Erm.... not quite. := Each wheel on the 747 weighs 160kgs. So 16 wheels weighing 160kgs doing 180knots is a serious gyroscopic force - 2.56 tonnes of gyro (half that actually as it is only the wing gear that retracts sideways, body and nose retract forward along the direction of gyro rotation) - which makes it extremely difficult to move the legs, so stopping the rotation removes the force and the legs move with 'ease'....:D applying the brakes prevents a very slow deceleration of rotation speed with added vibration as they will all slow at different speeds.
Certain MEL brake deficiencies require the gear to be left down for up to 5 minutes after takeoff to allow the wheels to stop rotating prior to retraction.

Thanks again for all the replies :ok:

I have some doubts about some explanations here. First, it are the wheels that are balanced, not the wheel/tyre assembly. Because the two wheel halves are not perfect symmetrical you have to balance that. But tyres wear, and some inbalance can occur. We've had that many times on nosewheels, when the left is worn to limits and the right is perfect, you get shimmy. But only in the case of unmatched wear. And mechanics will normaly change nosewheeltyres that are not matching. So if someone says here that you feel it every takeoff, I doubt it had to do with tyre wear. Second, the antiskid will activate the brakes before gear retraction, but this is to PREVENT high stress and vibrations. so I cannot see why they CAUSE vibrations.
I also don't believe that it can be worn wheel bearings, as bearings get changed together with wheel change, and this is quite often.
My guess the vibrations are just due to changing aerodynamic flow around the wing/body/empennage during rotation, just as extending flaps/gear/airbrakes cause more turbulent flight.

I just imagined this...similar to the gyroscopic effects of rotating wheels, wouldn't a take off with APU running cause a lot of gyroscopic stress/vibrations. Take an APU running at a few thousand revolutions a minute, at the very end of the aircraft, making a swing of a few meters during rotation.

Why do you doubt the explanations? I think the vibration talked about here is before automatic braking and gear retraction. I think it is worst when the wheels are unloaded off the ground and rotating very fast in unloaded bearings. Whilst the noise can be alarming when seated near to the undercarriage legs, with the general noise of the engines, just a few rows away you cannot hear it above the rest of the noise, and that explains the unconcern from the crew away from the wheels. If you run pushchair wheels very fast, then lift them off the ground, they can suddenly vibrate quite badly when unloaded from the ground. that is what is happening to the aeroplane wheels.

As for gyroscopic forces on the APU/engines, not a factor. They are designed to take it. Indeed, these forces were looked on as one possible cause of the Comet accidents in the 1950s and shown to be irrelevant. Aeroplanes are designed to manoeuvre with the engines at high power and the APU running. The actual swing has no effect on gyroscopic forces anyway, it is the angular change and rate that counts, not sideways or vertical movement.

With flap out, you can see marked vibration and shaking on the flaps, but at take-off, lower settings are used than on landing, and the shaking is in excess of the shaking on mid-flap settings. Again, not a factor I believe.

I still doubt it, but I can see the logic in it. (it's good to doubt even if there's no reason too, I've learned not to take everything for granted). Maybe if I encounter this in real it will be obvious.
But then, why is the vibration only on the 744? More wheels more vibrations?

It's there on all jets I've flown.

Mode7
If you disagree with my statement, perhaps you could explain why the 747 body gear (which retracts in a fore/aft plane) also automatically brakes during the retraction sequence? Your last sentence doesn't follow your initial line. You only have to look inside the nose bay to see how much debris gets thrown around.

done to death
 

this thread has been done to death bolty mcbolts answer is correct when it comes to how despin braking works as for wheel and tyre balancing(they all wear and yes could be a small factor)worn bearings i say blah blah blah what a crock. so lets just finish it by saying yes there is vibration but nothing to be alarmed about