An explanation for the 22,5 grades angle

[path_finder]

As mentioned above in an earlier post, I will give hereafter some data on the trilobed 'flowerbowl' (my personal quest since five years).
This strange object is today exibited at the Cairo museum.
Just for memory, there are a lot of URLs dedicated to the subject like here:
http://www.geocities.com/unforbidden_ge ... _3111.html
But my intent is not to discuss now and deeply all the discoveries I made about the 'flowerbowl'.
I want just show how this design can be used for my wheel building.

The animation below starts from the basic 12-bars frame
(as shown earlier here: http://www.besslerwheel.com/forum/download.php?id=6286)
and finishes on the first reduction shape of the 'flowerbowl'.
It shows the three major positions of the internal frame:
- centered (for the keeling rest position)
- 12:00 position on the small grey circle of the middle point
- 6:00 position for this same point
Every position of the grey circle is accessible, like any position of the internal area.
The 'flowerbowl' itself is here fixed: it's obvious that it rotates during it's use.
Any path is possible for the middle point of the frame, in particular it can rotates on the grey circle, or follow a spiral from the center reaching the grey circle.
In addition the last frame of the animation is given for a better understanding.

As you can see, one of the major feature of the 'flowerbowl' (apart it's simplicity) is the significative reduction of the main outsize:
by replacing the external rods by the three rollers we can pass from a 90cm size to an overall size of 66cm (per example).
Another some important advantages are:
- the absence of physical wheels
- the low level of friction
- the building with no sophisticated materials.

[path_finder]

I made some important discoveries during my latest tests on the various 'hamster design' wheels.
As explained before I'm mixing always the theory (simulations) and the praxis (building).
In view to verify one more time the validity of the 'hamster' concept and check again the good timing of the both primemovers synchronization, I made few animations representing the various phases of the attempted process.

The first discovery is related with the needed path during the active phase of the hamster (climbing free along the inner rim of the primemover).
An animal can run only between 6:00 and 3:00 (running on the floor).
After 3:00 she has no way to climb (except for some ape at the condition to be hanged on a roof supplied with some rods).
In fact there is no reason do not extend this active part within the full inner rim, if we have at our disposal a clever mechanism assuming the mechanical connection with this inner rim.
Based on the hypocycloidal curve (for memory here:http://www.besslerwheel.com/forum/download.php?id=6323 I found such as mechanical design, able to stick the hamster (in fact a circle) with the full 360 grades inner rim.
But this mechanism must be modified in view to include the whished unbalance for the primemover.
The solution is not really difficult: just keep the moving point at the center
The full motion is shown in the animation below.
This new version of the 'hamster design' is much more efficient than the previous one, and the synchronization of the two primemovers is much more simple.
Like for the previous design (see the posts earlier her: http://www.besslerwheel.com/forum/download.php?id=6444),
- during the free climbing phase the hamster is colored in green
- during the second half of the turn, where locked with the rim, the hamster is colored in red.
The big difference now consists in a full 360 grades turn, instead 45 grades multiple steps (so far the title of this thread could be obsolete?...)

The second discovery is deductable from the first: the two primemovers (if using this new concept) can be linked together (in phase opposition) assuming by the way a full balance of the static masses (then unbalanced when the workers are shifted).

At least and not the last, there is an third interesting point: this mechanism can solve an old question not really solved earlier.
How to get an horizontal sliding point at 3:00 of the circle without any physical connection to the axis?
If you remember an old suggestion (see here:http://www.besslerwheel.com/forum/download.php?id=6210) we have now a way to build this engine.
In addition we can for sure multiply this couple of weights (three other items dephased within 90, 180 and 270 grades with the first one).
I will build one as soon as possible for verifying (unfortunately I'm travelling for four weeks).

But, but, but..like shown this animation is only theoretical, there is why:
Few of yours were curious about the fact I'm not using the WM2 software at all.
Even if it's true that a single animation can not prove anything, nevertheless this kind of exercise has an enormous advantage: you can discover very shortly any wrong idea.
Precisely this is what happened with the animation below wich is wrong in first approach.
Indeed most of yours will immediately discover why: the rotation speed of the blue wheel is not correct
Normally if rolling on the inner rim of the red wheel, the blue wheel should rotate two times faster.
Fortunately there is a complementary design allowing to do the job, and if this animation is wrong when not completed, the researched effect still remains true.
What we need is just to modify the structure in view to give to the blue wheel a rotation speed equal with the half of the red wheel rotational speed.
This can be more explicit with a full animation.
For the moment I just give the principle with the following drawing:.
The green center circle A is fixed (grounded)
The red crown B rotates around A, and supports
-1- our hamster (the blue circle of the animation)
-2- the red circle where the hamster is rolling
The blue external crown is the outer cylinder of our primemover
These three parts are centered.
The rotation speed of the red B crown is the half of the blue C crown's rotational speed.
I will try to make an animation showing all these parts in motion. Please be patient. Thanks.

[path_finder]

Correction:
I apologize for the errors in the last drawing explanation.
You shall read instead:
- The hamster (blue circle) is free and centered on the main axis (not linked to the red crown B)
- The red circle is NOT a part of the red crown B, but a part of the blue crown C (in view to get the double speed)
- The dimensions of the orange rollers (parts of B) are not correct: their radius must respect a ratio of 1:4 with the radius of the green center pot.
- an additional crown is needed for transferring this reversed rotational speed from these rollers to the hamster axle (blue circle).
I'm pretty sure that the most suspicious of yours would have made the correction yet.
These corrections will be included in the full animation later.

[LustInBlack]

This idea is brilliant, but there must be a monster hiding somewhere..

[DrWhat]

Yes, always fascinated by your designs p_f.

If John doesn't achieve movement I'm sure you could dissect it and design something meaningful from it.

[path_finder]

Many thanks to LustInblack and DrWhat.
In fine, this should be more easier than you think.
Hereafter the corrected drawing.
There will be four hamsters (only one represented, the three others are the grey circles.
The self motion is coming from the fact that the attachment pins are repartited on two different mobile parts (the hamster and the red crown B).
Only a building can confirm this assumption.
N.B.: the locking/unlocking ratchet are not shown on this drawing, and must be added to each hamster axle.

[path_finder]

As information for those interested, the same principle applied within the 'flowerbowl' (mechanism of order three instead of order four).
In my opinion it should be used a couple of such as assembly (back to back on the same central axle). Then the full assembly can be put on the inner rim of a waterwheel, allowing to lift-up the water (contrary of the watermill). In that case the twin-flowerbowl assembly is acting like the hamster.
See an old drawing here:http://www.besslerwheel.com/forum/downl ... 41f134b364

[path_finder]

I made a first demonstrator (see the shot below) in view to verify the previous drawing and fix the true ratios between the gears.
So far I can confirm an important point regarding the number five for the designs of order four.
The rules for the size of the four intermediate rollers (in orange on the last drawing) is a quarter of the central cylinder (in green).
But after a full turn around this cylinder their effective rotation will be 5 (five) turns instead of the four as wished.
By the way we need to reduce this rotation.

The first idea is to adjust the number of the teeth.
Per example 60 teeth on the rollers and 192 on the central cylinder (instead 240).
But we need the same tooth size for the both cogs.
Therefore the ratio between the diameters will not be 1:4 anymore.
And the axles of the rollers will not be at the middle of the diameter, where should be located the hamster axle.

The second idea is to let rotate the central cylinder.
In that case this cylinder must compensate this fifth ghost turn by an advance of one fifth (72 grades).
But the mechanism for obtaining this shift will give a more complex assembly.

The best idea (in my opinion) is the use of a more appropriate 1:3 ratio between the rollers and the central cylinder.
If the diameter of the rollers is a third of the central cylinder diameter, the full turn of the rollers around this cylinder will be 3+1=4, giving the wished rotation speed (four times the rotation of the rosa sector in the above drawing).
The used values for the radius of the different parts are given in the next drawing.
(just for give the values. The three other rollers are missed and the ratchets also)
I will post a shot of the corresponding demonstrator used for my experiments.

Regarding the question of the 'fifth ghost turn' (and the number FIVE so strong defended by JC) I think Bessler found another way to counter (use?) this deviant effect. Could this point become an interesting new topic where somebody can suggest an answer ?.

[path_finder]

Just one more remark:
In an early post http://www.besslerwheel.com/forum/downl ... aca812a7f8
I said:

On a pure theorical point of view, the path in BLUE will be the most efficient, but it's impracticable...

If the first part of this assumption is still true, the second part was too much pessimistic.
The above design can now assume this rule (the OC blue path in the posted drawing).

[path_finder]

Some news of my tests with the 'hamster design'.

I have been busy for about one month with my job, and I returned back to these tests recently.
The different wheels implementing this kind of principle are still not working but I made some very good progress:

1. The principle is confirmed as valuable.
It is not perhaps the most efficient but it does work (I will justify below).

2. I solved all the mechanical problems and in particular this one related to the break of central axle.
The synchronization between the two prime-movers was in fact much more simple as previewed.
The picture below shows how the twin primemovers must be linked (remove the central cross with the bearing).
The experiments show now a real triggering every 45 grades (this was the researched purpose).

3. I know now, even if the principle is still correct, why my different wheels don't rotate more than about three turns.
Knowing why is the first positive step (if it don't work and in addition you don't know why, it's useless).
The reason is obvious but some evidence can be sometime very hidden.
At the beginning of the 'hamster design' it was assumed that each hamster was climbing on the inner rim of the wheel.
In view to reduce the mechanical process I decided at a certain time to suppress the gears ('the gears are not needed').
Deep error!..
Replacing the original gears by a rod equal to the radius, was a stupid idea: making so the hamster does keep the right and constant distance within the central axis, but also does loose the contact with the inner rim, and therefore don't pull down the wheel during the unbalanced phase.
Now the consequence is an important modification of the wheels (wich until now don't have any teeth on their outer rim).
I will make it. Give me the time.

4. But what I discovered is much more important: the most efficient path is not between 04:30 and 6:00 like above, but the full path between 12:00 and 6:00
I discussed this earlier in another topic. The hamster can not overlap the 03:00 position, because she must keep her feet on the inner rim.
Let's suppose now that the hamster can also be hunged to some bars located at the inner side of the wheel.
The efficient path will be an half of the wheel (and not only 45 grades).
This concept is shown in the next animation below named the 'crab design'.
I selected a crab because she has two claws she can use for any left or right linkage.
The idea is simple: on the down side the crab is hunged to the external pins (located on the outer rim of the wheel), and on the lift-up side the crab is hunged on the internal pins (located on the central small circle). The crab don't change his position versus the central axis.
It's like the maxwell daemon: not moving the crab don't consume any extra gravitic energy; she just moves the arms and changes the linkage.
This can be also obtained by the duplication of the crab (two crabs in opposite position).
I'm in way to build a wheel using this 'crab design' wich seems to be hopeful.

[DrWhat]

Best of luck path_finder.

[path_finder]

Dear DrWhat,
Many thanks for the encouragement.

Hereafter is an animation showing how the 'MT138 workers' mechanism can be used as locker (latch).
The hollow tube at the left side can be attached to the inner rim, and the right one to the outer rim.
This is just a theoretical example because the building is not so simple
(p.e. the hollow tubes must be mounted on an axis because the circular path of the rod's terminal).
I will build one and inform you on the results.

[path_finder]

Some results from the experiments made with my gears demonstrator:

First configuration, like in the drawing below:
- Outer crown (green): 4xN teeth
- Center gear (rosa): 2xN teeth
- Satellites (yellow): 1xN tooth
Note: the satellite assembly (circular link between the satellites axle) is not represented in the drawing.

1A.If the center gear (rosa) is locked:
A rotation of 90° of the outer crown gives a 60° rotation of the satellites assembly (same direction), for a rotation of 180° of each satellite (same direction). This configuration allows:
- a self rotation speed of each satellite of two times the rotation speed of the outer crown (same direction).
- a rotation speed of the satellites assembly of two-third (2/3) of the rotation speed of the outer crown (same direction).

1B.If the satellite assembly is locked:
A rotation of 45° of the outer crown gives a rotation of the central gear of 90° (in opposite direction), for a rotation of 180° of each satellite (same direction). This configuration allows:
- a self rotation speed of each satellite of four times the rotation speed of the outer crown (same direction)
- a rotation of the center gear of:
. - two times the rotation speed of the outer crown (in opposite direction).
. - one half the rotation speed of the satellites (in opposite direction).

1C.If the outer crown is locked:
A rotation of 180° of the center gear gives a 60° rotation of the satellites assembly (in same direction), for a self rotation of 180° of each satellite (in opposite direction). This configuration allows:
- a self rotation speed of each satellite equal to the rotation speed of the center gear (in opposite direction).
- a rotation speed of the satellite assembly of one-third (1/3) of the rotation speed of the center gear (in same direction).

1D.If the satellites are locked no motion at all is possible.

As you can see the results are pretty unpredictable so long you don't make the practical test, essentially because the mutual rotation of the elements modify the data observed on a static point of view.

[jim_mich]

the results are pretty unpredictable so long you don't make the practical test,

The results are completely predictable. Machinery's Handbook has tables that gives the formulas for any possible combination of stationary gears and rotatable gears for Simple Epicyclic Gearing and for Compound Epicyclic Gearing. There is no need for experimenting when the answer can be known simply by reading the book and using the right formula.

Of course, according to ovyyus, in order to get "legitimate" answers you still need to physically build things. My point being that using known proven formulas will give the same results as physical building.

[ovyyus]

My point being that using known proven formulas will give the same results as physical building.

Big call there Jim.