The Walter Paradox

[Sam Peppiatt]

Fletcher,
The top model, (yellow weights), doesn't look right to me. Shouldn't the arms be parallel,(with the ground), and facing in the same direction.-----------Sam

[WaltzCee]

Fletcher,

When I ran the SIM it didn't immediately flip. Maybe 30-40 swings

I notice on this animation you posted first

viewtopic.php?p=192954#p192954

The red mass2 seems to return to a higher level than it started at.

I would usually graph system CoM, & also keep track of the rotation of bodies.

Did mass2 return to a little bit of a higher level than it started?

[WaltzCee]

As I keep watching that animation, Fletcher, it seems the tidally locked mass1 breaks the 180° plane on the right side also.

Can you measure its rotation?

[Tarsier79]

Hi W.

It is clear Fletcher did a best case scenario. The COM is marked with the little black and white Quad-circle. If you build this, it will not go as high as in sim world.

[WaltzCee]

I understand that Kaine. I'm trying to examine a theoretical boundary.

When I SIM'ed it, my question was, "would it be balanced?". It turned out to be and I was surprised. The tidally locked mass1 is only being picked up at one of end, which should be a force of cos45° while the retrograding mass2 should be exerting its entire mass on the balance

Essentially the roberval is balancing 2 unequal forces and one should overcome the other.

Fletcher asked if he replicated as I did, yet no, he didn't.

I let it swing for 35-40 swings and also metered rotations & system CoM.

Thank you for your comments.

[Fletcher]

Fletcher,
The top model, (yellow weights), doesn't look right to me. Shouldn't the arms be parallel,(with the ground), and facing in the same direction.-----------Sam

Hi Sam .. Agostino Ramelli (Italian Engineer) in 1588 was the first to invent a torque-balanced rotational device (**providing opposite masses were equal), which he called his Book-Reading Wheel, or Bookwheel. His was a geared version. Roberval came along with his demonstration of a rotating torque balanced mechanism (the RB) using parallelograms in 1669 (100 years before Captain Cook of England first sailed to NZ :7) and 80 odd years after Ramelli's bookwheel). Yet they both do the exact same thing using different 'simple machine' mechanics, and have identical behaviour.

I called it the geared Ramelli balance I think .. anyways I think the Ramelli is the one you are talking about (with yellow 1 kg weights attached to the last entrained gears).

If you take any RB (or Ramelli) the "plate" attached to the verticals (or last gear for a Ramelli) can be set at any angle (opposites don't even have to be the same angle) .. it's a short step to do away with the vertical strut of the parallelogram and/or plate entirely and just have a big circle massive as you want (it acts as the vertical providing it is pivoted top and bottom of the horizontals like a vertical would be). Then you can attach a weight to it absolutely anywhere on that circle facing up or down or to either side you wish. Obviously that large circle of that RB is an analogue to the Ramelli last gear backing and to which the same applies.

As long as equal weights are attached to a backing circle they can be ANY position at all ! And the thing will be balanced i.e. no torque !

Why is there no torque ? .. because torque can only be present when one mass can lose more PE than another gains, and in a Ramelli or RB they both lose and gain the same amount of PE when physically moved. Add another small weight to one side and it has torque because that side CAN LOSE OVERALL PE.

This " 'Law' of Losing PE to have torque " is the real guts of Archimedes Law of Levers. No ability to lose more PE than gained >>> no turny spinny.

See uninteresting animation of things not moving because there is no torque below ..




..................


Walt .. T is correct as you understand. I'll get back with your outputs and analysis when I have the time to do properly - not just right now lol.

.................

[WaltzCee]

Thank you Fletcher.

[Sam Peppiatt]

Fletcher, I disagree; I think the torque has to be equal and opposite to be balanced but, no matter----------------Sam

[Fletcher]

Fletcher, I disagree; I think the torque has to be equal and opposite to be balanced but, no matter----------------Sam

The torque is equal and opposite (balanced) Sam .. i.e. zeroed out, cancelled, nulled, as tho there were no torque.

Because one weight can not lose more PE than the other gains .. If it can lose more than the other gains then there is a net torque in its favour !

This " 'Law' of Losing NET PE to have torque " is the real guts of Archimedes Law of Levers. No ability to lose more PE than gained >>> no turny spinny.

The Net lost PE transaction is a subtle but often not recognised as most significant requirement to have any torque. IMO !

[Leafy]

Is the Ramelli the same as Roberval?

Let’s examine them at 6 o’clock position.

A weight is attached to Roberval at 6:00. It exerts a torque but no movement.

A weight attached to Ramelli at 6:00. It also exert a torque on the third disk. I made the third disk so small to make sure if it moves or not.

[johannesbender]

Fletcher, I disagree; I think the torque has to be equal and opposite to be balanced but, no matter----------------Sam

Sam i tried to do a quick drawing to help explain , as shown here the red arm with its weight is attached to a RB on the blue arm .
Imagine the red arm is a spanner being pushed down at the weight , and where the red arm meets the blue arms is a bolt (welded to the arm).

The weight is being pushed down , and the weight on its arm wants to produce a torque on the blue arm , it wants to push the bottom of the blue arm to the left (shown as F with an arrow to the left) , and the top of the blue arm to the right (shown as F with an arrow to the right).

But it cannot torque the blue arm (the spanner cannot turn the bolt) because the blue arm's 2 pivots cannot move left or right , and the 2 pink pivots at the center of the RB cannot move left or right , so the blue arm can only move up and down , so the only force than can make them move up and down is the force from the weight's weight and not the weight's force of torque , hence why the RB removes torque and only allows the weight .

a.png

This is why the angles and positions of the weights does not matter , only its downward force on the arms that can only allow up and down movement shown in pink.

b.png

The same concept and principles apply to the Geared version Fletcher has shown.

[Sam Peppiatt]

johannesbender,
For the Roberval Balance; I couldn't agree more. The angle makes no difference. But, wouldn't the book wheel / geared version be different? With one arm vertical, it's torque would be more or less zero, in either direction. The one that's horizontal would have maximum torque. How could they be balanced? Maybe I'm wrong-------------------Sam

[johannesbender]

Sam , besides the limited mechanical movement of the RB , there is the physics of it , which makes it behave correct and is what Fletcher is writing about .

All the types of RB (just calling them all a RB) whether geared type or not , when the paths of both weights are traced , the paths will be the same, if the motion of the paths complete arcs then the arcs are the same , if the paths completed circles then the radius would be the same , both will trace the same motion ,distance , KE and velocity will be the same , GPE will be the same .

So what happens is , the torque forces (angle and positions) for the masses makes no difference , the only force that can be different for the two is the weight , the motion is independant of the angles and positions (torque).

However weights on a lever will trace different path motions , arc lenghts and distances and radius etc depending on theire positions , so its dependend on the torque.

[Sam Peppiatt]

johannesbender, I think you are right. I should stick to nuts and bolts-----------------Sam

[johannesbender]

Perhaps I'm nuts haha , we will let Fletcher explain.