are you sure you have the right design here?
i think you need the red gear and the black one on the same shaft, with the rack touching the red gear.
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
If the red and black were on the same shaft, they would both rotate in the same direction, forcing the rack down. Would that serve any purpose when the black could be the direct drive? Basically the black pinion has a key hole inserted inside, so the red could not mechanically fit onto the same shaft as the black. Sorry, I should have mentioned that before in my query.
the black cant be the direct drive because you cant make it small enough to get 8mm per half turn. your design in post #1 wont work because the diameter of the red wheel has no impact on how far the rack moves per half turn of the black wheel.
If you need the thing to go up at the required speed then do what i said in #2 and insert another gear between the red one and the rack.