Thank you.

I'd suggest a salutation of, "Dear Sirs" as there is more than one of us who does not understand your post.

Count the teeth on the pair of meshing gears. Divide one number by the other. This gives the gear ratio. Repeat for as many pairs of gears as may be involved in the gear train. Really easy.

This technique also works for sprockets as well as pitch-diameter ratios between belt pulleys. With versatility like that, how can one go wrong? Just make sure to multiply/divide the numbers in the correct order.

Two things you can do: 1. check out http://www.corrsys-datron.com/ and 2. Contact Prof. Krishna Kumar at IIT Madras who is the head of "Vehicle Dynamics" who can give you advise on this (by the way, IIT is using Corrsys-datron" for the same purpose. Hope this is going to point you in the right direction.

With gears or sprockets, there is no slip. Just do the ratios. Thus you need no fancy instrumentation to accomplish this. If belt drives or clutches are involved, then slip is possible.

Another way to check this is with a tachometer. Measure the rpm's of the shafts; divide these numbers to determine the ratio.

On the other hand, a steering gear may not have consistent rpm's for enough time to take such measurements; so back to tooth ratios, which should be easy to count.

It is my understanding that the steering box in a modern vehicle is not only powered actuated, but that this device incorporates variable ratio gearing, that is, the more the steering wheel is turned, in either direction, from the the neutral, or 'straight-ahead' position, the output, namely the steering arm, turns at a dis-proportionally faster rate.