The summary of my latest studies

[path_finder]

Dear Ralph,
Many thanks for your comments.

There are a plenty of variations in relation with the 'Raj Balkee's design.
Without to minimize the merits of Raj, some have been published on my own side much more earlier (see here: http://www.besslerwheel.com/forum/files ... swing1.gif dated 28/05/2011 and http://www.besslerwheel.com/forum/files ... dalist.gif dated 13/07/2011). Nevertheless I will still continue to respect the intellectual property of Raj on his specific variation. Not interested in any patent, I have no intend to be involved in any controversial contest about this subject, it is a lack of time.

The most interesting variations of Raj's concept are these allowing the temporarily relocating of the weights at the center of the wheel.
This is only possible if a geometrical ratio of 2:1 is strictly respected.
If you modify the length of a single rod, it don't work anymore like required.
In addition whatever Raj's design variation you have selected, this one alone cannot work: you need a doubler, as simplest as possible, as slimmest as possible, what is not obvious when passing to the building phase.

Another interesting variation is shown in the animation below, where no doubler is needed. Its simplicity is obvious.
The first drawing shows the path of the weights, but unfortunately not the contribution of the red weights Dynamical unbalance.

[path_finder]

After some further examinations the Schmidt coupling (previous page slim2X_fork2 animation) is not required for the relocator. I found a much more simpler way: see the animation below.
The green tripod is supposed to be maintained centered within the main wheel (linkage not represented).
The blue tripod, the orange rods of the relocator, and the centered green tripod are acting in three parallel vertical separated planes.
Looking at the path of the blue tripod terminators, I though at the kids jumping from pilar to pilar, the orange rods being the crutches. A verified clue?

[ruggerodk]

Interesting application PF - I like the reference to the jumping kids ;-)

Apropos 'walking': I made something quite similar of several tripods back in 2010.
Erasing the paht and guidelines, the movement looks like a walking man.

You can see it here: http://www.besslerwheel.com/forum/viewt ... 3599#73599

Keep it coming, PF.

regards Ruggero ;-)

[path_finder]

Returned back home from Cameroon, I can restart my experiments.
My next building is the direct application of the animation above.
The shot below shows the main part of the speed doubler, where the tripods will be hung, one at each side (for a good mechanical balance).

[path_finder]

The next step of the building, with the tripod, the relocator's rods, and the centered doubler.
The centering is obtained here by a set of three rollers, but can be obtained also by a single bearing itself centered by three spokes.
Only one side of the main cam is supplied here, this mechanical sub-assembly must be duplicated on the other side.
I am a little amazed by the similarity with the door keystone in BadKarlshafen: http://www.besslerwheel.com/forum/files ... _teeth.jpg

[path_finder]

Hereafter a shot of the next step of my latest wheel, in accordance with the above described concept.
In this version the doubler is a transparent disk with three grooved rollers rotating on the inner rim of the main wheel.
Only one side is ready to accept the Raj Balkee's double elbow primemover, the next step will complete the other side.
The building sequence is slow, but the hunt for the friction losses has been successful.

[path_finder]

The next step. The slim doubler is complete and included in the main frame of the wheel.
Now we can install the two primemovers (Raj Balkee's double elbowed pendula).

[path_finder]

A version perhaps more close from the way selected by Bessler: the same concept, but with a doubler including a cross instead a tripod.
The first animation below shows the principle:
- a half sized cross rotating inside a eight grooved cam (the peacock's tail?) linked on the both sides to a centering relocator (light blue rods).
- two rods (in light blue) relocating the motion at the center (this assembly being replicated on the second side of the cam, dephased of 90 grades)
- the doubler (in green, is supposed to be centered by an extra linkage (not represented, see the previous shot showing the transparent disk with the three rollers) with its two pins where the primemover shall be attached.

The second animation shows the full design, with the two elbowed pendula linked directly on the doubler's pins.
Note the parallelogram like in the toy (the hammer of the toy is at the center of the wheel, where the collision of the weights occurs).
Comments are welcome. Don't hesitate.

[raj]

Dear Path_Finder,
Please allow me to point out that, if we are to follow Bessler's clues, the rigid elbowed arms holding the moving weights, in your animation should be replaced by flexible cords or chains, to allow the swinging motion of the weights.

The end result of the swinging weights (torque-wise) will be as effective as that of the weights moving on rigid elbowed arms.

Raj

[path_finder]

Dear raj,
I'm afraid your are wrong: there is no place for any cord, the links must be absolutely rigid. This is the only way to stabilize the weights at the center during half the time.
The test has been made here: http://www.besslerwheel.com/forum/viewt ... 828#119828

[raj]

Dear Path_Finder,

I agree with you that this design shows the best geometrical path the weights can take to give us a possible runner.

Your simulation/animation proves it without doubt.

As I do not understand what data are fed into your simulation/animation program, I am, as yet, to be convinced that the net unidirectional torque surplus requirements for continuous rotation of the wheels, have been met by the simulation/animation.

In other words, have you been able to calculate the torque provided by the weights through 45 degrees (cyclic) rotation before resetting positions?

If you have tested the torque requirement, then you have a RUNNER.
BRAVO, mon ami.

Raj

[path_finder]

Dear raj,

As I do not understand what data are fed into your simulation/animation program

I did not compute nor estimate any data for the animation: let's the nature make it's job.
step 1: draw the big wheel in rotation (in this example, at 30 grades)
step 2: draw the second half size wheel in rotation (with twice the speed) within 60 grades
step 3: for each image fix the four pinions on the small wheel for introduction inside the grooved cam (peacock's tail)
step 4: locate the second half sized wheel at the center of the main wheel (look at this magnificent 'vesica pisces')
step 5: fix the pinion on the centered doubler
step 6: using your compass draw a circle centered on the pinion with a radius of R/2
step 7: draw a second circle centered on the rim of the main wheel with a radius of R
step 8: locate the crossing point of the two circles: it is the elbow where the weight will be attached.
step 9: fix the two couples of elbowed rods
step 10: fix the two weights (one is located at the center of the main wheel)
step 11: calculate the torque (the centered weight has no action on the torque).

As you can see, everything is mathematical not a invention.
Hoping this animation will answer to your questions.

[raj]

Dear Path_Finder,

Can you kindly calculate (quantify) the clockwise and counter-clockwise torques by each weight in the four drawings, drawn as per your specifications?

Your presentation above is excellent, showing the torque being applied (as in my drawing no 2.)

Can your presentation be applied similarly to my other drawings nos 1, 3 and 4.

Raj

[raj]

Dear Path_Finder,

I just thought of a very important question in relation to our ongoing discussion.

In your simulations/animations, how have you made sure that the smaller inner wheel turn at twice the speed of the larger wheel?

Raj

[raj]

I have studied computer science as part of my Maths degree way back in 1970, and learnt computer programing in BASIC language, on mainframe computer then. Micro computers did not exist then.

In 1980 I worked as Data Manager/Programmer, using an APPLE II in the Industrial Sector for a few years, but moved away from computers, except for personal use since.

Computers have since evolved thousands time, and I have not kept tract. So now, I am just an ordinary computer user.

Why I am telling you all this is simply because I just remembered the first computer jargon I learnt so many years ago:

Garbage in >>>Garbage out!

Simply computer program does no more and no less than what you tell it to do. For example if you write a computer program in which 1+1=3, then each time you use this program to add 1 to 1, the computer will give the answer 1+1=3.

In our current discussion, if the computer program that Path_finder is using has been given the instruction to rotate the smaller inner wheel at twice the speed of the larger wheel, then each time the program is run, the smaller wheel will turn at twice the speed of the larger wheel and the weights will automatically follow their path inside the wheels, as per the design.

But if the computer program has been instructed to work out the positions of each weight at an instant in time, calculate the torque applied to the wheels by each weight CW or CCW, then turn the wheels net positive torque direction.

Because the design in discussion is quite complicated to built, I would very much like to know the net unidirectional torque appplied to the wheels by the weights, to ascertain any continuous rotation

Raj