Force multiplier

[electrodacus]

Have not seen this particular one before but is basically the same setup as mine even the hardware is the same.
What you see there is stick slip hysteresis and energy storage. The front wheel slips else it will not work and by not work I mean wheels will not rotate and vehicle will move in the direction of applied force. 

[electrodacus]

Kinematics is physics, even though some call it geometry of motion.  It is the appropriate level of complexity for analysing mechanisms like these.

You do not model forces until you need to consider things like friction and acceleration.  Using only a subset of forces to try and describe a mechanism is an error.  OP's evocation of Newton's laws of motion is a straw man, because A) they are not relevant for the analysis of the mechanism behaviour at this level of complexity (ignoring friction and losses, assuming perfect traction, steady state operation with no acceleration), and B) OP has picked an arbitrary subset of forces that do not describe the system at the level of complexity where those laws would apply, i.e. their "model" does not sufficiently describe the systems at hand.

For an example of an analysis where a complete set of forces would be used, would be to assume the entire system at rest at initial time \$t = 0\$, and then integrate the equations of motion to find out whether the vehicle would accelerate or slip, when some specific (usually constant) force is applied to the paper or blue surface.  Both static and dynamic forces would need to be modeled, both linear and angular, as well as linear and angular momentums.  Again, picking an incomplete subset that happens to support your pet theory isn't physics or science, it is just an error.

If you want the definition here it is:
"the branch of mechanics concerned with the motion of objects without reference to the forces which cause the motion."

How will you describe what happens in the first 15 seconds of this video? https://odysee.com/@dacustemp:8/stick-slip-removed-from-front-wheels:0

In order for an object to move at constant speed when there is friction (always present in real world) a net force is required pointing in the direction that the object moves.
If an object can not move in the exact opposite direction of the applied force unless as it is the case here energy storage is used.

Not only what I say is true but I have demonstrated every single detail with real world tests.

[IanB]

Have not seen this particular one before but is basically the same setup as mine even the hardware is the same.
What you see there is stick slip hysteresis and energy storage. The front wheel slips else it will not work and by not work I mean wheels will not rotate and vehicle will move in the direction of applied force.

But it is working exactly the same as the geometrical model below.  Where is the stick slip hysteresis and energy storage here, since the geometrical model has neither of those, yet it still moves as shown?

[electrodacus]

But it is working exactly the same as the geometrical model below.  Where is the stick slip hysteresis and energy storage here, since the geometrical model has neither of those, yet it still moves as shown?

There are no forces involved in your model. Just take a slow motion video of the real thing and you will see the exactly same thing as in my slow motion video and that is generator wheel will rotate while the vehicle and output wheel do not move.
Then only when that input wheel slips so the friction loss instantly drops the vehicle starts to move accelerated by the stored energy.
The stored potential elastic energy gets converted in to vehicle kinetic energy. Since in real world there still is friction vehicle will slow down so charge and discharge cycles need to repeat many times each second to maintain the vehicle at some average speed.
Vehicle speed is not constant due to charged discharge cycles but you will not be able to see unless you take a high speed video of the device and slow it down.

[jonovid]

perpetual motion machine

[electrodacus]

This post is a great example of why physics questions that are poorly posed are almost unanswerable 

Torque isn't like any other force; it's an emergent property of flexible materials. You can't apply torque to objects with zero stiffness, and no solid objects exist with infinite stiffness that you can physically apply a torque to: https://scholarship.haverford.edu/cgi/viewcontent.cgi?article=1494&context=physics_facpubs

Towards the end of the video you posted, it's pretty clear that you've forced the smaller wheels of your roadster to spin (by very quickly applying force on the paper) before the rest of the system can react and stabilize -- before the front wheels can feel enough force from the rubber band to overcome their stiction and enough force to noticeably modify their rotational inertia.

The rubber band has elasticity; you can stretch it before it can react the same way that the surface of a musical drum has elasticity. If the drum wasn't elastic, your drumstick would shatter the second it touched it. In other words, there's a phase difference between forces applied at one part of an elastic object and forces/movement resultant on the other parts. All movement is a wave of some kind, after all.

Try repeating your experiment with a steel or chain belt and try to show us the same response. The front wheel will slip almost immediately because the steel is much less elastic than the rubber band.

This sort of vehicle can only move in the opposite direction of the forced applied due to a combination of energy storage and stick slip hysteresis as the trigger for the charge/discharge cycles.
What happens exactly can be seen fairly clearly in this slow motion video  https://odysee.com/@dacustemp:8/wheel-cart-energy-storage-slow:8

You can see it starts with an increasing F2 = F1 as the belt is stretched (elastic energy storage).
When F2 = F1 is large enough that the input wheel can slip (it is easier to slip than output wheel as it is already in motion). And the moment wheel starts to slip the force needed to slip is much lower that the force needed to unstick the wheel in the first place so this allows the potential elastic energy to be converted in to vehicle kinetic energy.
Since there is friction the vehicle will slow down so to maintain an average speed this cycle of charge discharge needs to happen multiple times per second and much faster than our slow brain can see.

What I did in this other video you likely seen (first 15 seconds) https://odysee.com/@dacustemp:8/stick-slip-removed-from-front-wheels:0  is reduce grip at output wheels suficient so that they will be the first to slip instead of the input wheels and in this case at initial acceleration the belt is still streched as F2=F1 increase but they will not be able to increase that much before the output wheels slip and the stored enenrgy is not discharged the belt remains at that constant streached level while speed remains constnat with the vehicle being draged as the mechanism as it is is just a locked gearbox.

So eliminating the stick slip hysteresis from the input wheel removes the ability of the vehicle to take advantage of the stored energy thus it can no longer charge and discharge that to move in the opposite direction of the applied force.


If I were to replace the soft belt with a stiffer belt then displacement for same force will be lower meaning less energy will be stored before input wheel slips and that means the cycles of charge discharge will need to be faster (more cycles per second for same constant speed).
If the belt is to stiff then amount of energy may be to low and not be able to cover the frictional loss and to have extra to convert to kinetic energy so vehicle will no longer be able to move in the opposite direction so it will be dragged or maybe stay in place while the paper is dragged under the input wheels.

[jonovid]

This post is a great example of why physics questions that are poorly posed are almost unanswerable 

Torque isn't like any other force; it's an emergent property of flexible materials. You can't apply torque to objects with zero stiffness, and no solid objects exist with infinite stiffness that you can physically apply a torque to: https://scholarship.haverford.edu/cgi/viewcontent.cgi?article=1494&context=physics_facpubs

Towards the end of the video you posted, it's pretty clear that you've forced the smaller wheels of your roadster to spin (by very quickly applying force on the paper) before the rest of the system can react and stabilize -- before the front wheels can feel enough force from the rubber band to overcome their stiction and enough force to noticeably modify their rotational inertia.

The rubber band has elasticity; you can stretch it before it can react the same way that the surface of a musical drum has elasticity. If the drum wasn't elastic, your drumstick would shatter the second it touched it. In other words, there's a phase difference between forces applied at one part of an elastic object and forces/movement resultant on the other parts. All movement is a wave of some kind, after all.

Try repeating your experiment with a steel or chain belt and try to show us the same response. The front wheel will slip almost immediately because the steel is much less elastic than the rubber band.

This sort of vehicle can only move in the opposite direction of the forced applied due to a combination of energy storage and stick slip hysteresis as the trigger for the charge/discharge cycles.
What happens exactly can be seen fairly clearly in this slow motion video  https://odysee.com/@dacustemp:8/wheel-cart-energy-storage-slow:8

You can see it starts with an increasing F2 = F1 as the belt is stretched (elastic energy storage).
When F2 = F1 is large enough that the input wheel can slip (it is easier to slip than output wheel as it is already in motion). And the moment wheel starts to slip the force needed to slip is much lower that the force needed to unstick the wheel in the first place so this allows the potential elastic energy to be converted in to vehicle kinetic energy.
Since there is friction the vehicle will slow down so to maintain an average speed this cycle of charge discharge needs to happen multiple times per second and much faster than our slow brain can see.

What I did in this other video you likely seen (first 15 seconds) https://odysee.com/@dacustemp:8/stick-slip-removed-from-front-wheels:0  is reduce grip at output wheels suficient so that they will be the first to slip instead of the input wheels and in this case at initial acceleration the belt is still streched as F2=F1 increase but they will not be able to increase that much before the output wheels slip and the stored enenrgy is not discharged the belt remains at that constant streached level while speed remains constnat with the vehicle being draged as the mechanism as it is is just a locked gearbox.

So eliminating the stick slip hysteresis from the input wheel removes the ability of the vehicle to take advantage of the stored energy thus it can no longer charge and discharge that to move in the opposite direction of the applied force.


If I were to replace the soft belt with a stiffer belt then displacement for same force will be lower meaning less energy will be stored before input wheel slips and that means the cycles of charge discharge will need to be faster (more cycles per second for same constant speed).
If the belt is to stiff then amount of energy may be to low and not be able to cover the frictional loss and to have extra to convert to kinetic energy so vehicle will no longer be able to move in the opposite direction so it will be dragged or maybe stay in place while the paper is dragged under the input wheels.

to impart oscillation in to the loop, a mechanical tank circuit oscillator. but still in need of continuous input

[PlainName]

So now the treadmill is unpowered free to move and you push the vehicle body to the right. Of course since you apply a force to the right to the vehicle body the vehicle body will move in that direction.

OK, well that's a start!

But it has basically nothing to do with the original problem where the only applied force is to the left (not to the right) and it is applied at the input wheel.

Do you want to learn that it does indeed have something to do with the original problem, or must you hide under your safety blanket?

Now, imagine the right wheel is not connected with a belt (and, sorry, I used 'horizontal belt' previously when I should has used 'treadmill' to save confusion). The wheel is locked rigid. You, the HoG or whatever push the vehicle to the right and that causes the treadmill to move to the right. I presume you are perfectly OK with that since it's pretty basic. So..

Let's say the vehicle moves to the right (via whatever strange force) at 2m/s. With a locked right wheel the treadmill will move to the right at 2m/s. Yes? Good. Clearly, any clockwise rotation of the right wheel will reduce the speed of the treadmill. We can thus have three distinct situations:

1. The connection between the wheels is 1:1 (that is, the left wheel drives the right wheel at the same speed). In this case, the vehicle moves right at 2m/s, the right wheel rotates at the same speed the vehicle is travelling  and the treadmill is stationary.

2. The connection is 2:1 (that is, the left wheel drives the right wheel at half the speed). In this case the vehicle moves right at 2m/s and the treadmill moves right at 1m/s (since the right wheel is rotating slower than is necessary to keep up with the vehicle speed).

3. The connection is 1:2 (that is, the left wheel drives the right wheel at twice the speed). In this case the vehicle moves right at 2m/s and the treadmill moves left a 1m/s (since the right wheel is rotating faster than is necessary to keep pace with the vehicle speed).

Do you agree with those? If not, which of 1..3 do you think is wrong? I can assure you that this will resolve your original problem if you stick with it.

[cbutlera]

...
Did you miss the Newton's 3'rd law ? It is present in all non accelerating frames and of course when whe are in an accelerating frame the 2'nd law also applies.
...

From your responses to my own postings and those of a number of others, it seems that you do understand the arguments that we are making.  However, in every case you throw a spanner in the works by bringing up your version of Newton’s third law.

Try a very simple experiment.  Extend the forefingers of you left and right hands, then press the tips of those two fingers together.  You will notice that the forces you can feel at your two fingertips are equal and opposite and there is no way of performing this experiment where that would not be the case.

You may regard this experiment as pointless, and that it just demonstrates a law of physics which is intuitive and completely obvious.  So obvious in fact that there would be no point in giving it a name.  But it does have a name, it is Newton’s third law of motion.  A key characteristic of this law is that the two forces involved always act on different objects, in this case the tips of your left and right forefingers.

The thing that you have been calling “Newton’s third law” is in fact the ”Newton’s Second Law – Net Force” (N2-NF) misconception that I have mentioned before, and is discussed in detail in the Teaching Science paper.  I have quoted the key paragraphs from page 5 below, because I think that it is so relevant to this discussion.  A key characteristic of the N2-NF misconception is that the two forces involved act on the same object.  In your example a), that object is the wheeled trolley. You always insist that it has a "locked gearbox" so that you can justify treating the trolley chassis along with its transmission and wheels as a single object, and thereby apply N2-NF.  Hence your need to introduce this "stick slip" behaviour, because clearly (to you) the transmission and wheels need to move at some point if the trolley is to move at all.

Quote from page 5 of the Teaching Science paper:

“In fact, there is evidence that many students construct a flawed mental model of the Third Law by conflating it with the Second Law (Dedic, Rosenfield & Lasry, 2010; Wilson & Low, 2015). Unlike some misconceptions in physics, such as the Aristotelian idea that objects move until they run out of impetus, this is not a common sense alternative conception based on every day experience. Rather, it is something that is learned during the study of Newton’s laws. We call this the "Newton’s Second Law – Net Force” (N2-NF) misconception.

Consider an object in static equilibrium, under the influence of just two forces. In the N2-NF misconception, students note that the two forces must sum to zero (a correct application of the Second Law) and hence the two forces must be equal in magnitude and opposite in direction (also correct, as a direct mathematical result of the first statement), and thus are a Third Law force-pair (incorrect). This reasoning is similar to the (il)logical sequence, “All cats have four legs; my dog has four legs; therefore, my dog is a cat”. While a Third Law force-pair are equal in magnitude and opposite in direction, not all forces which are equal in magnitude and opposite in direction are a Third Law pair. This subtlety is often lost on novice students; but the mental model which arises from the flawed sequence of reasoning is strong and resistant to instruction (Wilson & Low, 2015)."

[jonovid]

I remember this is somewhat similar to the infinity drive or torque amplifier conundrum.  a quest for a better continuously variable transmission.
a mechanical system of interconnected differentials in a mechanical circuit were torque and velocity are controlled by a third input
an order of magnitude less then the power throughput.

[electrodacus]

Do you want to learn that it does indeed have something to do with the original problem, or must you hide under your safety blanket?

Now, imagine the right wheel is not connected with a belt (and, sorry, I used 'horizontal belt' previously when I should has used 'treadmill' to save confusion). The wheel is locked rigid. You, the HoG or whatever push the vehicle to the right and that causes the treadmill to move to the right. I presume you are perfectly OK with that since it's pretty basic. So..

Let's say the vehicle moves to the right (via whatever strange force) at 2m/s. With a locked right wheel the treadmill will move to the right at 2m/s. Yes? Good. Clearly, any clockwise rotation of the right wheel will reduce the speed of the treadmill. We can thus have three distinct situations:

1. The connection between the wheels is 1:1 (that is, the left wheel drives the right wheel at the same speed). In this case, the vehicle moves right at 2m/s, the right wheel rotates at the same speed the vehicle is travelling  and the treadmill is stationary.

2. The connection is 2:1 (that is, the left wheel drives the right wheel at half the speed). In this case the vehicle moves right at 2m/s and the treadmill moves right at 1m/s (since the right wheel is rotating slower than is necessary to keep up with the vehicle speed).

3. The connection is 1:2 (that is, the left wheel drives the right wheel at twice the speed). In this case the vehicle moves right at 2m/s and the treadmill moves left a 1m/s (since the right wheel is rotating faster than is necessary to keep pace with the vehicle speed).

Do you agree with those? If not, which of 1..3 do you think is wrong? I can assure you that this will resolve your original problem if you stick with it.

As I mentioned in your imaginary setup the vehicle has 3 points of contact and that god will need to be real as a force will need to act against the vehicle body and not an imaginary one as you think.

If a real force acts against the vehicle body then due to 3 separate forces acting on the different vehicle parts the vehicle will work as you mentioned.

I already provided an example but in my example the vehicle body was rigidly connected to ground and in that case the mechanism acts as a functional gearbox and the red box can be moved by the treadmill and force acting on the box provided by left wheel can be 2x larger than the input force at the right wheel provided by the treadmill.

In case you do not understand what our disagreement is I will try to make it clear.

The setup in diagram (a) as well as the real setup in my video has only two points of contact (no HoG involved or anything else touching the vehicle body) and in this conditions you can not have a functional gearbox as that will require 3 points of contact.
With only two points of contact F2 can only be equal and opposite to F1 in non accelerating reference frames so when vehicle is not moving or when it is moving at constant speed. In accelerating reference frames to this newton's 3'rd law F2 = F1 you add the Newton's 2'nd law m*a.   

[electrodacus]

From your responses to my own postings and those of a number of others, it seems that you do understand the arguments that we are making.  However, in every case you throw a spanner in the works by bringing up your version of Newton’s third law.

Try a very simple experiment.  Extend the forefingers of you left and right hands, then press the tips of those two fingers together.  You will notice that the forces you can feel at your two fingertips are equal and opposite and there is no way of performing this experiment where that would not be the case.

You may regard this experiment as pointless, and that it just demonstrates a law of physics which is intuitive and completely obvious.  So obvious in fact that there would be no point in giving it a name.  But it does have a name, it is Newton’s third law of motion.  A key characteristic of this law is that the two forces involved always act on different objects, in this case the tips of your left and right forefingers.

Now you imagine the same experiment but the finger from right hand is under the right wheel and the finger from your left hand is under the left wheel.
Try to bring the hands together and you will understand why it is a locked gearbox and can be treated as a single object.

Your right hand will try to move to the left and you left had to the right and so the right wheel will try to move clockwise and the left wheel counter clockwise.
Due to the way the belt connects the two wheels it will be impossible for the wheels to spin in different directions thus what I call a "locked gearbox"

So unless you allow for one of the wheels to spin on your finger you can not move the hands closer and all you can do is apply a force that will be as you mentioned Newton's 3'rd law of motion.

[IanB]

The setup in diagram (a) as well as the real setup in my video has only two points of contact (no HoG involved or anything else touching the vehicle body) and in this conditions you can not have a functional gearbox as that will require 3 points of contact.

The requirement for 3 points of contact is not correct, so this argument can be rejected.

With only two points of contact F2 can only be equal and opposite to F1 in non accelerating reference frames so when vehicle is not moving or when it is moving at constant speed. In accelerating reference frames to this newton's 3'rd law F2 = F1 you add the Newton's 2'nd law m*a.   

With a kinematic structure neither forces nor Newton's laws are relevant to the analysis. Do you need forces or acceleration to analyze the movement of the gears in a clock? So this argument can also be rejected.

In summary, you have no arguments, therefore there is nothing to debate.

The best thing is for us to leave you to your own thoughts and let the thread rest. We do not need to care what you believe, it is not our problem, and it ceases to be entertaining after a while.

Why do you keep creating these threads anyway? This is what, the third thread now?

[electrodacus]

The requirement for 3 points of contact is not correct, so this argument can be rejected.

It is on you to prove that as there is no functional gearbox that can do force multiplication with just two points of contact.
Make a google search for "torque multiplier wrench" and if you can find one that only requires 2 points of contact (like a normal socket wrench one point hand and the other the bolt) then I will admit that I'm wrong.

With a kinematic structure neither forces nor Newton's laws are relevant to the analysis. Do you need forces or acceleration to analyze the movement of the gears in a clock? So this argument can also be rejected.

In summary, you have no arguments, therefore there is nothing to debate.

The best thing is for us to leave you to your own thoughts and let the thread rest. We do not need to care what you believe, it is not our problem, and it ceases to be entertaining after a while.

Why do you keep creating these threads anyway? This is what, the third thread now?

I offered video evidence that things work the way I say they work and you want to contradict a real experiment with kinematics only "the study of motion of a system of bodies without directly considering the forces or potential fields affecting the motion"

[IanB]

It is on you to prove that as there is no functional gearbox that can do force multiplication with just two points of contact.

It's not on me at all. You started the thread and are asking the questions. Neither I nor anyone else has any obligation to help you.

I offered video evidence that things work the way I say they work and you want to contradict a real experiment with kinematics only "the study of motion of a system of bodies without directly considering the forces or potential fields affecting the motion"

You can believe whatever you wish. Since everyone else in this thread can make an apparatus that does what the diagrams show it will do, and you alone cannot do so, that is your problem and not our problem.

[pcprogrammer]

The best thing is for us to leave you to your own thoughts and let the thread rest. We do not need to care what you believe, it is not our problem, and it ceases to be entertaining after a while.

 

And yet, you keep coming back 

Oooh damn now I did too 

[electrodacus]

It's not on me at all. You started the thread and are asking the questions. Neither I nor anyone else has any obligation to help you.

You seems to be the one making the claim that force multiplication is possible with just two contact points. So it will be on you to demonstrate that.

You can believe whatever you wish. Since everyone else in this thread can make an apparatus that does what the diagrams show it will do, and you alone cannot do so, that is your problem and not our problem.

The real device is not doing what the diagram shows. In the diagram there is no slip at any of the wheels while in real world there is slip at one of the wheels  else without slip vehicle can not move.
I showed how vehicle can move in the direction of the applied force when output wheel slips and I also showed vehicle moving in the exact opposite direction of the applied force which will normally not be possible but it is due to both energy storage and stick slip hysteresis and witch means none of the two sown cases match your kinematic only prediction.
You can not predict the way a real object moves using only kinematics and ignoring the net force amplitude and direction.

[cbutlera]

...
Try a very simple experiment.  Extend the forefingers of you left and right hands, then press the tips of those two fingers together.  You will notice that the forces you can feel at your two fingertips are equal and opposite and there is no way of performing this experiment where that would not be the case.

You may regard this experiment as pointless, and that it just demonstrates a law of physics which is intuitive and completely obvious.  So obvious in fact that there would be no point in giving it a name.  But it does have a name, it is Newton’s third law of motion.  A key characteristic of this law is that the two forces involved always act on different objects, in this case the tips of your left and right forefingers.

Now you imagine the same experiment but the finger from right hand is under the right wheel and the finger from your left hand is under the left wheel.
Try to bring the hands together and you will understand why it is a locked gearbox and can be treated as a single object.

Your right hand will try to move to the left and you left had to the right and so the right wheel will try to move clockwise and the left wheel counter clockwise.
Due to the way the belt connects the two wheels it will be impossible for the wheels to spin in different directions thus what I call a "locked gearbox"

So unless you allow for one of the wheels to spin on your finger you can not move the hands closer and all you can do is apply a force that will be as you mentioned Newton's 3'rd law of motion.

I can think of little further to add to what I wrote in my previous message.  You didn't disagree with anything, you just threw in a distraction.

You yourself have claimed to identify the understanding of Newton's third law as the fundamental difference between us.  A belt driven trolley is hardly the clearest and simplest example with which to examine that difference.

Here is a definition of Newton's third law that I regard as correct.

"To every action, there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts."

The left wheel of your trolley is a different object to the right wheel, the stationary block and the treadmill belt are also different objects.  So your F1 and F2 cannot be viewed as the mutual actions of two bodies upon each other, and are therefore not the subject of Newton's third law as defined above.

If you have a definition of Newton's third law that makes your F1 and F2 a Newton's third law force pair, then please write it down.

[electrodacus]

I can think of little further to add to what I wrote in my previous message.  You didn't disagree with anything, you just threw in a distraction.

You yourself have claimed to identify the understanding of Newton's third law as the fundamental difference between us.  A belt driven trolley is hardly the clearest and simplest example with which to examine that difference.

Here is a definition of Newton's third law that I regard as correct.

"To every action, there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts."

The left wheel of your trolley is a different object to the right wheel, the stationary block and the treadmill belt are also different objects.  So your F1 and F2 cannot be viewed as the mutual actions of two bodies upon each other, and are therefore not the subject of Newton's third law as defined above.

If you have a definition of Newton's third law that makes your F1 and F2 a Newton's third law force pair, then please write it down.

While you may consider the left wheel a different object from the right wheel in this particular example they are not.
The way let and right wheel are connected to each other makes them act as a single object.
This equivalent diagram to (a) may make it more visible to you

You can als imagine having this in your hands right hand applies F1 and the left hand will apply the equal and opposite force F2 else there will be no F1 so Newton's 3'rd law pair.

All this pairs in the above diagram are newton's 3'rd law pairs so F1 = F2, F3 = F4 and F5 = F6

[IanB]

You can als imagine having this in your hands right hand applies F1 and the left hand will apply the equal and opposite force F2 else there will be no F1 so Newton's 3'rd law pair.

Once again you are assuming something that isn't true. If you hold that object in your hands and try to apply opposing forces F1 and F2 then the object will simply move and rearrange itself to cancel out the forces, so that no force remains. It will be like trying to apply a force to an object that moves out of the way when you touch it. In reality there are no forces on that system, all forces are zero.

[electrodacus]

You can als imagine having this in your hands right hand applies F1 and the left hand will apply the equal and opposite force F2 else there will be no F1 so Newton's 3'rd law pair.

Once again you are assuming something that isn't true. If you hold that object in your hands and try to apply opposing forces F1 and F2 then the object will simply move and rearrange itself to cancel out the forces, so that no force remains. It will be like trying to apply a force to an object that moves out of the way when you touch it. In reality there are no forces on that system, all forces are zero.

Please explain what part moves when you apply F1 = F2 ?  There is no net force and F2 can not be anything other than equal and opposite to F1
The body when F5 = F6 acts is solid so there is nothing to rearrange and the  F3 = F4 act on a material that can not deform.
So there is no movement.

[IanB]

Please explain what part moves when you apply F1 = F2 ?  There is no net force and F2 can not be anything other than equal and opposite to F1
The body when F5 = F6 acts is solid so there is nothing to rearrange and the  F3 = F4 act on a material that can not deform.
So there is no movement.

How can the assembly be rigid when it has hinges and moving parts? You don't need to imagine this when you can easily make it with cardboard, paper fasteners and string. If you push on the two legs they will get closer together.

[electrodacus]

How can the assembly be rigid when it has hinges and moving parts? You don't need to imagine this when you can easily make it with cardboard, paper fasteners and string. If you push on the two legs they will get closer together.

It will act as a rigid object even if it has hinges.
I feel that you need to build this to test since you think there will be some movement when that is not the case.

[IanB]

It will act as a rigid object even if it has hinges.
I feel that you need to build this to test since you think there will be some movement when that is not the case.

I really have no need to do anything. It's not my problem.

[PlainName]

Do you want to learn that it does indeed have something to do with the original problem, or must you hide under your safety blanket?

Now, imagine the right wheel is not connected with a belt (and, sorry, I used 'horizontal belt' previously when I should has used 'treadmill' to save confusion). The wheel is locked rigid. You, the HoG or whatever push the vehicle to the right and that causes the treadmill to move to the right. I presume you are perfectly OK with that since it's pretty basic. So..

Let's say the vehicle moves to the right (via whatever strange force) at 2m/s. With a locked right wheel the treadmill will move to the right at 2m/s. Yes? Good. Clearly, any clockwise rotation of the right wheel will reduce the speed of the treadmill. We can thus have three distinct situations:

1. The connection between the wheels is 1:1 (that is, the left wheel drives the right wheel at the same speed). In this case, the vehicle moves right at 2m/s, the right wheel rotates at the same speed the vehicle is travelling  and the treadmill is stationary.

2. The connection is 2:1 (that is, the left wheel drives the right wheel at half the speed). In this case the vehicle moves right at 2m/s and the treadmill moves right at 1m/s (since the right wheel is rotating slower than is necessary to keep up with the vehicle speed).

3. The connection is 1:2 (that is, the left wheel drives the right wheel at twice the speed). In this case the vehicle moves right at 2m/s and the treadmill moves left a 1m/s (since the right wheel is rotating faster than is necessary to keep pace with the vehicle speed).

Do you agree with those? If not, which of 1..3 do you think is wrong? I can assure you that this will resolve your original problem if you stick with it.

As I mentioned in your imaginary setup the vehicle has 3 points of contact and that god will need to be real as a force will need to act against the vehicle body and not an imaginary one as you think.

If a real force acts against the vehicle body then due to 3 separate forces acting on the different vehicle parts the vehicle will work as you mentioned.

I already provided an example but in my example the vehicle body was rigidly connected to ground and in that case the mechanism acts as a functional gearbox and the red box can be moved by the treadmill and force acting on the box provided by left wheel can be 2x larger than the input force at the right wheel provided by the treadmill.

So, after all that, do you agree or not that each of the statements 1..3 in the context shown with the HoG, etc? If not, specifically which one are you stating is false?

Just for the moment, if you can manage to control yourself, don't relate this to your problem. Just answer the question honestly, without distractions or diversions, and we can move on.