Leverage & Torque - WM2D predictive abilities - are they representative of real world ?

[Fletcher]

Leverage & Torque - WM2D predictive abilities - are they representative of real world ?

I intend to add to this thread and invite discussion as we go along. So bare with me as I build the context, and as time allows.

I seldom look at Physics formulas before deducing what a real world (or sim) device may or may not do. I 'know' that none of them can work according to 'Physics' but I continue to explore for some avenue that we could exploit to make a gravity only PMM, as Bessler purportedly did.

I've reached the conclusion that if a gravity only wheel (that uses a conservative force as its only source of continued locomotion) is possible then it must change the circulation path of the system COM/CoG in such a way that it provides more positive torque than negative or back torque.

I just can not bring myself to believe that the Law of Levers can be broken so that for a given loss of GPE (by a device) we can get an increased system GPE gain over and above that loss (not considering normal system frictional losses here). That belief would instantly change though should one ever be demonstrated but right now my mind is incapable of accepting that premise.

Many times we have looked at levers and leverage, also torque. Often in terms of overbalance potential. Hopefully the coming discussion will shed some light on what I observe to happen in sim world with these types of things. I have mentioned previously what the final analysis is in terms of Working Models predictive abilities and COE etc but I want to make the case crystal clear and spell it out.

Ultimately one of you may find the logical weakness in the sim argument verses real world results. That would be high on my wish list and give us something to go on.

In a previous thread of mine I explored scissors (jacks) quite extensively. These are just leveraging devices that either take linear motion in one direction and turn it in to linear motion in another direction, or change circular motion into linear and visa versa. That's because of their physical makeup and how they are deployed. What I found was that they were force multipliers but could never be energy multipliers. The accelerations of attached masses could be altered by the geometry but the sum of the system KE v's GPE lost was always underunity.

Now I want to use some of that previous research/findings to explore leverage and torque basics and constraints as relate to WM2D's predictive capabilities and what results it consistently gives. This is in the context of straight levers and comparisons to pulley systems as I used previously.

ETA: If there is a logical exception to the Law of Levers in terms of torque and/or COE I hope it can be found and shared by someone reading this thread.

I know many of us look at the same things from time to time so we should all benefit and take what we want from this generalised discussion, if it helps with a deeper more complete understanding of levers and torque.

[rlortie]

I suggest those of interest take a refresher course found at:

https://en.wikipedia.org/wiki/Torque

If your read down to https://en.wikipedia.org/wiki/Static_equilibrium you will find the top as represented on MT 138, the toy page.

Ralph

[Fletcher]

Hi Ralph .. I must admit one of the people I was thinking about when composing this thread was Fcdriver. It will be interesting to see if he has any insights to share about what is discussed.

I intend to keep away from mathematical formulas where I can (KIS), and just use the sim kinematic program Outputs to summerise information i.e. what the sim predicts real world outcomes should be (in terms of COE), shown in a visually digestible form.

And I'll try and explain them as clearly as I can.

If there are any dissenters, or someone thinks they have a better explanation, or has something to add, or says there is something special about a particular arrangement, then they can state their case.

Having said that I fully expect the likes of ME to chime in with the math breakdown if it sheds further light on an explanation though. He's welcome to as he is good at the math and has a way of explaining sometimes complex things.

[DannyBouy]

Leverage & Torque - WM2D predictive abilities - are they representative of real world ?

I think they might be, with this caveat. The real world is malleable.

I've reached the conclusion that if a gravity only wheel (that uses a conservative force as its only source of continued locomotion) is possible then it must change the circulation path of the system COM/CoG in such a way that it provides more positive torque than negative or back torque.

It should. A good question would be how might it do that?


Thanks
Daniel

[Fletcher]

That's the 64,000 dollar question DB.

ME explained in a recent thread that MOI is correlated to RKE by virtue of squaring functions.

Rotational kinetic Energy is E[rk] = ½ I·ω²

We know (by mathematics and the nature of the angle in radian): ω=v/r
For a ring the I=1·m·r²

We can replace and get: E[k] = ½ (m·r²)·(v/r)² = ½ m·v²

Luckily this coincides, but you'll get different results when you have a different MoI.

We know kinetic energy is Newtonian, by mathematical equivalences:

To show a bit how we should 'know':

From height [h] and acceleration [a=G], the kinematics will be: h=½ a·t²
We can determine [t] to be √(2·h/a)

The velocity after dropping height [h] will be: v=a·t = √(2·h·a)

When v= √(2·h·a), then v²=2·h·a, or ½·v² = a·h

This is all mathematics, in this case derivatives of kinematics: [h] is position, [v] is change of position over time, [a] is change of velocity over time.

We can multiply by [m] to get E[k]=E[p] : ½·m·v² = m·a·h

The explanation what this actually should represents is physics...

My bet would be that in order to have a greater positive torque than negative torque that synchronicity would have to be modified by a special device capable of doing that. No, I don't know how to construct such a special device.

I tried exploring that in linear scissor mechs (gearing) but the ensuing inertia produced was always consistent with COE, in sim world.

[Fletcher]

These lever systems are in force equilibrium. They don't willingly move up or down because they are balanced.

To move up or down there must be a net torque and they must be free to move. This imbalance could be due to different masses.

If they did move it would result in a net loss of system GPE, whilst the components of each device would acquire KE.

But the summed component KE's (velocity dependent) is always less than the net GPE lost by the device (height dependent).

So this is a chicken and egg question.

What comes first ?

Torque imbalance is the cause of net loss of GPE ?

Potential to lose net GPE is the cause of torque ?

[agor95]

@Fletcher

Thank you for this thread. It is a commendable initiative on your part.

[eccentrically1]

These lever systems are in force equilibrium. They don't willingly move up or down because they are balanced.

To move up or down there must be a net torque and they must be free to move. This imbalance could be due to different masses.

If they did move it would result in a net loss of system GPE, whilst the components of each device would acquire KE.

But the summed component KE's (velocity dependent) is always less than the net GPE lost by the device (height dependent).

So this is a chicken and egg question.

What comes first ?

Torque imbalance is the cause of net loss of GPE ?

Potential to lose net GPE is the cause of torque ?

Since those lever systems are in equilibrium, then they don't have any potential to lose or gain net GPE. Even though they may be free to move, the cause of torque would have to be external to the system. They can't gain KE or lose and gain GPE internally. So it's a trick question. Neither one causes the other in a balanced system. What would have to come first would be an external torque. Then, the systems would be torque imbalanced, having gained KE from the external system, and the GPE lost and gained internally would be zero summed.

That's the way I understand what you're proposing, I don't mean to sound condescending and like I'm stating something everybody knows and has discussed before. Please elaborate if I don't seem to understand what you're saying.

[Fletcher]

EC1 .. you are welcome to state the obvious :)

Only by discussing the obvious might the unobvious be unmasked, or it might not, but we won't know until a few minds turn the question over and look at it in different ways.

It is a sort of trick question. You are quite right. With no external torque supplied to the system then nothing will move. There is no unequal torques around the fulcrum and also no potential to lose GPE.

I think of it this way.

Science likes coherent systems, and symmetries. I would say that each is the cause of the other, that they are codependent. I base that on the physics theorem of Work Energy Equivalence Principle (WEEP). It says that the integral of Force and Displacement is equal to Energy. They are equivalences.

Since torque is a force (rotational) and has a displacement then it is equivalent to GPE change (and we know that GPE = KE with no external torques supplied). That is at least the case for the simple balance lever and fulcrum because if we increase the 1 kg mass to 2 kg at the same distance we can imply that a torque arises. This will rotate the device and there will be a loss of GPE but the two masses will acquire summed KE's that don't exceed the net GPE loss (assume the lever itself is virtually massless).

We also know that the lever system will have an MOI which is usually derived by experimentation (the sum of the mr^2). This system MOI (inertia) stops the system over speeding or underspeeding so that the result is always consistent with conservative gravity force doctrine. And that happens regardless of where we change the fulcrum point to. The relationship is always the same (insert Fcdriver comment).

In the case of the second 4 to 1 pulley system figure then the torque is not so obvious as the first lever system. It will also move up or down if either mass is added to. And this is a straight forward F x D relationship. IOW's, the mass with the ability to lose the greater GPE (F x D) than the other can gain wins the race.

Part of my reason for covering this ground is because Oystein has found a mechanism in Besslers codes and writings. I know that he knows this stuff but ateotd that mechanism must conform to known physics, IMO. So I'm kinda doing a refresher to help him remain objective (although he hasn't asked for it ;). That is unless that mechanism is capable of upsetting the current laws of physics or mechanically manipulates the CoG in the way I described, though I don't know how that can physically be done without external torques applied. Perhaps it does something not at all anticipated.

[Fletcher]

Are there any instances when a system can have torque and not lose GPE ?

Ralph linked one. The top on Bessler's toy page. Once given rotational energy it will raise its CoG and gain in GPE.

AFAIK the current theory says that the gain in GPE is not at the expense of RKE (it does not slow down its rpm) ?

But I am guessing that the RKE given to the top must exceed the potential GPE gain acquired ?

[DannyBouy]

I seldom look at Physics formulas before deducing what a real world (or sim) device may or may not do.

The model or the simulation is going to do its own figuring. Best to let them go first.

Moment of inertia is a factor of rotational kinetic energy of a rigid body. In 2 dimensions, a rigid body can be defined by 2 point masses. Between these point masses might be a structure that exploits the difference between them working with gravity and fighting against it. IOW this rigid body is not so rigid. The space between it can expand or compress. Also this body can pass through itself and its internal structure defines where the boundary of zero is. Center of mass and center of gravity can be significantly different points. As this body does this, there is no deformation or smashing of atoms. However the information of the energy of deformation or smashing is stored for use at a later time.

My bet would be that in order to have a greater positive torque than negative torque that synchronicity would have to be modified by a special device capable of doing that.

It's just an idea.


Thanks
Daniel

[jim_mich]

Center of mass and center of gravity can be significantly different points.

Uh, I don't think this be right.

Gravity acts equally on all objects according to the mass of the object. Thus the center of mass and the center of gravity is always equal. Can you prove that I'm wrong in my understanding?

[DannyBouy]

Can you prove that I'm wrong in my understanding?

Yes I can.


Thanks
Daniel

[DannyBouy]

The center of mass is the mean position of the mass in an object. Then there's the center of gravity, which is the point where gravity appears to act. For many objects, these two points are in exactly the same place. But they're only the same when the gravitational field is uniform across an object.

Gravity can be fooled by reason of the structure between the 2 point masses that define the not so rigid body.

I'll admit it's only theory.


Thanks
Daniel

[Fletcher]

Center of mass and center of gravity can be significantly different points.

Are you sure about that ? I thought they were the same thing when all the system is analysed.

Other than to say that CoM is just that, the mass center as a point mass, which is invariable.

And the CoG is the gravitational center as a point mass equivalent. But it is affected by the 'g' constant for the locality.

Semantics maybe.

Anyways, at some stage I intend to draw up some scissors with segments that extend and contract along a radial in a wheel. The MOI will change with position (closed or extended) but I will figure in the Cf/Cp's and how that segment ratio (distance ratio) affects the force multiplier effect.

It might be interesting for some. Then I will also talk about ordinary levers and ratios used to pull up a mass and show that the force distance relationship seems to be the overriding consideration for any device.