Thanks for the clarification. It's so much easier when people know the real situation.
Like other people, I haven't really thought about this one before and am not sure how to describe it.
It's like a rack and pinion, which is sometimes called a gear.
I'm not sure you can talk about a gear ratio, because a ratio mathematically is fraction derived from a comparison of two similar quantities - like two diameters, two numbers of teeth, two lengths, etc.
But in more general parlance we do talk about mixed comparisons, such as power to weight ratio of an engine.(*)
A R&P is converting a linear movement (length) to rotation (angle), so while mathematically not a pure ratio, we could say the 4mm spinner did 80 turns per m and the 12mm spinner did 27 turns per m and call these turns per m ratios. That would help you make a comparison of the force required to give both the same acceleration. (Though the calculation of achievable speed is rather more complex.)
The big problem with such mixed comparisons is that we have to be very careful to state and remember the units attached to this number and you can't easily compare, say, 80 turns per metre with 29 degrees per mm.
For real ratios the number is the same whatever units we use (which, of course, must be the same for both devices.)
So could you call this difference between the 4mm and 12mm spindle and the users fingers a gearing ratio?
IMO you can call it what you like! But I'd just stick to calling it, the ratio of diameters or ratio of circumferences. That tells people what they need to know about the spindles.
What would you gain by calling it a gear(ing) ratio? You would confuse and mystify many people.(**) I don't think any of the text book material on gear ratios would apply or help you calculate the speeds, forces, etc.
(*)By which is actually meant, the power to mass ratio.
And there is a more acceptable technical term, the specific power.
(**) As witness the confusion during the first 11 posts of this thread.
