Simple 3D forward kinematics with easing. Place on any normal Transform and set fkParent in the inspector to the Transform you want it to follow.

SmoothFKMember.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;



public class SmoothFKMember : MonoBehaviour {
	public Transform fkParent;
	public float rotationSpeed = 10f;
	private Vector3 initialPositionOffset;
	private Quaternion initialParentRotation;
	private Quaternion initialRotation;
	[SerializeField]
	private bool _drawDebug = true;
	private void OnEnable(){
		initialPositionOffset = transform.position - fkParent.position;
		initialRotation = transform.rotation;
		initialParentRotation = fkParent.rotation;
	}
	private void LateUpdate(){
		transform.position = GetFKPosition();
		transform.rotation = GetFKRotation();

		if(_drawDebug){
			Quaternion targetQuat = (Quaternion.Inverse(initialParentRotation) * fkParent.rotation).Normalize();

			//this to parent
			Debug.DrawLine(transform.position, fkParent.position, Color.red);
			//this to target
			Debug.DrawLine(fkParent.position + targetQuat * initialPositionOffset, fkParent.position, Color.green);
		}
	}
	private Quaternion _currentParentRotation = Quaternion.identity;
	private Vector3 GetFKPosition(){
		Quaternion targetQuat = (Quaternion.Inverse(initialParentRotation) * fkParent.rotation);
		Quaternion deltaQuat = (Quaternion.Inverse(_currentParentRotation) * targetQuat);
		Vector3 axis = Vector3.zero;
		float angle = 0f;
		deltaQuat.Normalize().ToAngleAxis(out angle, out axis);
		
		Quaternion velQuat = Quaternion.AngleAxis(angle * Time.deltaTime * rotationSpeed, axis * Time.deltaTime * rotationSpeed);
		_currentParentRotation = _currentParentRotation * velQuat;
		return fkParent.position + _currentParentRotation * initialPositionOffset;
	}
	private Quaternion GetFKRotation(){
		Quaternion currentQuat = transform.rotation;
		Quaternion targetQuat = (Quaternion.Inverse(initialParentRotation) * fkParent.rotation);
		Quaternion targetRelativeToInitial = ((initialRotation) * targetQuat);
		Quaternion deltaQuat = (Quaternion.Inverse(currentQuat) * targetRelativeToInitial);
		Vector3 axis = Vector3.zero;
		float angle = 0f;
		deltaQuat.Normalize().ToAngleAxis(out angle, out axis);
		Quaternion velQuat = Quaternion.AngleAxis(angle * Time.deltaTime * rotationSpeed, axis * Time.deltaTime * rotationSpeed);
		currentQuat = currentQuat * velQuat;
		return currentQuat;
	}
}
public static class QuaternionExtensions{
		public static Quaternion Normalize(this Quaternion q){
        Quaternion result;
        float sq = q.x * q.x;
        sq += q.y * q.y;
        sq += q.z * q.z;
        sq += q.w * q.w;
        //detect badness
        float inv = 1.0f / Mathf.Sqrt(sq);
        result.x = q.x * inv;
        result.y = q.y * inv;
        result.z = q.z * inv;
        result.w = q.w * inv;
        return result;
    }
}