The Walter Paradox

[Sam Peppiatt]

I can hardly wait!---------------------------------------------------------------------------------------------------Sam

[agor95]

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

I like the hysterical laughter; it shows you are sane.

It's me that is nuts HAhAha !

Regards

[Fletcher]

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

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

Thanks jb .. you did a very good job of explanation. BTW we're all nuts to bother with B. and his PM-wheels lol. But only us nuts will crack it, everybody else is too sane and gives up.

Good news if you want to see a PM-wheel, at the end of this post - got yah attention ..

Sam's reaction is not unusual - how can the horizontal one not have more torque ?

The Ramelli really demonstrates why torque isn't at all that important in the scheme of things .. it's useful when doing quick Turning Moments Calcs etc but that's about it imo. The real 'boss' is which weight can lose vertical PE and that causes the turn.

Anyhoo .. I've decided to keep with this line of inquiry for now because I think it adds to the body of knowledge, before addressing Walt's stuff later today.

Below is a animation of a sim I built many years ago and rebuilt and updated yesterday.

It is a Temporary Self-Moving Wheel (temp PM wheel lol) - anyone could build it in sim-world and in real-world.

I changed the last gear ratio slightly to the left hand side yellow weights - regardless which angle the weights are at just ability to lose PE dictates whether it will accelerate in one direction or another etc reinforcing what I said earlier. (Sim included).

N.B. the sims accelerate up to about 21 rpm in 3 turns and about 20 seconds, but then begin to drop off rpm (see graph rpm sine plot) - IOW's I have made a complex pendulum that winds down losing GPE and can't reset itself without muscle help (Grandfather pendulum or spring clock analogy). The Yellow weights lose relative height (GPE) very slowly as does the system COM - you can see the Yellow weights changing orientation as they turn unlike a true RB. If this was very slow it would hardly be noticed. Fast or slow, big or small power - makes you wonder lol.

This would replicate some of B's. demonstrations and could also do some limited work in real-life if built well. Add more cross-bars and things get even more efficient and powerful etc.

I categorically state that imo B. did not fake his wheels like this (the sim is only my amusement to see a "Temporary Self-Moving Wheel").

Whilst this in real-world build could reproduce some of the tests it would only last a few minutes at best and the rpm running down would be a dead giveaway. And besides it in no way (not even close) explains the 54 days long duration test at Kassel.

Anyways .. it would be fun to build and see turning for a while ! Bit like my Savonius wind turbines galloping around today give me pleasure and are inspiring lol.



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

Sim Included ..

[johannesbender]

@Fletcher , change the gear ratio to 1.05 or such , when the x position of the gear is less than or equal to 0 (<=0) , change the gear ratio to 1 when the x position is greater or equal than 0 (>=0)...apply to both.

This should change it depending on when the weights are to the left or right side , like changing weights radius in and out , except were not using energy trying to physically move the weight in and out , but we are doing the same effect in a different way , kind of sidestepping the move of the weights , like i once said we cant move the weight we must change the radius of the structure , instead switching the gear ratio like you said affecting which can lose PE ...

Remember this one ? i could not figure out how to do it , how to do what it symbolised , ie switch between the properties of 2 radiuses on the structure (inside radius and outside radius) without changing the position of the weights on a normal RB because it would not allow the arms to stay correct during rotation, but thats what the gear ratio change is doing in your sim that seems plausible to me.

[Fletcher]

Good idea to investigate jb .. IIRC I did try such things over the years with no luck, particularly with the Ramelli and some with RB - sim jammed or exploded etc. IINM I ran into problems of resetting PE because something must lose PE to cause a rotation, and that needs manual restoration.

Gonna rain heavily in the next few days so may have some spare time to play around with the sims and see if we can make any progress or at least understand better the problems of that approach.

Cheers ..

[Fletcher]

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?


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?


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.

Here you go Walt .. sorry it took so long ..

Animation of the sim with Outputs ..

Both sims are identical except in the first it is ideal conditions of NO FRICTIONS, while the second I've approximated small frictions by turning ON Air Resistance to LOW - this acts to dampen down the sim and is more realistic.

In the first it did start swinging above the horizon line and the trend continued to grow until it leveled out - my sim did not keep "growing" until it swung to the top and exploded as yours did. All I can guess at is that NO TRUSS RB's are problematic - they have no "give" and this means the pin joints (pivots) are "tight" - and the program doesn't like this. That's why I cross-check with different build techniques when I can. N.B. animation of sim started well into its stride so you can see the trends.

In the second I did introduce some Air Resistance to simulate frictions of various sorts - the sims oscillations didn't grow (no trend) in amplitude and in fact began to dampen down as you'd expect - then suddenly it locked-up and violently exploded when vertical - reasons and best guesses given above.

Anyways .. if you think there is a physics reason for the amplitude to grow with each swing you will have to build a real-world model to study .. for me I can't fathom a reason why it might increase oscillations amplitude each swing - as you said the Blue Tidially Locked Disk shares its mass with the RB pin AND the COR pin i.e. half the mass on the RB, which causes the rotation. That we understand, but why it should cause an asymmetric swing is unknown to me.







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

[Tarsier79]

Hi Fletcher

in the above case, you might remove the locking up by putting a vertical sliding pin joint in the top of one vertical strut, probably the one on the red side.

That is interesting, but most likely a flaw, the PE gain in the top sim.

[johannesbender]

Good idea to investigate jb .. IIRC I did try such things over the years with no luck, particularly with the Ramelli and some with RB - sim jammed or exploded etc. IINM I ran into problems of resetting PE because something must lose PE to cause a rotation, and that needs manual restoration.

Gonna rain heavily in the next few days so may have some spare time to play around with the sims and see if we can make any progress or at least understand better the problems of that approach.

Cheers ..

I remember the sim you did , you showed it to me and george kunstler and you had it rotating slowly I cant find the post but anyway .

Yes the issue with almost every design is the restoration of lost(converted) PE , as a group we tend to end up looking around in the same places because the mechanics has common factors or problems and pitfalls we all experience , probably why so many have their own versions of the classic OB problem too.

ATM I am without a cause until new ideas are born haha

[Fletcher]

Hi Fletcher

in the above case, you might remove the locking up by putting a vertical sliding pin joint in the top of one vertical strut, probably the one on the red side.

That is interesting, but most likely a flaw, the PE gain in the top sim.

Thanks for the suggestion .. Slot joints have no stops so a thing just keeps sliding along. So I tried the "closed curve slot joint" (circle slot) with some success before it had a tanty.

Then I tried replacing the 4 corner pin joints with "rotational springs" which act as pin joints. Much better - but had to reverse the rotational force direction of 2 opposites so that all 4 were balanced out to zero. Went for a long time before finally exploding. I could have upped the accuracy and maybe it would not explode but I'd had enough.

I just tend to build sim RB's with trusses embedded somewhere workaround and save myself the headache later.

cheers

[WaltzCee]

Thank you very much for all the time you put in SIM'ing that roberval. Brought back a few ideas.

I do need to get into build mode. When I do I might take a harder look at that idea.

I don't think some mechanism is the answer yet I do think understanding them is important.

As you noted, the Tidally Locked Mass (TLM) only has 1/2 its mass on the vertical. It's suspended between there & the CoR.

This roberval begins pre-torqued.

I'm still looking at it. I'm slow.

[WaltzCee]

Picture please ..

OK. It's like a sandwich.


XXXX,..........................mass3
XXXXXXXXX..…...........mass2
XXXXXXXXXXX...........mass1

1 & 2 don't collide
3 & 2 don't collide
1 & 3 do collide

Can 3 skate on top of 2, until it comes to its edge & encounters 1?

was curious if this would work for Sam's casing weight design.

[Fletcher]

TBH Walt .. I couldn't visualise at all what you were talking about .. for instance "on top" like an 8 with a small circle above, or like side by side and overlapping ? If you can draw it I can think about it further.

[Fletcher]

Thank you very much for all the time you put in SIM'ing that roberval. Brought back a few ideas.

I do need to get into build mode. When I do I might take a harder look at that idea.

I don't think some mechanism is the answer yet I do think understanding them is important.

As you noted, the Tidally Locked Mass (TLM) only has 1/2 its mass on the vertical. It's suspended between there & the CoR.

This roberval begins pre-torqued.

I'm still looking at it. I'm slow.

Understanding is always important .. To my eye your mech unfortunately boiled down to a pendulum with energy already invested in it to its starting position whence upon release it had torque and began to rotate like a pendulum.

I built something similar a few years ago which I will drag out and update in its thread now that jb has kindly shown me how to use GifCam and Postimage software so you can see what I see when I run my sims. It makes a huge difference for the reader being able to actually see what the sim predicts thru its movements.

[Tarsier79]

Hi Fletcher.

The PE gain was annoying me, so I started to replicate the sim. I didn't have to build it all to see the problem. It is caused by the pin joints locking up, as suspected.

The only way I can come up with to build this without the vertical lockup and abnormalities was to add gearing to the horizontal struts and attach both verticals with a pin and slot...Attached

[Fletcher]

Hi Fletcher.

The PE gain was annoying me, so I started to replicate the sim. I didn't have to build it all to see the problem. It is caused by the pin joints locking up, as suspected.

The only way I can come up with to build this without the vertical lockup and abnormalities was to add gearing to the horizontal struts and attach both verticals with a pin and slot...Attached

Very nice workaround Kaine .. all runs good on my sim now i.e. no minute PE gain each swing and no locking up when vertical or exploding apart.

But as you say it takes 2 measures .. 1. adding gears to keep everything finely coordinated .. 2. must have at least one sliding slot on each vertical to remove some pin joint over-strain.

I tried removing the slot but leaving the gearing in and it locked up .. now we know what it takes if you don't use Trusses or Ramelli's.

Yes .. the 'tight' (not enough slop) pin joints/pivots are the problem BUT only in accurate Roberval Balance designs where the parallelogram sides must be always remain exactly parallel it seems. A bug and trap for players sorted !

Thanks a bunch for taking the time to investigate and find an alternative solution we can all benefit from ...