I'm trying to study the free body diagram of this differential-drive mobile robot:
So i started considering just a straight motion (torque on the right wheel is equal to the torque on the left wheel) and i wrote down the equilibrium equations about forces and torques. For each active wheel i considered 5 forces acting on it (mg, vertical reaction due to the surface, friction force, horizontal reaction force at motor bearing, horizontal reaction force at motor bearing) and a torque generated by the electric motor.
$A$ is the wheel center of mass, $F_N = R$, $F_T = F$. Since it must be a pure rolling motion:
I wrote the same equations also for the passive wheel, in which I did not have $\tau$ torque.
$B$ is the wheel center of mass.
About the platform I have something like this:
Assuming that the robot is moving on a straight trajectory with the same torque applied on each active wheel, I have this equilibrium equation about the x-axis:
From the equilibrium equations of the passive and active wheel, I got $P$ and $P_1$:
I have three unknowns and just and equation. Am I doing something wrong?