The answers I here from people that answered here is gearbox so force multiplication or just completely ignoring forces and using kinematics only.
If that was to be true a 1:1 gear ratio will still have the wheels rotate and that is just not the case.
How about you stop lying, please?
The kinematics analysis shows without a doubt that a gear 1:1 ratio is a singular point: if there is a driven wheel on a treadmill, connected (via e.g. a belt) to a driving wheel of the same size with a 1:1 gearing, with driven and driving wheels rotating in the same direction,
the vehicle does not work: the velocity ratio is undefined (division by zero) or infinite.
This has been told you time and time again, yet you somehow keep claiming that
we claim that even in that case the vehicle would work. That is a dirty rotten lie, and you should be ashamed.
The singular point at 1:1 gear ratio is also at the core of the explanation of exactly why the gear ratio matters, and how gear ratios like 4:1 and higher work much better for such a demonstration vehicle, as lower gear ratios involve high relative speeds, and for acceleration from standstill, require such forces that tend to twist and bend the vehicle instead of behaving as a rigid structure. To repeat once again, here is a graph of how the ratio of the velocities with respect to ground, treadmill surface speed (leftwards) to vehicle speed (rightwards), as a function of the gear ratio \$G\$ behaves:

At 1:1, the vehicle would need to move at plus or minus infinite speed, which is obviously unphysical and describes a nonfunctioning vehicle.
The graph describes the same information as the table in
reply #240.
The fact that at gear ratio \$G = 0\$ the velocity ratio is \$1\$ means that if the driven wheel is locked (will not rotate), the vehicle will move in the same direction and at the same speed as the surface of the treadmill. Similarly, at \$G = \pm \infty\$ the velocity ratio is zero, meaning that if the driven wheel rotates freely but the driving wheel is locked, the vehicle will not move at all.
All this, just from the kinematics analysis, which you refuse to review (and much less understand, even though it is the simplest level at which one can examine mechanisms).