MTs, WM2D, and WM Basic Language Script Code

[Wubbly]

Here's a simulation of the outer weights of MT-15.

A vertical (Y component only) force lifts each mass when it is between 80 and 90 degrees. This lift phase lasts for about 10 degrees of wheel travel.

Quadrant 2 is the torque phase that should accelerate the wheel.

A ramp in quadrant 3 forces the mass to retract to an inner radius.

A ramp in quadrant 4 and 1 keeps the mass retracted at the inner radius.

There is a break in the ramps so the mass can be lifted to the outer radius. At 80 degrees, the force kicks in again and lifts the mass to repeat the process. A MOD statement determines when to apply the force so it is lifted on each rotation of the wheel. The ramps eliminate the need for a Rod with an "ActiveWhen" statement to control the masses.

A previous version of this sim had the masses lifting from 90 to 100 degrees. It didn't work to say the least.

I would expect this simulation to keep accelerating, since an applied force is inputting energy into the system, but it doesn't. Depending on the initial angular velocity, the simulation either speeds up or slows down until it levels off at around some mean angular velocity. Friction is set to zero so that's not contributing to any slowdown.

Bessler's comments on MT015:

This ratchet-wheel derives from the previous model, except that the tensions are somewhat longer and have an additional special weight at the external ends. From this drawing alone, however, nothing of the prime mover's source can be seen or deduced although the figure shows the superior weight.

Bessler introduces the term "superior weight" which seems to indicate more weight on one side of the wheel, or overbalanced.

In the simulation, the applied vertical force acts as the prime mover, however we still don't know what Bessler used as his "prime mover".

[Fletcher]

FWIW you say the sim frictions are set to zero. If you open Window>Properties you can change the static and dynamic frictions of objects in contact. 1 is full frictional exchange and 0 is no frictions. If they are above zero the system will lose KE from the dynamic frictions eking away as simulated lost heat energy or somesuch. You can also alter the frictions of pivots etc by using the generic co-ord constraint bottom left of the side tool bar.

While I don't use a script for rings or spirals I do build them occasionally the old fashioned way. A curved polygon with many data points that I then reshape using Edit>Reshape and move them around etc. Laborious.

Lifting method near tdc or the bottom wouldn't be such a concern in a design if torque were overwhelming. External ramps are problematic because the torque is insufficient to overcome the back-torque of the object on the ramp. See MT12. And MT13 makes a mention of how good it would be. IMO rolling objects on ramps take the path of least resistance. When the gaps closes (lifting effectively) the object and carrier wheel prefer to widen the gap and lose GPE than gain it.

[ME]

If interested I think fellows like yourself and ME (but not limited too by any means), will perhaps collectively be well able to pass thru my bottleneck and will have alternate strategies and analysis insights than my own. I'd welcome the input and the discussion.

Not sure what you're exactly asking (sorry for only paying half attention) but if you're looking for a variant of one of your designs then I can always take a look at it.

As you will see my sim program is limited in what it can perform in terms of complexity of modeling. Too many dynamic parts (like an outer Chain Link Prime Mover that I suggested for example, or latches) and it crashes badly.

When complexity is the problem, then simplification is part of the solution. Easier said than done!.
Let's look at MT-38 where those scissors are not easy to create in a simulation, or otherwise seriously add to complexity.

MT038 - What would be the benefit, besides the visual aspect, of those scissors with respect to transfer of force, or speed, or distance?
MT037 - We could ask the same about those "oval discs".

For MT038 my suspicion is that it's simply a useless addition: Anything you would gain by the scissor on one side, would be undone by the mirrored other side.
The scissors also reminds me that I never seem to be able to make those scissors sturdy and smooth-going at the same time. They always feel a bit springy to me. That could be caused by my own lack of build-skills, because of slack in the pivots.
Anyway, when I regard those "oval discs" as being bellows, then I guess we could replace those radial connections for MT038 with a spring-limited slider and for MT037 with a dampened slider.
While it is an interpretation of the actual mechanism, it surely saves on complexity in this case.

I am still amazed that you guys can build sims as complex as your "Correct Handle-Construction (Gaffle and Pulleys)" simulation using the WM2D user interface.

Each method has pros and cons.
I think the interface is good enough for creating most designs. It's relative easy to just copy a single mechanism and then copy per 180°, then two per 90° and finally four per 45° to get 8 mechanism.
I think creating a program becomes useful when looking for variants, making complex designs, or use polygons. But that's not an easy undertaking either!

For me it is the tweaking that takes most of the time.
Editing values is easy, but altering a construction for 8 or 16 symmetrical mechanism is almost un-doable. Usually better to start over.
Those kinds of complexities makes the programming option more appealing.

While I don't use a script for rings or spirals I do build them occasionally the old fashioned way. A curved polygon with many data points that I then reshape using Edit>Reshape and move them around etc. Laborious.

A method to consider:
Via [Menu:>Window>Geometry] you can edit the coordinates directly.
Copying the table somehow doesn't work for me, but pasting a table does -- the values get added, so you need to remove the previous values.
With this you could use a spreadsheet to do the laborious calculation without scripting.

[ME]

Any action on this construction will cause an imbalance, self amplifying.

Any action on that construction will cause a reaction of the construction.

With the total energy this construction receives it induces an action on the whole system pendulum, which will cause an action on the side pendulums, which will cause an action on the spring which will cause a reaction on the side pendulums, which will cause a reaction on the system pendulum.
Because each part has its own resonance the oscillations will try to match that frequency.
Each part will cause a frequently changing leverage, or "imbalance", affecting how the totality of energy gets split between the parts instead of causing "self amplification".

A simulation will just show a sum of frequencies where the integral remains constant.

I'm confident that your design will not show self-amplification.
Perhaps only causing a periodic maximum amplitude because frequencies happen to be momentarily constructive, yet never exceeding the energy input.

[Fletcher]

Not so much a variant of a design ME .. as other sets of eyes to look at my hypothesis and conditions for the generation of Excess Torque and objectively critique it as best you can. I prefer the term Excess Torque to Preponderance, or Excess Weight, or Excess Impetus because it's easy to identify with. But they would all apply equally well to a result that allows true mechanical PM from gravity.

Yes, I think MT38 was always an odd-ball for the reasons you give. There were better ways, the ovals (spiral springs) of MT37 for instance. So their inclusion in that MT9 variant must have been strictly related to B's. comments about "but here is not the place to show the correct application of the stork's bills". And in 41 "I can assure the reader that there is something special behind the stork's bills". I then built sims of many of the MT9 groupings with simple rope connections from weight to weight as shown, and even from weight to adjacent lever etc to alter the leverage factor. None could lift the lws and spread the Iris Wheel anything like shown in those groupings (the lift in particular). I had expected that from previous sim experience in other modeling I had done in the past. For those interested in why not, it is due to the angle of applied force/torque thru the rope connections without going into the math.

It was somewhat obvious that to get the lws to act the way portrayed in MT38 for example the SB's would have to be arranged differently and have a different purpose than to unbalance a wheel from their mass displacement. It would be to use their ability to generate directional force, or change directions of force, or rotational to linear for example. As mentioned previously SB's can be simplified down to a single Gaffle lever and slot, and do the same job as a single or multi-sectioned SB. That is if symmetry of the SB opening and closing isn't important. Then they would need to be linked in series by individual pulley systems. All doable in WM so I set about it and now the lws could fan like a peacocks tail.

Yeah .. I've used the geometry co-ord table before. And had problems with it too. I sometimes use it to add new data points into a shape if I haven't put enough in when making my polygon. I guess we each use what is expedient and least frustrating for us. I tend to zoom right in on the polygon and then reshape and move the data points around to get the shape I want which is least frustrating for me. But then I hardly use polygons so just bash something out.

[Fletcher]

I was thinking of opening my new thread (when I get to it) with these pics. But decided to produce them now in light of ME's above discussion and my reply.

They show side by side 8 lw wheels that are anchored so they don't rotate. It is a study of the Gaffle Rope Pulley System of sideways and upwards Force Generation Capability v's Direct Weight-to-Weight Rope Connecting as seen in the MT9 Groupings that I discussed earlier.

The first pic is the 'Start' conditions before the sim is activated.

The second is the 'End' at 50 frames when basically all the movement has occurred that is gonna occur.

I include the basic sim for those interested.

The number 2 LW is free to move -15 degrees from vertical, if it can, by the Pull Method shown.

You can see that the Weight-to-Weight Direct Rope connection method on the RHS won't lift LW 1 and any preceding it, thus not fanning the top or sides like B's. woodcuts all show ! But the In-Series Gaffle (SB equivalent) & Rope Pulley Systems will, and quickly !

[Wubbly]

You can see that the Weight-to-Weight Direct Rope connection method on the RHS won't lift LW 1 and any preceding it, thus not fanning the top or sides like B's. woodcuts all show! But the In-Series Gaffle (SB equivalent) & Rope Pulley Systems will, and quickly!

Yes, your In-Series Gaffle & Rope Pulley systems lift quickly. I never would have thought of something like that.

After I did my sim of MT-09 I thought it was one of the more worthless designs because it worked so badly. You obviously improved on it.

I then built sims of many of the MT9 groupings with simple rope connections from weight to weight as shown, and even from weight to adjacent lever etc to alter the leverage factor. None could lift the lws and spread the Iris Wheel anything like shown in those groupings (the lift in particular). I had expected that from previous sim experience in other modeling I had done in the past. For those interested in why not, it is due to the angle of applied force/torque thru the rope connections ...

In version1 of my MT-9 sim, if you spin up the motor to -60 deg/sec, the weights in the sim look somewhat like bessler's drawing. If you run it backwards (counter clockwise), the weights look even more like Bessler's drawing.

In version 2 of my MT-9 sim I flipped Bessler's drawing to run CCW, and I modified the pulley system to go from weight, to inner rim, to outer rim, to weight. This would get better leverage when pulling on the weights. It looks like we were both trying to solve the same leverage problem in different ways.

[Fletcher]

Yes, trying to maximise the pull force at the right time and place with simple rope connections and pulley ropes alone was a challenge. Yet B. persisted with it in his visuals. As you found in your V2 there are better ways to accomplish things by re-routing forces as you did.

I was looking for something that could 'activate' in the static state, rather than induced in the dynamic state when inertia and Cf's could assist.

And B. had said that there was "something special behind the SB's", and a "correct application of the SB's". And a correct handle-construction was required. I tried to join the dots.

I had done a lot of work with SB's over the years and knew they were excellent for turning rotational force (torque) of a pivoted lw into linear pull or push force. And because of the necessity to simplify my sims down, that used multi-sectional SB's, so they wouldn't crash from too many parts complexity, I had reduced the SB's down to the Gaffle and slot routinely. And this fitted with the notion of an X being an adjustable Jacob's Staff or Kreuz that Oystein postulated, fwiw.

I suggest if you want to build multi-sectioned SB's that you just use the simple Gaffle and rope pulley system to turn rotational force into linear etc and save yourself some laborious building and sim execution problems.

Here is a study I also did on altering the length of the Gaffle lever and its attachment point to the lw in the same environment. This is the equivalent of having more or less SB sections/segments. As suspected it made virtually no difference to performance other than the pulley rope length changed slightly and this changed some downstream lw angles.

This was the jumping-off point for the Excess Torque Hypothesis I'm about to present which is based on hyper-imbalance ( <>> ). I need to build that picture of the road to Potential Excess Torque Capability carefully because there is still some way to go from here and explain why I detoured.

ETA: as explained the mental imagery hopefully will be quite easy to follow but the math analysis on whether it would work as desired became a bit of a burden (I couldn't sim it all to avoid that). That's where fresh eyes and energy may open the door further or slam it shut.

[FunWithGravity2]

Kind of wish i had more pictures still around of this platform. Found it here among my old pictures, which were a lot less than i thought were here. This wheel platform and the design of this series of hanging weights was valuable to learn from. I started building these two foot wheels just to feel the forces and how they acted in the MT examples. I have always thought JB really wanted us to hold it in our hands until we could feel what he found.

Crazy Dave

[ME]

Fletcher, I don't think I'm much help on the theoretical aspect here. As you know I advocate that it's a geometric requirement that masses need to be raised before a positive torque appears.
Now that I have spilled my standard disclaimer, l'll try to continue but I honestly don't see how we can make this principle work.

It's possible to lift one preceding weight near the top by a dropping weight on the RHS.
But, at least in a static situation, it can only do that when their combined CoM drops.
Maybe you can use a pulley system where the already dropped weight pushes the other upwards by two ropes: going half the distance but with double force at an angle;
Still the combined CoM needs to drop in order to operated by gravity.

Added a WM2D simulation with twelve levers. It shows the rotational velocity and the path of the leverweight-CoM. The outer circle is just there as a reference radius.
When it tries to settle for balance (starting from its design-position) that CoM is not always a true torque indicator (translated into angular acceleration). Despite the weight positions, weights don't apply force on the wheel when in free-fall -which may be handy to know in some other design.
You can see that a RHS weight is able to lift a preceding weight, but it's just not enough. At the bottom it distances itself more from that reference circle. When we combine the effects of the top and bottom then we can see that unfortunately it doesn't raise things, it lowers.
The result, which needed an extremely long time to compute as a background-process, will eventually end-up just as yours where the CoM (average of weights) acts like a dampened pendulum and will eventually settle exactly below the axle... at rest...
That's unfortunate because the raising of a preceding weight was actually part of the design.


Edit: Replaced the illustrative gif
Because of upload size limitations I removed some frames. I forgot one frame, so it glitched. Should be better now.

[Fletcher]

Nice build Dave .. I thought the same, that he wanted us to 'feel' the forces rather than intellectualise them.

Simming is great for design purposes, and watching the dynamic interactions etc. Sometimes you get a surprise in that it predicts a behaviour you didn't anticipate or fully appreciate. If you don't introduce finger troubles.

You can see them in action but you can't 'feel the forces in play' as you eloquently say.

So I too built a small static table top model as a starting point. So I could touch it, feel it, and move the arms around at will to different positions easily. It added another level to the experience. And I built sim analogues when I could to cross-check predicted performance against. The carrier wheel being a 15 cm diameter disk with 12 roller lws (I'll post a pic in the next thread) with an outer chain link 'Prime Mover' analogue running around it.

I wanted to explore the system CoM/CoG changes the chain addition brought to the table but primarily the lifting ability of the chain to act as an 'stationary, co-ord locked' internal ramp to lift at the bottom quarters. I was able to sim a basic analogue of the chains lifting ability with a massless all-of-wheel pulley system and it worked a treat without crashing.

The idea was that pulling methods via ropes and pulleys etc acting on other lws elsewhere can do lots of things but are incredibly hard to coordinate for a bottom lw lift action over unequal distances, such as MT12 hints as necessary imo. The tension in the chain from a predetermined circumference I reasoned would negate all that drama of timing of lift and lift distance (normal leverage rules); and that the sideways shifting lws on the down-going side (the Jack) would simultaneously lift upwards at the bottom where needed once latched again to improve torque characteristics of the whole shebang. The results were encouraging.

[Fletcher]

Thanks ME for your efforts .. I'm outta time for the next wee while and gotta go.

Let's say that I may have a workaround to the problems you and I know so well.

I'll read your post thoroughly when I get back and digest it properly. But I think it is the problems I also recognise.

[Fletcher]

OK thanks again ME .. very nice sim. Have had a chance to read your post again in detail. All good.

I would suggest that you start the sim as I did with some of the levers already against the inner rim in the top quarter. So that the Jack Effect can work. It's there imo to provide an outwards side-ways thrust on the down-going side at around 3 o'cl in a CW direction. FWIW the contributing Jack movement lws sum to the movement of ONE single lw moving thru a large arc because they are incremental movements with each lw increasing the relative angle from the proceeding. So we are really only getting the benefit of one lw repositioning of which its force can potentially be redirected.

Of course you are right and the CoM/CoG MUST fall lower and find equilibrium. It's the ol' 'width for height' problem so no need for the disclaimer and I understand completely your concerns. If you were to plot the later sections of your CoM.x and CoM.y graph just before the sim settles down you might find the CoM.x wander left and right of the center line like it does, equal distances or thereabouts in your sim. In mine it had a pronounced CCW bias from my starting positions.

For others benefit this indicates that there is NO asymmetric torque capability in this design as it stands. It will seek and find equilibrium position and eventually oscillate to a stop with normal system losses such as windage and normal pivot friction etc robbing the system of energy as heat and sound etc. A completely normal response as we know it of equal positive and negative torques canceling each other in any one sector (1 of 12). The Stevin's Problem.

So in summary we can generate an oscillation of the system CoM but not an excess of positive torque at this time, which shows it is a normal false OOB PM concept, unless it can be augmented differently perhaps ?!

As mentioned in my reply to Dave above I went to a first stage augmentation by adding an externally revolving chain, running over the roller lws. This had mass and so theoretically no lifting of lws could occur in the top quarters because of the oppressive weight of the collective chain holding them down against the rim. But the 3 o'cl lw could still deploy to the right if the collective chain mass weren't too great in theory. The chain (what I call the Prime Mover apparatus or structure of my hypothesis) CoM is theoretically then displaced to the right of center of rotation/axle. And because the chains circumference is predetermined it bulges out as it follows the roller lw at 3 o'cl and also flattens inwards/upwards in the bottom sections, effectively creating a universal lifting device IF that were desirable. The chains CoM then shifts to the right opposing to some degree the negative CoM of the carrier wheel. I'll post a sim tomorrow for your consideration of the actions.

But still I wouldn't expect to end up with whole-of-wheel asymmetric torque from the combining the two systems. At best some system CoM mitigation effect. Perhaps even close to a balanced total wheel and chain ? You can't lift higher than the GPE lost ! Newton and Wagner would roll in their graves.

[WaltzCee]

This thread is incredibly interesting. Not only is that my opinion it should be yours too. :-)

[ME]

I'm outta time for the next wee while and gotta go.

I think, till next week.

<Long and good post + a brilliant new topic>

I think, a "wee" means probably an extremely short week on the other side of the globe :-)

Of course you are right and the CoM/CoG MUST fall lower and find equilibrium. It's the ol' 'width for height' problem so no need for the disclaimer

For other readers I would like to elaborate on that.
One of the reason I disclaim is that it's not my fault that Geometry works the way it does.
The "width for height" vs "raising weights" may look like a semantics issue but I see a difference.
I think the 'width for height' covers the recovery issue (height) for aiming at easy leverage (width), while 'raising weight' (height) is the required investment to get an overbalanced path (width).

I see "width for height" in designs that focus on leverage.
For example, MT039 illustrates a situation where a heavy scissor is contracted at D (left), because it is 'lighter', so the side at A (right) is 'heavier'. It only works because 'A' drops.
En-passant the C (top) part is getting 'raised' towards 'E', yet the opposite/bottom part is lower.
While talking about MT039, also note that nothing metaphysical is happening to the scissors. They just keep having the same weight. Bessler's mentioning 'Lighter' and 'Heavier' is just leverage here. And maybe important elsewhere.

I see "raising weight" in designs that empasizes just that. MT040 is one of them, just like MT013, MT014, MT017 (etc).

I would suggest that you start the sim as I did with some of the levers already against the inner rim in the top quarter. So that the Jack Effect can work. It's there imo to provide an outwards side-ways thrust on the down-going side at around 3 o'cl in a CW direction. FWIW the contributing Jack movement lws sum to the movement of ONE single lw moving thru a large arc because they are incremental movements with each lw increasing the relative angle from the proceeding. So we are really only getting the benefit of one lw repositioning of which its force can potentially be redirected.

I'll try that.
But I hypothesize that the whole combination is a combined pulley. While it splits the work, the average of all those masses still need to drop when you want it to work.

I'm actually just waiting/looking/hunting for a literal magic-trick - a-la self-untying knot or something that mezmerizes just like a jacobs-ladder ribbon toy, but then cyclical and with physics.

You can't lift higher than the GPE lost

Could this statement imply that Bessler's wheel had a limit on the total amount of weight it could lift while demonstrating its capability (from reset till reset)?