# Finding transformation of forces and moments

I have two sets of forces and moments, measured by two 6 DOF force/torque sensors at position A and B on a robot arm (B at end effector). My goal is to use this measurements to relate the forces/moments at position A to those at position B, i.e. find a transformation of $$F_A, M_A$$ to $$F_B, M_B$$. The transformation is static and no other external forces apply.
The related formulas for that are: $$F_B \approx RF_A \\ M_B \approx RM_A+t\times F_B$$ Is that correct (it's addaped from this)?
My goal is now to find an optimal (in a least squares way) matrix R and vector t. How would I do this? Is the Kabsch algorithm suitable for this?

Update:
Below a small sketch of the setup. It is some sort of handle on the robot arm. A force is applied (and measured) at Sensor A, the goal is to use the measured force at sensor B to find the transformation.

• I updated the question, hope that helps. Unfortunately I don't have a photo or real technical drawing at the moment due to the current crisis. – Sebastian E Apr 15 '20 at 9:26
• If I understand well your problem, the sensor B is at a "free edge" of the robot's arm. If it is the case, no forces or moments will ever be registered by your sensor, since by definition a free edge is stress free. – ClariB Apr 15 '20 at 10:15
• It is at the end effector and measures all forces applied to the robot. Maybe my drawing is not perfect :D – Sebastian E Apr 15 '20 at 10:39
• Maybe that is not s clear, but of cause this is just a detail. At the right would be a joint and other links of the robot. – Sebastian E Apr 15 '20 at 12:29