What distance would the rack move in one revolution of the crank when a 20 tooth pinion gear is used?

Answer 1

You haven't provided all the information necessary.

If the rack is driven by another gear (or there is another gear on the crank), you need to know how many teeth it has to determine the gear ratio.

If the rack is simply toothed, you need to know the number of teeth-per-inch (or teeth -per-foot). The rack then moves the same distance as twenty teeth (assuming the 20 tooth pinion is directly driven by the crank).

Answer 2

20 times the pitch of the rack or pinion gear, which you don't give in your question.

If each tooth measures 1cm from center to center, it would move 20cm.