In most small aircraft, steering on the ground is controlled by brakes and rudder pedals. This is through a mechanical linkage pulley system that's pretty old school, also referred to as a free-castering system.
However, as planes get heavier and faster the need for a different system came into place. The Learjet 60 is a perfect example of an aircraft with this. Thus nosewheel steering became the solution. Nosewheel steering facilitates better directional control on the ground for takeoff and landing and sharper maneuvering at slower speeds such as taxiing to park.
Nosewheel Steering depicted by FlightMechanic.com
There are various designs for nosewheel steering but this is the basic depiction of how it is designed. Most are hydraulically powered and have mechanical, electrical, or hydraulic connections that transmit the pilot input to a steering control unit. The range that these inputs can control the movement of the nosewheel are important, as you don't have full range to move the nosewheel 90 degrees in either direction at just any speed. Most systems only operate up to about 90 knots, and the faster the aircraft is increasing speed towards those knots the less movement the wheel will move.
Hardly any aircraft manuals depict or discuss this range in detail but this is the best photo I could find that helps illustrate this. Just remember that the faster the aircraft reaches, the more the system goes from nosewheel steering back to your usual rudder pedal system.
Another important component to know about in this is shimmy dampers. There are torque links attached to the stationary upper cylinder of a nose wheel strut that work to control rapid oscillations, otherwise known as nosewheel shimmy. You'll feel these oscillations sometimes when you're taxiing too fast and/or have too much pressure centered on the front wheel. Simply slow down or try pulling the yoke back then gently back forward and 9/10 times this will stop unless it is a mechanical issue that needs to be addressed.
There's a lot of components that are a part of the nosewheel steering system. These however seem to be the most common issues pilots have when transitioning to using one and trying to keep their operations smooth and comfortable for passengers. To understand the system better on YOUR aircraft however make sure to always read your flight manual in depth and talk to your mechanics when you can. Usually they're happy to share knowledge and teach you how to not break things as much ;)
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