Relative quaternion difference | How does FixedJoint caluclate rotation

Quaternion are hard please help!

I am trying to link a player's hand rotation to the rotation of a GameObject when a button is pressed (grib button). But I am unable to produce the effect I want and have only been able to do what I want to using a work around using FixedJoint.

T$$anonymous$$s is the code that I tried to use, but it does not do what I want it to do:

 Quaternion RelativeHandRotation = HandStartingRotation * Quaternion.Inverse(Hand.rotation);
 Object.rotation = RelativeHandRotation * ObjectStartingRotation;

I want to know how the FixedJoint rotation is calculated so I can implement it myself without needing to use a FixedJoint.

Here is how it want it to work (t$$anonymous$$s is the work around using the FixedJoint):

Here is how it (incorrectly) works with the code given above: