These are really interesting and I never realized that there are so many of them. Railways use "easements" to guide trains in and out of curves, so rather than just changing from straight track to the radius of the curve, there's a section that approaches the radius. If the train is making a right angle turn, it will do somewhere around 85 degrees of that turn at the expected radius.
Very interesting! For anyone else that's curious, I found a Wikipedia article [0] with more information. It turns out that an "easement" can also be a right to use land that you don't own for things like roads and structural support [1], so it took a minute or two before I found it.
Cars and bikes do that, too. You don't instantaneously go from 'axles parallel to each other' to 'constant angle A between front and rear axles'. Instead, you go from 'not turning the axles' to 'turning it at constant speed' to 'keeping it at a fixed angle' and back.
That's why road exits and a cloverleaf interchanges should never use perfect circle arcs to connect straight road parts. The curvature of the road should change continuously such as in various splines or parts of superellipses (http://en.wikipedia.org/wiki/Superellipse). An Euler spiral (http://en.wikipedia.org/wiki/Transition_curve) is optimal, but for cars, small deviations from the optimal aren't as bad as for railway cars.
Though on a bike, you can lean to turn if you're going the right speed. The turn is made because you're riding on the sides of the tires which will give way to the side you're leaning towards.
