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I'm trying to study the free body diagram of this differential-drive mobile robot:

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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.

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$$x:m\ddot{x_A}=-(P+F_T)\\y:F_N=mg+P'\\J\ddot{\phi}=\tau+F_Tr$$

$A$ is the wheel center of mass, $F_N = R$, $F_T = F$. Since it must be a pure rolling motion:

$$F_T\le f_aF_N$$

I wrote the same equations also for the passive wheel, in which I did not have $\tau$ torque.

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$$x:m\ddot{x_B}=-(P1+F_{T1})\\y:F_{N1}=m_1g+P1'\\J_1\ddot{\psi}=F_{T1}r_1$$

$B$ is the wheel center of mass.

About the platform I have something like this:

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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:

$$m_c\ddot{x_c}=2P-P_1$$

From the equilibrium equations of the passive and active wheel, I got $P$ and $P_1$:

$$m_c\ddot{x_c}=2\left(\frac{\tau}r-\frac{J+mr^2}r\ddot{\phi}\right)-\frac{J_1+m_1r_1^2}{r_1}\ddot{\psi}$$

I have three unknowns and just and equation. Am I doing something wrong?

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  • $\begingroup$ Hello! I have edited your question using MathJax (LaTeX) math typesetting. For future questions, you can refer to MathJax basic tutorial and quick reference. Thanks! $\endgroup$ – Jonas May 29 at 21:28
  • $\begingroup$ Oh, thank you. What about the dynamical analysis? Can you help me? $\endgroup$ – xWalle May 30 at 9:37
  • $\begingroup$ @xWalle Better ask it on engineering stack exchange. You will definitely get someone to answer your Q. $\endgroup$ – Srijan M.T Jun 2 at 14:42

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