Translational and rotational forces in a vehicle moving along a string

[praskatonik]

Hi.

I've been working on a project of angle stabilization for a vehicle moving along a string, looking like this:

The propulsion system is connected to the central wheel, while the outer two wheels are used for support.
I've observed that during acceleration the vehicle rotates. I would estimate that this angle is proportional to the translational acceleration, and I need a way to quantify (or refute) my estimate.

My model is following:

τ - torque force generated by the propulsion
a - translational acceleration (αr = a)
r - radius of the driving wheel
F1, F2 - tangenial forces of chasis torque due to motor torque
Fw1, Fw2 - forces by which the wire opposes the deformation that the chasis torque would cause
θ' - angle velocity of the driving wheel

Is it correct to say that the following equation holds:
I*θ'' = τ - r*m*a
where I is the inertial moment of the chasis, and θ'' angle acceleration?

How to I model the tangenial forces of torque acting on the end-points of my chasis and the forces of deformation opposition exhibited by the wire?

I presume if it were a perfect, unbendable wire, it would be true that:
F1 = -Fw1 and
F2 = -Fw2
and no chasis rotation would be possible.

In my case, as in any real case of object hanging on a wire, this is not true.

Thank you all :)

Ana

P.S. This is my first dabble in anything rotational, so excuse my ignorance. This is how far I can get by using brain+Google.

 

[moogull]

Wouldn't the supporting wheels need to be on the other side of the wire? If the wire is stiff enough maybe you can change the supporting wheels so that there are two on each end of the chassis, kind of like a pitching machine. Just more design ideas, no math yet from me.