This is also why I strongly oppose incorrect modeling (picking a few random forces, and claiming they describe the system, when they clearly do not), and prefer to start at kinematics, which is much easier to understand, and harder to get wrong. Understanding is not achieved by convincing others; it is achieved by making testable hypotheses, applying ones understanding, and comparing the results to the real world observed results. Because of this, I find Popperian falsifiability a more valid approach to science than basic verifiability. It is also exactly why instead of posting a video, I posted the exact description/recipe/model of a vehicle anyone can build and reproduce the findings: no need to take my word for truth, here is how you can find out for yourself.
I know now I cannot help electrodacus understand, no matter how much effort I spend, but I do hope I've helped anyone else reading this thread to not be convinced by electrodacus' physically daft but linquistically clever writings. On the surface, it looks so reasonable; but if you examine the questions and answers, you can see the lack of logic, rationality, and any kind of scientific rigor: only the opposite, a religious stance on incorrect assertions that no proof will ever shake.

Yes kinematics is easier to understand and harder to get wrong but it does not represent reality.
I did not picked random forces as you claim. There is a single force F1 that is the input to the system. You can not expect any movement if you do not apply any forces. F2 and all others are consequence of the applied F1 so I did not made up forces.
I appreciate you trying to make me and others understand how this works as that is the same thing I try to do.
But kinematics is just not the tool you can use to find how this device works.
No unpowered device will be able to move in the opposite direction of the only applied force without using energy storage.
When have you ever pushed something and thing pushed against you with more force than you applied ?
You claim (let me know if I'm wrong) that vehicle in case (a) can move without any wheel slip ? But my videos of the real machine shows wheel slip in all cases.
The reason you can justify that is because you are imagining a different setup from that in case (a).
What you imagine is a free wheel treadmill and the applied force between the ground and vehicle body (that will get you exactly what the kinematic model shows and no slip involved).
But the problem in case (a) specifically asks that applied force is provided by the powered treadmill so F1 is applied to input wheel (right) relative to ground and not relative to vehicle body.
While the result will look very similar with the kinematic model the mechanism involved is very different.
You and it seems most others prefer the simpler kinematic model as it will look to predict the same motion (it is close but not the same) but I think the reality of what happens while more complex (involving energy storage and stick slip hysteresis) is important.
The reason I try to explain this particular device (a) is because people (multiple) have made the claim that it represents the equivalent of the direct downwind faster than wind vehicle when it is in fact representing the direct upwind vehicle and that is because they confuse the input with output.
As for the direct downwind faster than wind, what chance will I have to explain that witch is even more complicated as it involves pressure differential energy storage.
But I can make multiple prediction witch if tested will show the prediction to be super accurate.
For example the claim is that such a vehicle can drive for unlimited amount of time above wind speed and I know that it will start to slow down as soon as it gets to peak speed since at that point pressure differential stored energy will be used up.
Nobody even bothered to take a video from the side on the treadmill model (the one with propeller) to see that acceleration rate drops and not increases as they predict from wrong (invented) equations.
Anything that can be predicted from this vehicle I can predict accurately and I have not seen any real world example of behaviour that is not predicted by my current understanding.
And it seems strange to me that reality (ultimate test of any theory) showing energy storage is ignored or blamed on my setup which is exactly the setup in diagram (a) so the model of interest. Same with the slip that is also seen in the video. The locked and dragged example is again ignored.
All this behaviours are explained fully by Newton's laws of motion. My mistake is probably to assume that everyone will be at the same level of understanding as Newton itself because so much time has passed and we tested his theories but human genetics has not changed at all since his time so the amount of people able to understand and not just memorize his discoveries is still very limited.
"If there is no net force the vehicle will not move."
A net force will accelerate a vehicle, not "keep it moving". Completely ignoring Newton's first law of motion, and accusing others of not understanding physics, is utterly, religiously, strange.
A net force is needed for a stationary vehicle to accelerate so increase in vehicle kinetic energy. An ideal vehicle will then maintain that speed (kinetic energy) without any additional energy input.
A real world vehicle will experience friction meaning that in order to maintain speed (maintain the same kinetic energy) it requires constant input power that ends up as heat.
So if you start form not moving relative to a reference say earth/ground a force needs to be applied relative to earth/ground for the vehicle to move.
You by using kinematics just ignore forces but to get that result you get from kinematics (it is possible) the force will need to be applied to vehicle body relative to ground or to any of the wheels relative to body but it will not work that way if applied force is relative to ground to the wheel on treadmill.
So yes ignoring forces you can get whatever you want but is not the correct description of what happens when force is applied to wheel relative to ground.