Rotating rigidbodies with moveRotation along external axis

Hello, I'm in a process of programming a robotic arm in Unity. I've created 3D model and would want to move them but with a caveat that if (for example) I rotate the base, the arm rotates as well. The catch? I wanted Unity to handle collisions for base objects (like cubes, spheres, etc.). My goal is to have objects which I could pick up and let go. At first I've tried using " transform.rotate" in order to move the arm's joints. It all seemed great, as I had parented the objects from base - up and whenever I " transform.rotate" the base, the rest of the robotic arm rotates as well. But then I was told that one should use rigidbodies for collisions and this is where things have started to fall apart. First thing is that when I use rigidbodies, they no longer rotate when parented (when using “transform.rotate”). Second, when I use “transform.rotate” I'm able to phase into objects. I guess that’s since this function works as a teleport of sort. And so, I wanted to use “Rigidbody.MoveRotation”. This works, but only for one of the elements. They, of course, don't move when parented, so I've thought that maybe I could use “Rigidbody.MoveRotation” to rotate each of the arm's elements along their "lower tier" element's axis (see tiers below)

base – boom – arm - gripper

but I'm stuck at getting it to work. Am I understanding correctly, that “Rigidbody.MoveRotation” applies rotation ONLY along the local rotation axis?

I paste my code below, but I don't think if will be of any use:

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 
 public class Manipulator_movement : MonoBehaviour
 {
     public GameObject Obrotnica;
     public GameObject Wypad;
     public GameObject Ramie;
     
 
     public float myInput;
     public Vector3 m_EulerAngleVelocity;
 
     public float tempRotationOfObrotnica;
     public Quaternion tempRotationOfObrotnicaQ;
     public Quaternion GG;
     
     // Start is called before the first frame update
     void Start()
     {
         GG = Wypad.transform.rotation;
     }
     
     void Update()
     {
     
         if (Input.GetButton("Right_Shoulder_Trigger") || Input.GetButton("Left_Shoulder_Trigger"))
         {
             Debug.Log("LJH: " + Input.GetAxis("Left_Joy_Horizontal") + "LJV: " + Input.GetAxis("Left_Joy_Vertical") + "RJH: " + Input.GetAxis("Right_Joy_Horizontal") + "RJV: " + Input.GetAxis("Right_Joy_Vertical"));
         // this is for controller support debugging
         }
         else 
         {
             //obrotnicaAngleSpeed = 0;
         }
 
 
     }
 
     void FixedUpdate()
     {
         Rigidbody temp_rigidB_Obrotnica = Obrotnica.GetComponent<Rigidbody>();
         Rigidbody temp_rigidB_Wypad = Wypad.GetComponent<Rigidbody>();
 
         Quaternion deltaRotation = Quaternion.Euler(m_EulerAngleVelocity * myInput * Time.deltaTime);
         temp_rigidB_Obrotnica.MoveRotation(temp_rigidB_Obrotnica.rotation * deltaRotation);
 
         tempRotationOfObrotnica = temp_rigidB_Obrotnica.transform.rotation.eulerAngles.y;
         //tempRotationOfObrotnicaQ = Obrotnica.transform.rotation;
         tempRotationOfObrotnicaQ = Quaternion.AngleAxis(Obrotnica.transform.rotation.y,new Vector3(0,Obrotnica.transform.rotation.y,0));
         //temp_rigidB_Wypad.MoveRotation(Obrotnica.transform.rotation);
         temp_rigidB_Wypad.MoveRotation(GG);
         //temp_rigidB_Wypad.MoveRotation(temp_rigidB_Wypad.rotation * tempRotationOfObrotnicaQ);
         //Obrotnica.transform.Rotate(0f,obrotnicaAngleSpeed*Time.deltaTime,0f,Space.Self);
         //Obrotnica.transform.ro
 
     }
 }

Maybe there’s a different way to do it and I'm just to blind to see it?

I'd be grateful for any help you guys can spare. Thanks in advance.

Cheers, Rafał