Double Pendulum Power

[nybtorque]

Hi Gyula!
Thankyou for your sincere questions.

I assume for simplicity the gear has a 1:1:1 ratio, okay? Now I also assume wheels B and C have to be able to rotate around their own shafts (see axle B and
axle C) so that the pendulum weights could exert their force, okay? 

This is correct.

Now my question is why arm D (which holds the wheels B and C) should rotate in accordance with wheel A?  I mean what force rotates arm D? because wheel A can rotate wheels B and C and maybe arm D will turn a little but why it should transfer useful torque towards the generator shaft?

It does not rotate according to A. Exactly as you say it only turns a "Little" depending on the weights of the pendulums and machinery. This is what I call the amplitude (s) in the equations. Ideally it only moves with an amplitude of about half the radius of of the pendulum wheels. It will vibrate with the frequency of A. And vibration is continous acceleration/deacceleration of mass. If there is no load it will oscillate with maximum amplitude and if the load excedes the centrifugal force it will stop. However, for all loads between zero and maximum there will still be amplitude and acceleration, which equals power.

This is because we are utilizing the centrifugal forces of the pendulums. There is no torque (apart from setting B and C in rotation) at all transfered from A to B and C. It does not take any more power to rotate an unbalanced wheel than a balanced (if it is stabilized and frictionless etc.).

Consequently...

I ask: will wheel A start rotating?   I am afraid wheels B and C will "circle" around wheel A as if they were planetary wheels and the rotation of wheel A remains casual,
without transferring any significant torque. And this is what I think may happen when the input motor starts wheel A rotating.

Exactly. No torque is transfered in that direction either. The trick is to consider the centrifugal force of B and C and what happens at the other end of that newtonian equilibrium, You could fix D to the ground and transfer the vibrations to the fixture and surroundings and actually the earth would shake a "little"... Or as I propose you could optimize the damping and use an AC generator for the purpose (which is fixed to the ground) and actually get AC power.

One more thing: you wrote in the Figure: fixed axis on the right side of the generator. What does it mean? Is it a theoritical reference axis of the setup, maybe the axis of symmetry for the setup?

I guess both! The axis needs to be fixed in position in relation to the ground. I believe bearings could be useful. Also the input motor and the output generator needs to be properly fastened.     

[gyulasun]

Hi nybtorque,

Thanks for the explanations, now the operation seems to be clear. Practically the arm D moves as a 2 arm lever, back and forth, with a limited and load dependent amplitude. To utilize this 'back and forth' like motion, you need to use a special generator to have 50 Hz AC power (what you indicated) or you need to convert this back and forth motion to continuous rotary motion to drive a conventional generator.

>

One more thing: you wrote in the Figure: fixed axis on the right side of the generator. What does it mean? Is it a theoritical reference axis of the setup, maybe the axis of symmetry for the setup?

I guess both! The axis needs to be fixed in position in relation to the ground. I believe bearings could be useful. Also the input motor and the output generator needs to be properly fastened.     
Practically, which axis you mean here?  The axis of the generator driven by  arm D?

Thanks,  Gyula

[nybtorque]

Hi Gyula!

To utilize this 'back and forth' like motion, you need to use a special generator to have 50 Hz AC power (what you indicated) or you need to convert this back and forth motion to continuous rotary motion to drive a conventional generator

.

Theoretically you could use any DC motor in the desired load-range as a generator. The back and forth torque from the the D arm will result in a AC current out from the motor/generator. If it is a 12V DC motor you will get 12V AC current. To get 220V AC you need some sort of transformer.

Practically, which axis you mean here?  The axis of the generator driven by  arm D?

In the schematic I use the same axis for the input motor and driving cogwheel as the axis of arm D and the generator. I did it that way because I found it easy to understand. However, there could be other designs with other benefits.

[gyulasun]

In the schematic I use the same axis for the input motor and driving cogwheel as the axis of arm D and the generator. I did it that way because I found it easy to understand. However, there could be other designs with other benefits.

Now I am confused.  If the axis of the motor and driving cogwheel as the axis of arm D and the generator is the same axis, then wheels B and C cannot rotate.
In your drawing you used a dotted line, probably for indicating the center line (this is what I meant in my question on the fixed axle above) and you used cylindrically shaped shafts for both the input motor and the output generator axle, there is no any continuos and cylindrical axle lines in your drawing to connect the motor and the generator axles. 
The best would be to clear this setup if you make another drawing which leaves no questions.
You used a circular arrow for the input motor to indicate its rotational direction and you drew a two-way arrow for both arm D and the generator shaft: how can it be if you now has said you use the same axis?

Gyula

[nybtorque]

Hi Gyula!

Ok, I see. You are right. It's not the SAME axis. It's only the same theoretical axis. And that is basically a design issue. Exactly as you say the input axis is rotating and the output axis oscillating. I hope this clears it up.