A place to get answers about which CNC products to look at for your specific application. We have everything from complete controllers in different sizes and in both stepper and servo configurations. A good place to start and get basic answers
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About 3:1 with 1" dia pinion. The pinion diameter defines the final ratio because it multiples the distance by the circumference (PI times the diameter) The bigger the wheel the furthers it rolls per rev. Teeth just make sure it does not slip. So if you increase the Diameter the ration needs to increase to match. The goal it to acheive to as close to 1" of linear motion per one motor rev as you can using off the shelf components.