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I would like to know if there's a way to increase the linear travel of a rack relative to the rotation of the driven shaft, either through a gearing system or some other means?

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    $\begingroup$ Just use a larger pinion. $\endgroup$
    – Eric S
    Aug 25 '20 at 12:12
  • $\begingroup$ I would do that, only I want to house it all within a confined space, hence the question. $\endgroup$
    – Joe Bloggs
    Aug 25 '20 at 12:53
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    $\begingroup$ I would do that, only I want to house it all within a confined space, hence the question. Your question is asking if there's a way to do it through a gearing system or some other means, and this is the only answer. Use a bigger gear. Length of travel on the rack must equal the arc length on the pinion. You change arc length of a circle by changing its radius or by changing the total rotation. Since you specify relative to the rotation of the driven shaft, the total rotation must stay the same, and so you're left only with changing the radius of the pinion. $\endgroup$
    – Chuck
    Aug 25 '20 at 13:20
  • $\begingroup$ Multistart threads on a rod $\endgroup$
    – joojaa
    Aug 25 '20 at 14:52
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The linear travel of a rack in a rack and pinion is always going to be the radians of rotation multiplied by the radius of the pinion it meshes with, less any initial backlash. Otherwise the teeth on the rack would need to pass through the teeth of the pinion. You could add an epicyclic gear train before the pinion to increase the total revs of your rack-pinion compared to your new input.

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  • $\begingroup$ Thanks for your input, however I think that an epicyclic gear is a bit complex for what I'm trying to do. $\endgroup$
    – Joe Bloggs
    Aug 25 '20 at 12:54
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    $\begingroup$ jko's suggestion is quite good as it represents the most compact option available within your constraints. It's strange that you consider a set of gears in a planetary arrangement to be too complex. Eric S' comment and jko's are about the only choices on the low end of complexity. Hydraulic or electric boost will be much more complex. $\endgroup$
    – fred_dot_u
    Aug 25 '20 at 13:31
  • $\begingroup$ @joebloggs you can get commercially available planetaries that are very compact with good ratios for a decent price, check out Boston Gear. what is your definition of a "confined space"? $\endgroup$
    – jko
    Aug 25 '20 at 13:48
  • $\begingroup$ Sorry, just to clarify, I'm a hobbyist and model maker, so I was thinking along the lines of something that I can make using a milling machine. Now you mention I have noticed some planetaries that are commercially available and aren't too expensive. I'll look into it. $\endgroup$
    – Joe Bloggs
    Aug 25 '20 at 14:55

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