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Force multiplier
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Nominal Animal:

--- Quote from: electrodacus on February 11, 2023, 04:11:33 pm ---I will not say that 2:1 is anywhere close to 1:1. I will understand if it was 1.1:1 but not 2:1
--- End quote ---
That is because you do not understand the kinematics here.  Review the math in my reply #92.  In your vehicle, the wheels are the same size, \$r = R\$.  Per your definition, gear ratio \$G = 1/\lambda\$.  Using \$x\$ for the vehicle speed right, and \$y\$ for the treadmill surface speed left, kinematics analysis shows that
$$x = y \frac{\lambda R}{r - \lambda R} = \frac{y}{G - 1} \quad \iff \quad \frac{x}{y} = \frac{1}{G - 1}$$

Let's look at what kind of velocity ratios \$x/y\$ different gear ratios \$G\$ yield:
$$\begin{array}{c|rcr}
G & \frac{x}{y} & ~ & ~ \\
\hline
1:8 & -\frac{8}{7} & \approx & -1.143 \\
1:4 & -\frac{4}{3} & \approx & -1.333 \\
1:2 & -\frac{2}{1} & = & -2.000 \\
1:1.1 & -\frac{11}{10} & = & -11.000 \\
1.1:1 & \frac{10}{11} & = & 10.000 \\
2:1 & \frac{1}{1} & = & 1.000 \\
4:1 & \frac{1}{3} & \approx & 0.333 \\
8:1 & \frac{1}{7} & \approx & 0.143 \\
\end{array}$$
A gear ratio of \$G = 2:1\$ requires the vehicle to move as fast as the treadmill surface.  This requires very good traction, because there is very little torque; only about half the linear force provided by the treadmill surface at the point where the driving wheel contacts the surface.
A gear ratio of \$G = 4:1\$ requires the vehicle to move only one third as fast as the threadmill surface, with so much torque that the linear force in the driving wheel at the point where it contacts surface is three times the force provided by the treadmill surface.

There is a HUGE difference between \$G = 2:1\$ and \$G = 4:1\$, and it is exactly because of the relationship \$x = \frac{y}{G - 1}\$.

That relationship also tells you that changing the gear ratio (from say \$G = 4:1\$ to \$G = 1:4\$) is sufficient to change the direction where the vehicle will move; but because for \$G \lt 1\$ we always have \$\lvert x \rvert \gt y\$, you do need good traction to show that.

That also tells you that with \$G = 1:1\$, this scenario is impossible (no smooth movement with the wheels turning in the same direction), since it is a singular point.  On the other hand, \$G = -1:1\$, i.e. wheels turn the same amount but in opposite directions, yields \$x = -2 y\$, i.e. the vehicle travels in the same direction as the surface of the treadmill, but at twice the speed.  This too requires good traction in the wheels.

You also keep claiming that kinematics is not a good way to analyse such mechanisms, but seeing as I've derived the continuous velocities for any given gearbox, it actually yields testable, verifiable mathematical model of the behaviour of the system.  This is experimentally verifiable stuff.  You just refuse to experiment with it, making all sorts of imaginative excuses as to why you do not need to.

Instead of testing these, you rely on your hand-eye coordination and a single video clip as "proof".  That is not science, it is religion.
electrodacus:

--- Quote from: IanB on February 11, 2023, 06:55:58 pm ---That question does not have any relevance.

However, we can easily arrange for this to happen:



--- End quote ---

So what are you saying exactly ? Will that gearbox be able to move towards the wall ?

Will the human move relative to the wall ?
Will you mind explaining what is inside the gearbox to allow it to move ?
You realize that F1 applied by human equal with F2 at the wall so there is no net force. Not only that but this time there is also no slip posible.
electrodacus:

--- Quote from: cbutlera on February 11, 2023, 07:47:20 pm ---
--- Quote ---In any case you isolate the subject and look forces acting on each of them.

--- End quote ---

No, no, no!  You are confusing it with Newton's first and second laws of motion.  Newton's third law of motion applies to "the mutual actions of two bodies upon each other". It has no relevance to the forces acting on any one body.  Do you understand the difference between one and two?

--- End quote ---

You misunderstood what I wanted to say (it is my fault as it was not clear).

When I say isolated I mean you look at groups for two objects (there are a total of 3)
So a pair is book and table and then the other pair is table and ground.



--- Quote from: cbutlera on February 11, 2023, 07:47:20 pm ---
--- Quote ---
A better example of Newton's 3'rd law will be the one in the below image.
I asked multiple times if you can think of a device that will replace the newton meter and will be able to use the input from human to pull the human towards the wall ?



--- End quote ---

How would the answers of either yes or no to this question have any relevance to Newton’s third law?  Either way, the force exerted by the right hand end of the rope on the hook/elephant, would be equal and opposite to the force exerted by the hook/elephant on the right hand end of the rope. And similarly for the pair of forces between the left hand end of the rope and the man’s hands, and the pair of forces between the man’s feet and the ground, etc.

--- End quote ---

Correct so that also means the that you have the same force on each side of the Newton meter and if you replace that with whatever else you want like a gearbox with input connected towards the human (left) and output towards the wall (right) the forces will remain equal on both sides of the gearbox as the gearbox with a floating body can not do any force multiplication.
But IanB apparently think that is possible based on his answer.
Looking forward to your answer.
SiliconWizard:

--- Quote from: Nominal Animal on February 11, 2023, 06:48:24 am ---"If there is no net force the vehicle will not move."

A net force will accelerate a vehicle, not "keep it moving".  Completely ignoring Newton's first law of motion, and accusing others of not understanding physics, is utterly, religiously, strange.

:horse:

--- End quote ---

How can anything accelerate if there is no time, though? :popcorn:
Nominal Animal:

--- Quote from: SiliconWizard on February 11, 2023, 10:07:48 pm ---
--- Quote from: Nominal Animal on February 11, 2023, 06:48:24 am ---"If there is no net force the vehicle will not move."

A net force will accelerate a vehicle, not "keep it moving".  Completely ignoring Newton's first law of motion, and accusing others of not understanding physics, is utterly, religiously, strange.

:horse:

--- End quote ---

How can anything accelerate if there is no time, though? :popcorn:

--- End quote ---

:-X

Here's the simplest experimental demonstration setup demolishing electrodacus' arguments, using Lego Technic:

Pull the chain left, and the gears rotate clockwise, moving right.  Any motion of the chain corresponds to exactly 0.4× (16:40) movement of the gears right.  With continuous motion of the chain, the motion of the gears right is smooth and continuous.  No slip-stick and no jerking, unless you jerk the chain yourself, jerk.
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