The summary of my latest studies

[path_finder]

Here are the principles of my latest design, based on the path of the astroid curve (for the 'order four' devices).
Few weeks earlier I made visible an animation of this concept (here: http://www.besslerwheel.com/forum/files ... cator1.gif), now the first animation below, where the motion of the four sliding weights have been obtained by the rotation of four gears (radius R) rolling on the inner rim of the main wheel (radius 2R). The envelop of the four sliding weights is an astroid.
Even if such as building is still possible, I don't like this kind of mechanism, the creation of the teeth being a great job because the accuracy needed for a reliable intensive use.

Then I remembered the famous 'double generation' theorem giving an alternative creation of the cycloids. See here:http://xoday.posterous.com/trochoid-epi ... he-ellipse section 'history'.
So far it seemed to me the alternative building could be much more simpler.
According with the theorem I'm using now a central cylinder (radius R) where four rollers (radius R/2) rotates around the outer rim.
IMHO in that case we don't need the teeth anymore if the pressure of the rollers is enough strong: in that case my previous experiments gave to me a high level of efficiency, see here (again): http://www.besslerwheel.com/forum/files/flowerbowl6.jpg.
This new arrangement is shown in the second animation below.

In view to show the final motion of the weights I made the third animation below, where only the weights are represented.
The motion is exactly this one made by the light blue weights in the two first animations (more complex and where the exact path is difficult to observe).
The summary of the potential energy is obviously null, but the most important point is the position of the COG, always excentered.

Note there are several ways to implement this concept, the most efficient consisting in four rear wheel clutches linked to a pedalier thanks a classic bike's chain, like here above in the previous post.
As explained many times before I'm interested more specially with the 'order three' design, used in the flowerbowl. In that particular case the astroid shall be replaced by a deltoid. If the principle is the same, the friction is less important and the mechanism more simpler.

[path_finder]

The building still continues during the brainstorming. Some news from my experiments:
Hereafter a shot of the first step of the building.
The parts are coming from a game for the kids intitled 'Motorised Marble Race' from 'Universe Imagination', on special SALE in 'Toys'rUs': 19,90 euros (about 27 USD).
The four cogs have ten teeth, and I manufactured myself the inner transparent cog (20 teeth) in two parallel planes with some spacers.
The chain is in plastic but rigid enough, and has a major property: it is breakable and adjustable just by the finger pressure.
Nevertheless I cannot get a full satisfaction: the low number of teeth don't allow an accurate dephasing of exactly 90 grades between two consecutive cogs.
This requires a step of about an half tooth.
But there is another way to correct the failure: extend a little bit the distances between the four bearings and the central axis.
In addition a tenser roller can be added.

As explained many times earlier, the building is a mandatory. You cannot discover this kind of inconvenience with a virtual software chain.
Anyway I had to make some other important modifications, so far I will include this above correction in the new assembly.

[path_finder]

The below discussed design is based on the cardiod curve, obtained by rolling a gear around a central gear of the same size.
This motion is well known, in relation with the tricky question: if you let rotate a quarter around another quarter, how many turns will rotate the coin.
Like for the Ferguson paradox, 95% of people will answer: ONE, for sure, they are equal.
In fact the answer is TWO (one effective replication of the circumference, added to the turn of the coin itself around the other one).
But it was not the purpose of this topic.

The animation hereafter shows the idea in few steps:
- step 1: we have FIVE cogs of the save size. The four rollers are linked to the orange ring, every 90 grades. Each one has a pin fixed near the rim, the position being indicated by the blue radius. These four pins will be used later for the mechanism linkage.
-step 2: the cardioid is added (in red): this is the path of all four pins when the rollers move around the central cog (supposed fixed). The orange ring (supporting the four rollers) rotates clockwise at the OMEGA speed. By the way the rollers rotate clockwise at a rotational speed of: 2xOMEGA
- step 3: So far the distance between each pin and the center of the central cog, varies from R to 4xR. This is represented by the green area.
- step 4: The linkage mechanism for the 9:00 pin is now installed. We are using the famous 'A shaped' pantograph where the two weights are at the end of the longest legs.
The attachment pin (moving along the cardioid) is for the moment at the 9:00 position (violet cross). At this place the distance is the shortest one, and the angle of the pantograph is opened at the maximum. So far the COG is more closer from the main axis.
- step 5: the pantograph is now at another intermediate position, with the main angle more closed.
- step 6: The pin of the pantograph is now at 3:00 on the cardioid, and the angle is at its minimum value, the COG being almost remote from the main axis.

Note the A point (the central point of the pantograph) has been eccentered from the main axis, because there are some good reasons to believe this assembly of pantographs will NOT work if they are connected to the center of the central cog.

[Unbalanced]

Amazing build P_F, starting to look like clockwork. You bring a whole new level of quality and expertise in your design, builds and thinking.

Good luck with this one and good luck with your kids when they find out you cannibalized their toy.

The concept looks sound. Friction will be an issue perhaps.

I have never had success in any of my designs that fit the critique of Bessler's:

"Many would-be Mobile-makers think that if they can arrange for some of the weights to be a little more distant from the center than the others, then the thing will surely revolve. A few years ago, I learned all about this the hard way. And then the truth of the old proverb came home to be that one has to learn through bitter experience." - pg 295-296

though perhaps I haven't had enough "bitter experience(s)" as I keep coming back to designs that reflect this "more distant from the center" concept.

[rlortie]

"Bitter Experience"!

Bitter experience through wheel building is a wonderful thing.
It allows you to recognize a mistake when you make it again and again.

Just ask anyone who is chronological gifted.

Ralph

[jim_mich]

... chronological gifted.

I like that.

[murilo]

Path,
as ever, you are a kind of master in sharing, mind vision and building!

Much than me, you deal to what in other thread I called as 'karma'... due to the 'pressure' and 'malabarism' with stuffs that still don't exist and MAY never come to existence.

Should we call 'karmastorm' instead brainstorm?

Many will not support the prices for this game.

The problems I see with some CAME mechanisms is that centrifugal forces will play against.

Best!
Murilo

[Bill_Mothershead]

chronological gifted

I like it too.

Jim, go to: http://goldenyearshumor.blogspot.com/

Half way down the page is the "Boomer Zoomer Memory Test".

Fun stuff. I only had to guess on one, (got them all right!)

[jim_mich]

I only missed one. I knew peter pan was played by a girl, but I did not know her name. (I think I only saw the movie one time.)

There were only three that I made an educated guess and I got two of those guesses right.

All the rest I knew before even looking at the choices. I didn't even need to think, I just instantly knew.

[AB Hammer]

I got them all correct, no guess needed. Does this mean I'm Old?? Yet not feeble. LOL

[Unbalanced]

Missed two, never read Pogo and hadn't heard of Mary Martin.

For those interested, here's another good memory test of a different kind:

http://www.bbc.co.uk/science/humanbody/ ... ns_1.shtml

got 100% and 66% respectively.

Sorry for the temporary thread hijack path_finder. Please let us know how that wheel works out. It is one and the same as your avatar correct? I have long admired that one. Your red dot animation was particularly enlightening in visualizing the paths.

[path_finder]

Many thanks for all posters interested for my experiments.

Two shots from an intermediate step in the building.
The above mentioned modifications have been made, in particular the frame of the four sliders, the four cogs position, and the rubber shock absorber.
The purpose of this step was to fix the distances and the final size of the assembly.
This is the reason why the bearings have not been repositioned yet.
Some adjustment are still needed for a perfect 90 grades dephasing: always this question of teeth.
It seems to me the number of the rings in the chain must be dividable by the number of the teeth on the cogs.
This is perhaps Bessler shown ten rings in the chain of the MT137. Who knows?

[to.late]

I like your wheel very much :-)

[path_finder]

I can now confirm what I suspected before: the number of the rings in the chain is relevant.
In the previous shots this chain had 86 rings: although many attempts in the relocation of the sliders axle position, I cannot obtain the good positioning (in quadrature) for the four sliders.
This number must be a multiple of the teeth per cog, and a multiple of four (number of sliders), therefore the chain now consists into 80 rings
And for the mechanical perfect motion a tenser is a good improvement.

[path_finder]

A new step in the building.
This time the central cog is not centered on the main axis like before (it was just for tests) in the first shot below.
As you can see on the second shot this 20 teeth cog is now fixed and centered on the cross, allowing a double circular motion around the main axis.
There are a lot of expert in mechanics in this forum, and I hear the first comment: it will never work because the fixed length of the chain
Precisely!...The purpose of this geometry is to oblige the wheel to find a solution: the only one is to move the cross. Think about why.


edited:
for those members not familiar with the 'fixed point'/'crossbar' concept, see here again:
http://www.besslerwheel.com/forum/viewt ... 6502#56502