Mechanics of a car turning left

[sophiecentaur]

A train would work as well with independent wheels

That sounds right but the above video implies that the axle needs to be rigid for directional stability. To work with a rigid axle, the rotation rate must be proportional to 1/radius of curvature for both wheels, if slipping is to be avoided so the slopes on the cones need to be appropriate. The video doesn't actually say how the optimum cone angles are calculated; they will depend on the gauge of the rails, I guess.