If the wheel has an octagon in it the number of knocks would be 8.5 or more. If the number was 8.5 this would mean that the difference between the sizes of the two constructions was very small. The amount of lateral movement would be very limited and the offsetting of the COM minimum. The effort to do this is not worth the offset gained.I agree that there are not exact 8 impacts per turn of the Hamster cage, because the octagon is smaller then the inner radius of the Hamster cage, let it be lower then 8, the eyewitness can not count 7.5 per turn, they will give you 8 back as a number.
With 9 or more knocks per revolution the possibility to increase the offset increases with the number of knocks. It can then be considered to have an offset that could potentially make the wheel turn. The problem then becomes how to keep the offset octagon permanently offset? This requires an additional mechanisme. The additional mechanisme needed to do this cannot do it if the mechanisme itself has the exact same problem that you have observed in all the wheels you have seen and tried. You know that weights going around in circles cannot make a wheel turn, why do you think they can make an octagon in a wheel turn?
We most certainly agree on many things, we cannot agree on a rocking construction of any form or size because from all my experience i have come to the conclusion that it just moves the problem.
How to make a wheel turn and how to make an octagon turn. The problem is identical and the reason they don't work is identical. Moving the same problem is not what i would call a wheel with a fundamental difference. It is the COM that must walk around the wheel and not a construction. The end result is the same, the wheel would turn. You can see clearly that if you could get the octagon to do what you would like it to do, you would have a runner. I think it is easier to achieve this without a construction than with. As i have already said, i would very much like to be proven wrong.
Good luck with your try Georg,
RH 46