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### Author Topic: Double Pendulum Power  (Read 69291 times)

#### nybtorque

• Jr. Member
• Posts: 50
##### Double Pendulum Power
« on: June 10, 2013, 07:03:21 PM »
Hi all!

I've put together a report where I try to show how Euler Lagrange and classic Newtonian physics of a double pendulum can explain why certain mechanical and gravitational systems produce "excess" power.  The key is that we are dealing with an open system. The machine have to by firmly attached to the ground, or something heavy enough, to work and the other side of the Newtonian equilibrium is the minute movements of this heavy object.

By rotating a pendulum/unbalanced wheel we create vibrations originating from the centrifugal force.  By tuning the damping mechanism for example by an AC generator we can extract AC power directly from these mechanical vibrations. The interesting part is that it does not take any more power to keep this unbalanced wheel rotating except to initially set it in motion and to overcome friction. The vibrations however create power and the amount can be derived from Newtonian physics.

There are of course issues of construction and material strength.

http://www.scribd.com/doc/146232946/Douple-Pendulum-Power

Quote
"If you want to find the secrets of the universe, think in terms of energy, frequency and vibration."  -Nikola Tesla

#### truesearch

• Sr. Member
• Posts: 277
##### Re: Double Pendulum Power
« Reply #1 on: June 10, 2013, 08:31:57 PM »
@nybtorque:

That's an interesting concept you have developed. Have you built any proof-of-concept models in your research? Any photos you care to post here?

truesearch

#### nybtorque

• Jr. Member
• Posts: 50
##### Re: Double Pendulum Power
« Reply #2 on: June 11, 2013, 10:56:54 AM »
truesearch:

No, unfortunately not. I dont have the skills and resources to make a prototype myself. But an easy experiment to verify the effect is to put a bicycle upsidedown and safely fasten a heavy tool of sorts inside the wheel, which then becomes seriously unbalanced. Then pedal by hand, try to keep one point fixed and measure amplitude and weight at another point.

The interesting part is that you do not need to pedal any harder with the tool fastened inside the wheel than without. And you can certainly feel (and measure) the output difference. This is the power of vibrations. And it becomes greater with increased frequency of rotation by a power of three.
« Last Edit: June 11, 2013, 01:05:11 PM by nybtorque »

#### Ghost

• Full Member
• Posts: 165
##### Re: Double Pendulum Power
« Reply #3 on: June 13, 2013, 10:16:02 AM »

#### gyulasun

• Hero Member
• Posts: 4079
##### Re: Double Pendulum Power
« Reply #4 on: June 13, 2013, 05:28:16 PM »
Hi all!

I've put together a report where I try to show how Euler Lagrange and classic Newtonian physics of a double pendulum can explain why certain mechanical and gravitational systems produce "excess" power.  The key is that we are dealing with an open system. The machine have to by firmly attached to the ground, or something heavy enough, to work and the other side of the Newtonian equilibrium is the minute movements of this heavy object.

By rotating a pendulum/unbalanced wheel we create vibrations originating from the centrifugal force.  By tuning the damping mechanism for example by an AC generator we can extract AC power directly from these mechanical vibrations. The interesting part is that it does not take any more power to keep this unbalanced wheel rotating except to initially set it in motion and to overcome friction. The vibrations however create power and the amount can be derived from Newtonian physics.

There are of course issues of construction and material strength.

http://www.scribd.com/doc/146232946/Douple-Pendulum-Power

Hi nybtorque,

I have a problem to fully understand your setup shown in Figure 2 of your report file at scribd.com. I edited your Figure and uploaded below to refer to the parts.
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?
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?

To understand my question better, let us examine the setup from the generator side: suppose you switch off the prime mover (input motor) in your setup, everything is at standstill  and you grab arm D with your hand where the generator axle connects to arm D and you start to rotate arm D, okay?  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.

What I am missing?  please comment.

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?

Thanks, Gyula

#### nybtorque

• Jr. Member
• Posts: 50
##### Re: Double Pendulum Power
« Reply #5 on: June 13, 2013, 06:48:46 PM »
Hi Gyula!
Quote
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.
Quote
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...

Quote
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.
Quote
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

• Hero Member
• Posts: 4079
##### Re: Double Pendulum Power
« Reply #6 on: June 13, 2013, 10:54:27 PM »
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.

<blockquote>
Quote
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?</blockquote>

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

• Jr. Member
• Posts: 50
##### Re: Double Pendulum Power
« Reply #7 on: June 14, 2013, 08:45:54 AM »
Hi Gyula!

Quote
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.

Quote
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

• Hero Member
• Posts: 4079
##### Re: Double Pendulum Power
« Reply #8 on: June 15, 2013, 12:13:18 AM »

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

• Jr. Member
• Posts: 50
##### Re: Double Pendulum Power
« Reply #9 on: June 15, 2013, 06:24:53 AM »
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.

#### Low-Q

• Hero Member
• Posts: 2840
##### Re: Double Pendulum Power
« Reply #10 on: June 15, 2013, 09:40:32 AM »
truesearch:

No, unfortunately not. I dont have the skills and resources to make a prototype myself. But an easy experiment to verify the effect is to put a bicycle upsidedown and safely fasten a heavy tool of sorts inside the wheel, which then becomes seriously unbalanced. Then pedal by hand, try to keep one point fixed and measure amplitude and weight at another point.

The interesting part is that you do not need to pedal any harder with the tool fastened inside the wheel than without. And you can certainly feel (and measure) the output difference. This is the power of vibrations. And it becomes greater with increased frequency of rotation by a power of three.
This is true only if the unbalanced bicycle wheel is 100% fixed, or can viberate without friction. As soon as you try to get energy out from the viberation, there will occour a phase shift less than 180 degrees between the position of the weight and the position of where the bicycle wheel finds itself during bouncing up and down or side to side. This <180 degree shift will counterforce rotation, so that more input on the pedals are neccessary - ofcourse as much more input as the energy output are.

A perfect pendulum exchange kinetic energy with potential energy with 180 degrees delay. Friction or any form of attempt to take out energy will reduce this shift to less than 180 degrees and the pendulum will finally stop - even a double one.

Vidar

#### nybtorque

• Jr. Member
• Posts: 50
##### Re: Double Pendulum Power
« Reply #11 on: June 20, 2013, 06:35:32 AM »
Hi Vidar,

Maybe I'm missing something here. But I cant see how friction in the inner pendulum can make the outer pendulum stop if it is frictionless. Friction in the inner pendulum will make the inner pendulum amplitude smaller, as well as a large inner pendulum mass will, but none of these forces are transfered to the rotation of the outer pendulum. This is what I try to show using Euler Lagrange in the report. Please elaborate on the physics here if you got another idea.

To be honest, I'm not suggesting any magic, merely exploring the case where we supply energy by rotation of the outer pendulum and examining the work performed by the inner pendulum mass. The reason why I find this interesting is because to do this we have to consider the energy of the vibrations, ie. both static and dynamic forces in the fixture point origination from the centrifugal force of the outer pendulum. If we want to eliminate the dynamic vibrations we need to apply a equally large force as the centrifugal force to move the inner pendulum mass. That is why I'm talking about an open system because it is normally done by the fixture point and the mass of the surroundings.

#### Low-Q

• Hero Member
• Posts: 2840
##### Re: Double Pendulum Power
« Reply #12 on: June 20, 2013, 08:22:06 AM »
Hi Vidar,

Maybe I'm missing something here. But I cant see how friction in the inner pendulum can make the outer pendulum stop if it is frictionless. Friction in the inner pendulum will make the inner pendulum amplitude smaller, as well as a large inner pendulum mass will, but none of these forces are transfered to the rotation of the outer pendulum. This is what I try to show using Euler Lagrange in the report. Please elaborate on the physics here if you got another idea.

To be honest, I'm not suggesting any magic, merely exploring the case where we supply energy by rotation of the outer pendulum and examining the work performed by the inner pendulum mass. The reason why I find this interesting is because to do this we have to consider the energy of the vibrations, ie. both static and dynamic forces in the fixture point origination from the centrifugal force of the outer pendulum. If we want to eliminate the dynamic vibrations we need to apply a equally large force as the centrifugal force to move the inner pendulum mass. That is why I'm talking about an open system because it is normally done by the fixture point and the mass of the surroundings.
These two pendulums are in one way or another connected to eachother, directly or indirectly (If I understrand right). For every action there is a reaction, and if you change the reaction in one part of a system it will also change the reaction in another part of the same system. Because one part of the pendulum is depending on the behaviour of the other part. Any condition that you affect by friction or energy output, will affect the rest of the system as you are tapping it from energy.

Vidar

#### nybtorque

• Jr. Member
• Posts: 50
##### Re: Double Pendulum Power
« Reply #13 on: June 20, 2013, 01:14:35 PM »
Quote
These two pendulums are in one way or another connected to eachother, directly or indirectly (If I understrand right). For every action there is a reaction, and if you change the reaction in one part of a system it will also change the reaction in another part of the same system. Because one part of the pendulum is depending on the behaviour of the other part. Any condition that you affect by friction or energy output, will affect the rest of the system as you are tapping it from energy.

Yes, the Euler Lagrange equation describes what happens. That is the basis of my argument. There is no way you can reduce kinetic energy in the outer pendulum with friction in the inner one, since it can only act on the outer through that arm, which is always in a 90 degree angle in relation to the movement of the pendulum mass.

However, as I state; the two pendulum per se is not a closed system. So to be able to set up the equations for action/reaction the Newtonian way for the inner pendulum we have to take into account the forces that act on the fixture, both as momentum and as push/pull through the inner pendulum arm. The other side of that equation in my example is the centrifugal force from the outer pendulum. This is what I try to show in my report. The forces on fixture have to be part of the system. These are the vibrational forces I want to examine, and which a propose can be used to generate power.

#### Low-Q

• Hero Member
• Posts: 2840
##### Re: Double Pendulum Power
« Reply #14 on: June 20, 2013, 03:42:33 PM »
@ nybtorque:
Maybe you could build a small prototype and take a video of it while playing with it. Because I'm not sure if I follow you on this

This is the design you're describing, right? http://htmlimg4.scribdassets.com/7720h8reps2iacuk/images/1-d7d911a5c0.jpg

Vidar.