Matt, the key to simplify “cog-wheel” calculations is to count teeth. The belt has 75 and the wheel has ten. (… don’t worry, I didn’t count all the 75, I measured the points of 10 and extrapolated to the complete length, but counting works as well).
The ratio of 75/10 is 7.5 So the number was 360º x 7.5 = 2700º. (Given the 0-100% as input in the Range Mapper)
I know there is always the suggestion to take radius or diameters, but that has to be in the center/middle of all parts, and then it becomes a longer number story. Teeth need to fit into each other, and it is a simple math then which just works very precisely. This is the way I have suggested to do it since over a decade, no one has complained so far.
Since I noticed that they move initially backwards, the number had to be negative. More in detail: My first set up was, scene time to 0-100 frames and the animation 0-10%, first as a spline then as a linear interpolation, just to get clear what happens. With this set up, I was able to see the relation of frame and offset. Just to get familiar with the scene, while assuming anything could be a problem. With this new knowledge, the next step was just counting teeth.
My best wishes