;
         transform.eulerAngles = headmodel.transform.eulerAngles;
     }
 }

However it doesn't work properly. I want to mention that I made the Slices configurable joints so they move in only one direction when grabbed. I made a video that explains my problem a bit further.

Your help would be really appreciated!