This is another antique store find, apparently a device to measure rim width on a car. It appears to be a complicated device with several scales, the importance of which is unclear. I could understand a bit of difficulty measuring a rim with a tire in place, but a large caliper would do just fine, I would think- if it was important. Unfortunately, the directions on the back have faded, but one feature seems to be the ability to measure tire wall thickness, another possibly the rim material thickness. Searching unsuccessfully online for info, the former Canadian tech giant Rim (Research in Motion) gets in the way!
All in all, a tool that I did not feel I needed to buy.