Is the front wheel supposed to turn 360 degrees?

Came across this youtube video where a tug does a 180 degrees turn while towing a gulfstream and then at minute 00:50 adds 180 degrees more to complete a 360.

If you notice closely the wheel actually turns with the tug all the time (is not static).

Are airplanes wheel structure supposed to behave that way, and can you as well turn the wheel 360 degrees from the cockpit?

Note how the wheel steering linkage (arm) has been disconnected:

The wheel freedom is limited to about 80°, the arm must be disconnected in order to go further. In this video, while this disconnection is neither shown nor commented, you can see the arm connected at 0:43 and disconnected a second later.

This 80° limit is for a good reason:

You can see only one tire would touch the ground at 90°. The wheel actually stands on the tug platform, the tug supports the aircraft weight while turning.

Note how the lower part of the wheel jack has turned, but the upper part didn't. The disconnected arm moves with the wheel, but the arm anchor points position hasn't changed. They are in the position last commanded from the cockpit.

Details of the cradle and turntable from Lektro:

The operator disconnects the arm, hooks the wheel with the yellow U-hook, moves the wheel onto the turntable and locks it by retracting the hook with the flat strap.

Some airplanes have nose wheen steering, some do not.

Nose wheel steering does not allow the nose wheel to turn full 360 degrees, unless the steering system is disconnected from the lower assembly. It should be noted that not all freely pivoting nose Wheels can turn 360 degrees there may be limiters/limitations in the system preventing this.

In the planes with freely pivoting nose wheel the steering is achieved by differential braking such that the pilot applies brakes on either side of the plane to make it turn.this is not as convenient and precise as a nose will steering.

As a rule of thumb: the smaller the plane is the less likely it is to have a steerable nose wheel. This is because the system adds complexity and weight

• I highly doubt that a Gulfstream does not have nose wheel steering at all. More likely they can disconnect the nose wheel steering during tow operations. Can you add a source? Commented Sep 5 at 6:20
• The G450 AOM (from this site) says: "The nose wheel steering linkage must be disconnected for aircraft towing by removing the connecting pin on the torque link between the actuator and the nose wheel." Interestingly, it also says "Care should be taken to ensure that the nose wheel is not pivoted in excess of the 80° limit." No idea what they were doing in that video. Commented Sep 5 at 6:39
• @Bianfable thanks, I stand corrected! Commented Sep 5 at 8:43