Once upon a time I had to transport a few large wheelie bins in my little hatch back. Rather than do a few trips I decided to stack them inside of each other. To do this I had to remove the wheels.
This was a few years ago so there may be gaps in my knowledge. I took the photos then and promised to write up an instructable 'soon'. Better late that never I suppose.
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Step 1: Get Cutting
Turn the bin on its side to give yourself a flat working area. The wheel has spokes moulded into it. One of these spokes has a rounded section running along it. If your wheel looks different to this then this is not the instructable that you are looking for.
Using a sharp sturdy craft knife cut out a small section of the rounded section to reveal...
Step 2: The Secret Locking Mechanism
... a lug and a spring.
Using something pointy but not sharp (I used a souvenir letter opener from Madrid), slide the spring and lug away from the centre of the wheel to release the wheel from the axle.
Now you have one wheel free the other wheel and the axle should be able to be removed as a single piece from the other side.