At a rough approximation, assuming a rectangular car, with wheels on the corners:
The inner wall needs to have a radius of AT LEAST r1, where r1 is the stated minimum turning circle radius.

The outer wall needs to be AT LEAST
r2 = SQRT( (r1 + x)^2 + y^2 )
where x is the width of the vehicle, and y is the length of the vehicle.

It is the Pythagorean formula for the circle which goes through the opposite corner of the vehicle.

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The practical application of this is that this tells us how the wheels move to attain movement in the cabin. If you sketch this idealized picture with the corners of the rectangle at the center of the area where each tire meets the road, the diagram accurately represents the movement of those points.