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The rack and pinion is supposed to turn each of the front wheels differently, such that lines orthogonal to the wheels will intersect in line with the rear axle:

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  1. Which components of the rack and pinion mechanism are modified in order to account for different spacing between the front wheels, and between the front and rear axles?

The only parts I see to play around with are the steering arms, the tie rods, and the rack itself. For the latter two, I imagine you could play around with their relatively lengths, and the steering arm gives a length and an angle.

  1. How do I calculate the necessary dimensions of these various parts for a given set up?
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  • $\begingroup$ I believe I may have found a way of setting about this with this article: ijser.org/researchpaper/… I had thought Ackerman steering to be a different mechanism though, but it looks correct. $\endgroup$
    – Rekov
    Jul 1, 2021 at 0:26

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You should look at Ackerman Steering. You don't really need to modify anything apart from the length of the rack. What you need to modify are the steering arms and ties. A simplified version is shown in the image below.

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Figure 1: Ackerman steering geometry (source: Wikipedia

The easiest way, is use a parametric design software (Inventor, Solidworks etc) and for different length, see what are the maximum limits of the rack and pinion.

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    $\begingroup$ Some 80 years ago no software existed, so trailers that had front steering would be towed around the yard and the wheel angles adjusted untill the turning circles reduced scrub and the turning circle matched the towing unit. $\endgroup$
    – Solar Mike
    Jul 1, 2021 at 4:34
  • $\begingroup$ It's my understanding that Ackerman steering is just an approximation of 'ideal' steering. Simple mechanisms are not able to achieve ideal steering at all turning angles, but can be calibrated to achieve perfect steering at specific angles (say 40° of the inner wheel), and approximate very closely at all other angles. As far as I can tell no rack & pinion, or recirculating ball steering system can achieve ideal steering either, but they still use the Ackerman angle in the steering arms and achieve close approximations. $\endgroup$
    – Rekov
    Jul 1, 2021 at 19:06

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