Part Three is the Charm

[Tarsier79]

I modified each lever and incorporated a bend that will go around the pivot of the lever below it.

FYI, this does not improve efficiency, or help rotation in any way.

[mryy]

I modified each lever and incorporated a bend that will go around the pivot of the lever below it.

FYI, this does not improve efficiency, or help rotation in any way.

It doesn't hurt to have the cog farther away even if its shift is minor, no?

[Tarsier79]

It depends what you are trying to accomplish with the movement.

In this instance, the COG is vertically in line with the axle, even if it doesn't look like it.

[mryy]

It depends what you are trying to accomplish with the movement.

In this instance, the COG is vertically in line with the axle, even if it doesn't look like it.

It's a diagram drawn with much eyeballing so accuracy is not guaranteed. The levers from 12:00 to 4:00 will need to be closer in future diagrams. Anyway the cog is supposed to on the descending side.

[Tarsier79]

It doesn't matter how you draw it. This design: MT9 and 10 are balanced, which means the COG is directly below the axle. It will be slightly unbalanced depending on its exact orientation, but only slightly. In a simple design like this you can calculate the COG. There are a number of ways to do it, both visually and mathematically.

If you had 8 arms, I would say do it by drawing lines between weights and bisecting the line. Because you have 12, I think it would be easier to calculate it.

To do this in the most basic way:

1. Draw a vertical line through the axle.
2. Measure the horizontal distance of each weight to the line. All weights on the left of the line will be negative the amount. The more accurate the better.
3. Add up all the numbers. The answer should be very close to 0.

ADD: Attached is a page from JCs MT.
(I wouldn't use the above method on MT10. It isn't drawn properly.

[Fletcher]

It depends what you are trying to accomplish with the movement.

In this instance, the COG is vertically in line with the axle, even if it doesn't look like it.

It's a diagram drawn with much eyeballing so accuracy is not guaranteed. The levers from 12:00 to 4:00 will need to be closer in future diagrams. Anyway the cog is supposed to on the descending side.

Here's a 2 minute eye-ball approximation of your sketch mryy.

I arbitrarily set the yellow weights to 1 kg each, and the reds to 0.1 kg each.

System COM / COG is just right of center vertical line beneath axle. Make the reds 0.001 and the System COM is almost exactly on the line i.e. no torque to speak of.

I measured the connecting ropes in my render and when they are at full stretch their lengths are a bit off imo.

Clearly a lot of functionality will depend on whether the red weights can be flung that high by the mechs you've designed.

Best -f

[mryy]

Alright guys, I made the effort to re-space the levers as accurately as I can and there are now equal number of weights on each side of the wheel. (No need for a bend along the lever arm this time.) I did measurements per Tarsier and the COG is on the descending.

My concern is the moment a lever approaches the 5:30. There is one fewer weight on the descending side during that instance, BUT some weights on said side are farther from the center vertical line than some weights on the ascending. At worst I am hoping both sides cancel out at 5:30. I do imagine that the red weight position and the lever striking the rim stop between 3:00 - 4:00 will propel the rotation despite a temporary movement of the COG nearer the center line.

[Tarsier79]

The other thing that might affect it is if the levers are lifted as shown. The other good thing about a simple mech like this is you can just build it and see

[mryy]

I have been pondering the optimal length of the levers relative to the size of the wheel. In the next version of the ??O$$ the lever's swing arm will be extended by a selected ratio of 1:3 -- that is 1 part radius of the inner wheel ("grindstone") to 3 parts length of the lever swing arm. Using the Gera wheel as a reference, a grindstone with a radius of 7 inches (17.5 cm) will have levers with swing arms of 21 inches (52.6 cm) mounted all around its edge. The advantages of a longer lever are:

1. Greater torque/angular momentum transfer to the rim of the wheel.
2. Greater leverage to fling the red weight.
3. Better keeping of the system COG on the descending side. (Notice the three levers from 7:00 - 9:00 hang vertically which means their lateral distances from the center line is the same no matter the lever length; this is a benefit to the descending side.)

On another note, I am thinking B.'s quarters clue (1 lb fall and 4 lb rise) might not be applicable to the uni-directional wheel. This clue is mentioned in his rebuttal of Wagner's review of the Merseburg wheel, a bi-directional. B. stated that his one-way and two-way wheels operated on very different principles so the clue might not be relevant to the one-way. The implication of all this is that it's important to know the wheel to which any documented information is referring, as it can possibly be constructed with a dissimilar mechanism. One could start off on the wrong assumption using a clue about a two-way in the design of a one-way. Thank you B. for yet another level of obfuscation ...


Select Quote:

"Wagner says that my machine does not derive its motive force from the noisy weights. He declares that the mechanism that causes all the clattering is not the thing which causes the rotation of my Wheel. The clattering noise you refer to is, I assure you, a phenomenon caused directly by the real motive power of the machine, and nothing else. You also wish me to inform you why the Draschwitz machine did not create a similar noise. The two machines worked on quite different principles. The Draschwitz one turned in only one direction, but the Merseburg one turned both ways. The former [Draschwitz] was provided with felt coverings, the latter was bare. I have many other machines of various types - some, for instance, with weights, others without." AP 339 Collins

[mryy]

??O$$ version with the length of lever swing arm being 3x the grindstone radius (1:3 ratio). Yellow weight is secured to lever end needless to say. I left out the springs from the diagram for an uncluttered view. A 1:4 ratio or higher could be considered as well. Hope you like ...

[mryy]

The ??O$$ wheel at 1:4 ratio (1 part grindstone radius to 4 parts lever strike arm). The cross members that connect the cords are placed a little farther out from the fulcrum this time. I have noted that their dimension and placement along the arm, tied to the cords, affect the angle of the levers around the wheel. Springs not shown.

[Fletcher]

Hi Mryy .. hope you don't mind the input ..

I took the liberty this am of building a couple of quick sims (first part) of your previous drawing - dimensions eyeballed as best I could. I think it is a close representation of what you showed tho generic.

I couldn't/didn't sim the catch and release and hefting levers and springs etc - just wanted to go to first principles (of the together-hung) and examine some of the assumptions about such a design. So I made pivoting levers and weights etc set at close to the angles you drew.

Anyhoo .. I'll leave you to study the 2 animations to follow and see if they make sense to you. The sims predict a certain behaviour.

The first one the levers have no stops closer to the axle but do collide with other levers which act as that stop.

** The premise I believe was that the descending side entrained CW lever-weights would pull the ascending side upwards and at the same time have enough contact force to set the hoisting spring lever etc when that is added in a real-build. Watch the direction of the levers relative to the wheel background, and the system COM icon move around etc.

Second animation will follow in the next post.



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[Fletcher]

OK .. here is the second animation ..

This is the same sim as before except I have added internal stops to reduce the back-swing of the connected levers. They are placed there because the lever hanging directly down at 9 o'cl sets where these stops should be.

Anyways .. the sim predicts a slightly different behaviour in terms of back-swing and the number of degrees the disk rotates to etc.

N.B. I left out in both sims the 2 red weights to be flung upwards and caught on the descending side.

First there has to be sufficient lever torque to set the levers with springs I would think.

Best -f



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[mryy]

Thanks for taking the time to make these sims. What I *imagine* happening -- if I imagined correctly -- are three actions occurring simultaneously to propel the wheel:

1. Net torque on descending
2. 3:00 lever striking the rim stop (think hoop and stick game)
3. Red weights cycling on one side to maintain the net torque

The problem with the previous uploads was that on either side of the 3:00 lever the cords are at full stretch and the levers trailing could be tugging it back. There needs to be cord slack to allow the spring-loaded lever the freedom of movement to swing down at the rim stop with force and transfer its energy/momentum. I have been working to correct this by lengthening the cords and the lever cross members. Again, all three actions above have to work together for the wheel to spin ... as I imagine it.

Reviewing your sims there is some swinging of the levers from 6:00 to 9:00, like pendulums. I don't imagine it happening to this extent when the springs are present but I could be wrong. The COG is very close to the center line, more than I was expecting ... The wheel sims behave like the typical OB nonrunners. :)

[mryy]

Here is an improved 1:4 ratio wheel showing both start and spin states. Note where the cords are fully stretched in either diagrams. In the imbalanced start state the red weight is in the 2:00 lever. When the wheel is released, it begins to turn CW due to the starting net torque. What I imagine happening is the 12:00 (you see leaning diagonally to the left) will lift up quickly as it moves into the 1:00 by action of its spring under tension and by the tug of the lever to its right. The cord on the right of it then slacks as seen in the second diagram (12:00 lever is now the 1:00 lever). All cords on the descending side are now slack and the 3:00 lever can strike the rim stop unrestrained. The force of the impact causes the red weight to fling and land onto the lever above. The process repeats.