An explanation for the 22,5 grades angle

[path_finder]

Let me just a minute go back to the theory.
Hereafter is an analysis of the need for some springs in the move of the parts.

On the first drawing below (supposed to be in a vertical plane) all the green parts are some equilateral triangles linked together with horizontal axles (pivots). Only the blue pivots are located (fixed) on the main outer circle.
All other red pivots (linking two triangles) are free to move with the only restriction do not overpass the main outer circle.
In this configuration it's obvious that everything is stable (no way to move) because there is no way for the red pivots to move in the direction of the main center. In addition this assembly has a full symmetry (therefore no unbalance).

On the second drawing below we have a modified geometry using the same parts but arranged in a different way.
On the right side two red pivots have been moved on the center, BTW moving four triangles (in light blue) creating a asymmetry (therefore an unbalance).
To permit this move the only solution was to disconnect the two related blue pivots from the main outer circle and shift them a short time outside this circle. This is only possible if these two blue pivots (identified by the black arrow) have been previously linked with some springs to any outside point.
Another way to obtain the same effect is to attach these blue pivots to a pantograph (the 'A' of Bessler?...) located outside the main circle.

If we implement a such mechanism, and if we create a rotational triggering of the pivots, we win!...

[DrWhat]

I like your thinking p_f.

I've often thought the BW was a simple geometrical structure, hence his comments about FORM being the key.

Lets see where this goes.

[path_finder]

Dear DrWhat,
Are you alone here?
Many thanks for your comment, I agree with.
This principle can be implemented including some different shapes.
Hereafter is another geometry using some parts of specific shape.
Some moving pivots with springs are required here also.

[AB Hammer]

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DrWhat/Damian isn't the only one here. Even though it is an interesting approach. The placements are one thing but getting them to make those placements are another. I have seen other devices with good placements before but what had to be done to get those placements was the problem.

Alan

[path_finder]

First, many thanks for AB_hammer for the encouragement.
I was in travel and not able to go forward in my experiments.
Nevertheles I found the time to improve the design of the hamster wich gave to me the most efficient results (see above).
The new hamster is now like in the shot hereafter.
Because the changes in the ratios for the length of the rods I hope now to overpass the barrier of the 22,5 grades.
The geometry of the assembly don't having obviously a radial symetry (because the parts added for the reinforcement), I have perhaps to correct it first before any other test (may be this point is not relevant? I will see). But the first quality of this assembly is it's perpetual unbalance what rod (indicated by the couple of letters) you are using for suspend this device. Some news asap.

On another side I think the solution for transfering the contact point from the bottom to the top (for hanging the hamster on the roof) could be a design using the cycloidal reductor. see here:
http://www.youtube.com/watch?v=HJ6ISfsQB9c
I'm preparing a small explanation about this concept.

[path_finder]

On the MT138 the item on the right side has been discussed many times in this forum.
The used terminology for depicting this item was often 'Jacob Ladder' (certainly by first level analogy) although it was not certain.
In the picture hereafter I suggest a more detailed mechanical description in accordance with the original drawing.
The yellow wheel is perhaps too much large and not at the scale, but it's intentional for a better comprehension.
This is different from the common 'Jacob Ladder' toy, but the principle is similar.
The purpose of this design is to flip the short and the long segments alternatively by an effect coming from the rotation of the yellow circle, transferring the obtained gap counterwise versus the rotation of the wheel.
I hope using a such as mechanism for the linkage between the inner rim of the main wheel and the hamster shown above.

[path_finder]

The latest results from the last experiments with the hamster design.
The previous shot 'hamster_w15e.jpg' showed an 'order three' hamster (dephasing of 60 grades between two workers).
The animation hereafter resumes the motion of this device.Click in the image for a better view.
It's not a theorical concept: the physical behaviour is absolutely conform with the animation.
The next step now is to use this device as controller of a second set of weights (the horse before the car...)
Please observe the back motion of the rods termination between 1:00 and 11:00 wich can be used for lift-up the 4:00 weight.
The first tests are really encouraging.
Next complementary infos follow soon.

[path_finder]

The second set of weights (in yellow) is now installed.
I leave you thinking where the springs must be connected.
The relative dephasing between the two sets is here not optimized.
The retaining wires of the ascending side on the left are not represented also.
In addition the first set of weights can be simplified (one single weight at the center of the middle bar, instead two like now).
Only the building will give you the best solution.

[path_finder]

Just few comments on the previous design.

As indicated above, this device is of 'order three', with three workers triggered by the gravity every 60 grades.
The number of weights is NINE: three for the workers (if optimized, not the case in the both animations), and six (two times more) for the second set (yellow).
If this assembly is covered with some tissues and hidden from the witnesses, they can only hear SIX noises on the outer rim for each turn of the wheel.
Note that the number of shocks does not allow to determine the exact number of the weights inside the wheel (we hear SIX altough there are NINE)
Note that the yellow weights reach the inner rim first gently, then increasing until the Centrifugal Force reaches it's maximum because the limited size of the rim, were the shocks can be more important.

Now if we try to apply the same concept for a device of 'order four', will will have TWELVE weights inside the wheel: FOUR for the workers, and EIGHT for the second set. The witnesses will hear only EIGHT shock noises, altough there are TWELVE weights inside the wheel.

A big question is: on a practical point of vue how to apply all this staff inside a wheel with a thickness of about 10 inches (25cm) approximatively.
The solution could be to split the inner of the wheel in four parallel planes.
But this supposes that the weights are flat enough and that each worker is in the same plane than it's outer corresponding weight.
Another solution is to reduce the size of the four workers and leave all external room free for the outer weights. The shape of the weights in the workers would be different (flat) but with the same mass. In that case the dimension (length of the cylinders) of the weights can be about identical with the thickness of the wheel. But on the other side the torque could become not sufficient enough for lift-up the opposite weight. What compromize?

[path_finder]

The previous animations were for an 'order three' device.
The next one uses the same principle, but shows an 'order four' device.
As explained elsewhere, an animation shall be taken as a goal (the result to be reached).
The path between the concept and a working wheel passes through the building, wich is not a neglectible step: hereafter is a good example.
The first attempt to build the corresponding device was in fact a 'dead end'.
The shot is explicit: even if the four workers are correctly assembled, the selected way does not allow the addition of the active yellow weights. There is no room at all.
It was necessary to think again on a new space repartition, and rebuild another assembly.
It's done yet, more shots tomorrow.

[path_finder]

The modified assembly.
The workers are now in the central room of the wheel, by pair.
The yellow weights (assuming the overbalance and the motion) will be located in two active rooms (in yellow), there is now enough space.
Each pair consists into two workers dephased with 90 grades and keeps the control over FOUR yellow weights.
The pairs of workers are dephased mutually with 45 grades.
So far each worker retriggers one of the EIGHT weights every 45 grades.
The linkage between the two elongated arms of each worker and the appropriated weights is made first by a rod allowing the change of vertical plane and then by another rod in the yellow 'active room'. This multiple motions created a real problem of space allocation, in particular with the mechanical interconnection of the different planes inside the wheel. You can see the alternate linking rods, no full pass-trough being allowed because the trouble given to the motion of the arms.

Now there are some very important deductions from this design:
- The workers cannot be left in that state: it's impossible to make a single full turn because the amount of the shocks when the workers are shifted on the maximum allowed path.
It's obvious that on the start position all the weights of the workers must be centered on the main axis.
Caution: this is not the case for the yellow weights, only for the workers!...
- Therefore the springs are a mandatory. There are several ways to implement them. One has been already explained here:
http://www.besslerwheel.com/forum/download.php?id=7102
In the wheel used now this is a little bit different.
- When the wheel starts to run the workers weights are excentered by the centrifugal force until the full expansion allowable (limitation given by the inner rim of the wheel), BTW limiting the rotation speed (the 'peacock effect')
- The big question now is: at the starting position how to obtain an expansion wide enough for lift-up the yellow weight?
Indeed if the workers weights are very close from the center at the starting step, the expansion will be about null and at least not able to make the job.
This suppose also that in the starting phase all the yellow weights should be very close from the main axis. True?

[path_finder]

The full assembly, now completed with the active weights (in yellow on the reference animation hamster_w16-5g.gif above).
The yellow weights are attached with some rubber bands (but not how our friend nicbordeaux is intended to): it's just for the first tests and may be also for a preliminary phase of balance adjustment (I presume it's better).
The four workers are mutually much closer, allowing more room for the yellow weights (I can change the value at any time).
For the moment the workers are supplied with some 500 grs weights (black in the shot, they are 'body building' parts). In my next test I will not change them, but almost change (if necessary) the 125 grs of the yellow weights (note the ratio 4:1).
The actuators are the violet crosses in the shot: here will be attached the linkers with the opposite yellow active weight.
The cords for retain the yellow weights will be some nylon wires, as experimented in the past. They are NOT represented in the shot (anyway not visible by any observer nor the camera).
It's a long way, but each step is important.

[path_finder]

Dear all,
Returned recently back home, I still continue my experiments.

The 'hamster design' is based on the interaction between the main wheel and the rolling weight (the hamster).
Remember, the principle of this design was based on a rolling cylinder containing a mechanism allowing the shift of the COG every 90 grades.

In the animation below we can see the motion of the two parts (the clockwise rotating wheel, and the internal rolling cylinder/hamster).
The assumptions were:
- during the first 30 grades rotation of the main wheel, the cylinder is free and climbs on the inner rim, because its unbalanced internal structure (cylinder colored in green).
- during the next 15 grades rotation of the main wheel, a ratchet (clutch) locks the cylinder wich is transported back until 6:00 by the clockwise motion of the mainwheel (cylinder colored in rosa).
- returned back to 6:00 keeling position, the cylinder made a 90 grades rotation on itself and thanks its internal mechanism, recuperating a new unbalanced state, restart the process.
This exactly what was described in this animation.
Although the principle is good, why this don't work?

On the animation you can see the COG of the active cylinder (the black cross, retrigered every 90 grades), but also the contact point (violet cross) between the main wheel and the hamster. If you look carefully you will find easily where is the fault in the animation.
The next drawing is more explicit: when the hamster is free, she can only climb when the COG (black cross) is more at right side than the contact point (violet cross). Indeed this situation is only valid for the first 22,5 grades rotation of the main wheel.
Here is the justification of the title of this thread...

So far the hamster will never reach the 30 grades position by itself.
But there is a solution. Coming soon, be patient.

[AB Hammer]

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It seem that it is just that one little inch more and we have it. That is probably what keeps us going so hard. The wheel in the bottom is always trying to walk up an eternal escalator going down. That IMO is the reason it doesn't make the grade for it would have to go twice as far per action to make the grade.

Alan

[not_me]

First, many thanks for AB_hammer for the encouragement.
I was in travel and not able to go forward in my experiments.
Nevertheles I found the time to improve the design of the hamster wich gave to me the most efficient results (see above).
The new hamster is now like in the shot hereafter.
Because the changes in the ratios for the length of the rods I hope now to overpass the barrier of the 22,5 grades.
The geometry of the assembly don't having obviously a radial symetry (because the parts added for the reinforcement), I have perhaps to correct it first before any other test (may be this point is not relevant? I will see). But the first quality of this assembly is it's perpetual unbalance what rod (indicated by the couple of letters) you are using for suspend this device. Some news asap.

On another side I think the solution for transfering the contact point from the bottom to the top (for hanging the hamster on the roof) could be a design using the cycloidal reductor. see here:
http://www.youtube.com/watch?v=HJ6ISfsQB9c
I'm preparing a small explanation about this concept.

P_F,
I worked on a design of a wheel in wheel concept. If the hamster could go from the top of the inner wheel to the outer wheel, it would have maximum force. By using a wheel that can hold the hamster by the sides, it can walk on a plank to the outer wheel.
One thing to be mindful of is when the hamster is within 45 degrees of bottom center, it's path will become longer not allowing it develop as much force. That is, the vertical drop to lateral (sideways) travel.
Within 30 degrees, the lateral travel will be twice the vertical drop.
Thinking of Newton's a body at rest and opposing force, what is the hamster 180 degrees away doing ? Another way force could be factored.