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Force multiplier
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Nominal Animal:
[Edited to add the illustration.]
Can I ask you a simple question, electrodacus?  I believe this would be illuminating for us both.

Let's assume we have a vehicle much like your front-wheel-on-treadmill, rear-wheel-on-ground, but with a busted gearbox so that all wheels just turn independently and freely, without slipping at all.  Say, it is being towed by something else.


The radius of both wheels is \$1/(2\pi)\ \approx 0.159\$ length units (diameter \$1/\pi \approx 0.318\$ length units), so that their circumference is exactly one length unit.

In one time unit, the vehicle travels one length unit with respect to ground, the rear (red, left) wheel making exactly one rotation. 
At the same time, the treadmill surface moves one length unit in the opposite direction with respect to ground.

(The yellow arrows indicate the directions of the movement; their lengths are not to scale.  The hatching indicates ground.  The treadmill is stationary with respect to ground; it does not move.)

The question is, how many rotations does the front (right, blue) wheel on the treadmill do, in the same time unit?

  A) It does not rotate/it slips
  B) One turn
  C) Two turns
  D) Three turns

(I would have made this a poll, but I don't have the rights to create one within an existing thread, only if I start a new thread.)
To repeat, this is not a trick question; it is a straightforward mechanical detail of the model being discussed.
pcprogrammer:
One more video to proof that slip is not an issue, and there is no energy storage involved. It is just my hand pushing and pulling the center track that provides the needed energy. It is semi constant. The idea originates from Nominal Animal and I just build it to see for myself how it behaves. Instead of a chain I'm using a rigid track to drive the input sprocket. This to eliminate as much of elasticity as possible.



It works as expected, just like the other vehicles with normal wheels.
PlainName:

--- Quote ---One more video to proof that slip is not an issue
--- End quote ---

Above and beyond!  :-+
PlainName:

--- Quote from: electrodacus on February 14, 2023, 01:47:14 am ---since this is not my area of expertise

--- End quote ---

You ain't kidding there. It's not your area of study either.


--- Quote --- and energy storage where I'm by definition an expert.
--- End quote ---

Nope, it's absolutely clear that you're not. You may know a bit but you don't know how to apply that presumed knowledge here.
electrodacus:

--- Quote from: pcprogrammer on February 14, 2023, 06:58:17 am ---I would say get yourself a mirror and take a good look. You will see a person that is afflicted with that condition, you know, unable to admit he/she is wrong.

--- End quote ---

I'm happy to do so but for that you need to provide a correct theory of how this machine works.

If you have a good understanding of how this works then it should be no problem answering this simple question
 "
Vehicle in case (a) has the output wheel (left wheel) on a slippery surface say ice while input wheel (right wheel) has excellent grip on the treadmill.
Vehicle start as stationary and the treadmill is turned ON

Question is what will happen with the vehicle ?

a) Will wheels just spin with vehicle not going anywhere.
b) Will wheels spin and vehicle will also be accelerated to the left.
c) Will wheels spin and vehicle will be accelerated to the right.
d) Will wheels not spin and vehicle be accelerated to the left.

Explain also why will wheel's spin or not speed depending on the prediction you made.
"


In regards to your last video (I truly appreciate that you want to understand the mechanism and put in all the effort). The slip stick hysteresis is not eliminated due to the shape of the tooth.
You have basically an upside down triangle climbing at an angle on another triangle. The only way to really see what happens is to watch the mechanism from the side seeing how that single input wheel rotates storing energy and when it slips the back two wheels/sprockets will push the input wheel/sprocket over the tooth.
If mechanism had no flexibility (very hard to do unless you reduce the gear ratio) then entire mechanism will lift up (again due to the triangular tooth shape) but if you had special shape tooths to prevent lifting the vehicle then the entire mechanism will be just locked unless you push hard enough to break the tooth.
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