Sum of torque

[EOW]

I think I forgot the force -F6 on the big pulley. So:

At start, the support turns clockwise at w, the big pulley turns clockwise at 2w and the small pulley turns clockwise at 6w. The belt don't slide. Pulleys accelerate more and more (no brake), the energy is recover after (kinetic energy). An external motor keep constant the angular velocity of the support (need energy because the support receives a torque F3/F4).

At a time:

The motor needs -3FRwt, the motor gives F1 and F2 to the big pulley, the motor gives F3 and F4 to the support
The support receives -3FRwt (F3 and F4)
The belt gives the force F5 to the big pulley, this gives the force F6 to the support and -F6 to the big pulley. The belt gives the force F7 to the small pulley
The small pulley receives 6FRwt
The support receives the torque F6/F8, and the energy 2FRwt

The sum is 2FRwt, no ?

[dieter]

Hi EOW,


Again, this has knocked out my brain  ... I guess you understand this much better than I. Personally, I would rather construct it in 2 hours than to (fruitlessly) think about it for 4 hours. In fact I brought home some plywood, so maybe I will. I just don't know how to provide the pulleys with power when the support rotates.


BR

[EOW]

Maybe it's possible to test the torque on the support without a motor. The big pulley has a mass and it's possible to turn it at 2w before to turn the support, the big pulley can drive the small pulley with the inertia. With no friction to the axes of rotation => no torque must be appear to the support, if a torque appear that could say the system can give en extra energy. The small pulley is braking on the support at the radius R, for me the sum of energy is:

The big pulley lost -2w*3R*F*t = -6FRwt
The friction win 5w*F*R*t = 5FRwt
The support win w*F*3R*t = 3FRwt

The sum is at 2FRwt. The small pulley has a mass as lower as possible.

I think the key is the torque on the support.

[dieter]

Maybe you're right. But then there is still an other problem in a practical implementation: There will be friction on the pulley shafts. The skate bearings are made for about 20 kg, they have a lot of friction. It can he reduced by cooking out the grease, but still... so we wouldn't know if the torque is caused by the friction.


Bearings from CD players would be better, but I got only one right now... (those with the "clickable" cd shaft, not the normal PC cdrom drives).


Maybe I'll find one more in my pile if stuff


BR

[EOW]

For test easily, it's possible to put all things on the support and filmed for watch the energy input/output. The DC motor drives the big pulley, the small pulley drive a DC generator, the generator can give energy to a resistor, all instruments are on the support, need only 4 instruments. If the generator is fixed on the support, there is no torque on the support. I calculate the energy from the system and it's not a factor of the angular velocity of the motor but factor of the angular velocity of the support:

E=2FRwt

The generator must recover energy from the motor: the force F

If the support turn slowly the energy recover is low

With :

R=0.1 m
F=0.5 N
w=200 RPM
The power is 1W