How is it possible that the MIG 21 has the rudder to the left, but the nose wheel moves freely to the right, and then straight or to the left on the runway?
See timestamp 1 min 11 sec in this video:
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Davidw mentioned the book "Red Eagles". It has a passage about steering the MiG-17 and says the MiG-21 used exactly the same system. In the following passage, he is quoting pilot Jose Oberle.
Red Eagles: America's Secret MiGs, Steve Davies, 2011
Taxiing the airplanes was a bit of a trick. If you wanted to turn right, you pushed the left rudder bar in and you pulsed this lever on the control stick. That dumped the pneumatic pressure to the brake on the left wheel and transferred it to the right wheel. You would get the free-swinging nose wheel to start to turn to the right, and then as you got ready to come out of that turn you'd have to push the left rudder bar past neutral and you'd have to start pumping the little paddle again to get the power back on the left wheel, to get the nose to straighten out so you could taxi straight!
Per this, the nosewheel is not part of the steering system.
Most larger jet aircraft do not have a full time link between rudder pedals and nosewheel steering. In planes I have flown there is a nosewheel steering button on the control stick. It is spring loaded, and as long as it is held down (i.e. during taxi and initial take-off roll) the nosewheel will steer with the rudder pedals.
This is done because the steering sensitivity needed to make a 90 degree turn taxiing at low speed would be way too much on the runway at high speed. For smaller GA aircraft this isn't so much of an issue, and the relative simplicity of not needing a method of disconnecting the two overrides any small advantage.