My maths is rusty, but I know the basics of gear ratios, enough to say a rack and pinion works of a 1:1 ratio.
See attachment for the overview of what I am hoping to achieve.
I need the rack to move a total of 24 mm over three 1/2 turns of the black pinion gear.
The black pinion can be no smaller than 10 mm radius. It can increase in size.
The red gear can be no smaller than a 5 mm radius (due to machining tolerance), but can increase in size.
Number of teeth is unknown, but ideally a smooth operation would exist. So far, I have been basing my calculations on having 20 teeth.
This should be simple, but can't get my head around it. If anyone knows, your help will be highly appreciated! I'll keep at it. Cheers