How to remove mechanical advantage from a lever

[zeek]

I have a simple lever with two points of equal force, each at a different distance from the fulcrum.

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What I want: As the arm turns, one point of force moves at a faster rate than the other.

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What I DO NOT want: One point of force having a mechanical advantage over the other.

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If I were to introduce two tracks in parallel, with each point of force on a track, but able to freely slide up and down the same lever arm as they moved across the tracks, would this remove the mechanical advantage from the force point farthest from the fulcrum?

If not, is there another solution such as some lattice configuration, or even gears or something other than a lever?

Again, all I want is two points of force moving together with one point of force moving at a faster rate than the other. Thanks.

 

[Topher925]

What I think you are describing violates the laws of thermodynamics. If you have two equal forces then they must have equal displacement. That is:

F1 x D1 = F2 x D2

where:
F = force
D = displacement

The only way this relationship can not hold true is if there are losses in the lever or mechanical system you are using. There are two ways of accomplishing these losses.

1. A mechanical device with multiple degrees of freedom where one of those degrees is subjected to a damper, removing work from the system.

2. A hydraulic/pneumatic system where a working fluid is subject to some type of transformation that it absorbs external work in the working fluid itself, ie compression.

Sorry if I misunderstood your question. If I have, can you draw a picture?

 

[mgb_phys]

Exactly - because if you turn it around, you are asking.
I want a lever where I can press down a short distance and have the other end move a large distance with the same force.

It would be useful, but would have to create energy from nothing!

 

[Dale]

It should be possible to build such a device as an active device. It certainly wouldn't be a simple lever. Probably the easiest way would be to build an electronic device to monitor the force and displacement on the control and then use something similar (in reverse) to produce the same force but a different displacement.

 

[russ_watters]

Btw, you said you want to remove the mechanical advantage, but the mechanical advantage is simply a ratio and it manifests with both a change in displacement and a change in force. So really you are saying you want to keep the mechanical advantae but remove the mechanical advantage - an oxymoron.

 

[zeek]

Thank you for your replies. You have in essence, answered my question. I was wanting to know if there was a sort of 'commonly known' way of removing the leverage 'gained' to the force position farthest from the fulcrum. I see now that there is not. Thank you.

Because of my limited knowledge of physics terminology (and principles unfortunately) it's hard to explain my dilemma.

I am now thinking that the only way to achieve my goal of two points of force acting on the same arm at different distances from the fulcrum but without the farther position having a leverage advantage is to somehow change the angle of force on the farther position, so that it is not directed at a 90 degree angle to the arm, thus weakening the 'active' force.

I've been reading the web about angular momentum. Times like this I really wish that I had a head for this sort of thing. If you have any thoughts on this 'angle of force' approach, please post them. Thanks again for your time and attention.

FURTHER EXPLANATION: Just FYI, another way to explain what I am needing is this... I need a lever-arm with say 1 lb of force acting on the arm at 6 inches, and a second 1 lb force acting on the arm at 12 inches, but in the opposite direction. My problem is finding an arrangement in which these forces are balanced so that they cancel each other out and the arm doesn't move due to either force.

Am I correct in thinking that I could achieve the scenario above if the force acting on the arm at 12 inches was arranged so as to point in a 45 degree angle to the arm, thus halving the 'active' force acting on the arm?

 

[DaveC426913]

FURTHER EXPLANATION: Just FYI, another way to explain what I am needing is this... I need a lever-arm with say 1 lb of force acting on the arm at 6 inches, and a second 1 lb force acting on the arm at 12 inches, but in the opposite direction. My problem is finding an arrangement in which these forces are balanced so that they cancel each other out and the arm doesn't move due to either force.

Am I correct in thinking that I could achieve the scenario above if the force acting on the arm at 12 inches was arranged so as to point in a 45 degree angle to the arm, thus halving the 'active' force acting on the arm?

I suspected this was what he was asking about.

He's looking for a practical solution, not a principle, so he has a braid range of ways he can get the dsired effect without violating any laws.

There are lots of ways of balancing the forces. We'd need to have a better understanding though. How are the two levers connected? Where are they connected at the other end?

 

[Topher925]

Zeek, try doing some research on mechanical CCPM (continuously collective pitch mixing) for model helicopters. Some of the geometry gets a little complex but I believe accomplishes something similar to what you are after.

 

[russ_watters]

Angling the forces doesn't matter - the vertical component is the only component that is used on the lever.

No, I suspect what you are looking to do isn't possible.

 

[DaveC426913]

Angling the forces doesn't matter - the vertical component is the only component that is used on the lever.

Right but ... wouldn't angling the components distribute the force between vertical and horizontal? Then you'd just ignore the horizontal component (say, by using some sort of sliding attachment), leaving you with a weakened vertical component?

 

[DaveC426913]

I have whipped up a really simple diagram to ensure I've captured what's going on.

Have I missed anything? Input welcome.

It does NOT contain the solution yet, it is merely the starting point. I'll modify it if anyone has any ideas.

 

[LURCH]

What if you split the difference between the two points of contact, like this?

(hope that shows; I've never tried adding an attatchment before).

Anyhow, the two things that look like pneumatic cylinders could be repalced by springs. In theory, the mechanical advantage of each point of force would also be a mechanical advantage for the spring resisting that force. The point of force with the greater mechanical advantage would also have a resistance that has greater mechanical advantage. Wouldn't the two cancel each other out?

 

[russ_watters]

Right but ... wouldn't angling the components distribute the force between vertical and horizontal? Then you'd just ignore the horizontal component (say, by using some sort of sliding attachment), leaving you with a weakened vertical component?

My point is that the horizontal component is pushing against the fulcrum. It isn't doing anything, so it can just be ignored completely.

 

[russ_watters]

What if you split the difference between the two points of contact, like this?

Wouldn't the two cancel each other out?

Clever-looking, but no. The blue points are still where the torques are applied and the device still moves.

 

[DaveC426913]

Zeek, could we understand a little more about what's applying the force and the relation of the forces to the arm?

I get the feeling we're overthinking it.

 

[DaveC426913]

No, I suspect what you are looking to do isn't possible.

I would be useful to establish whether this is true or not, before everyone offers a zillion hare-brained modifications.

It seems to me there's no reason why it couldn't work. As simple a solution as a spring to dampen the force of F₂ accomplishes what he wants in principle, would you agree?

 

[stewartcs]

I would be useful to establish whether this is true or not, before everyone offers a zillion hare-brained modifications.

It seems to me there's no reason why it couldn't work. As simple a solution as a spring to dampen the force of F₂ accomplishes what he wants in principle, would you agree?

How exactly would this not move? If F1 = F2 then the torque at the fulcrum from one direction would be double that from the other direction since the distance from the fulcrum and the points of applied force is double. The rotation would be counter-clockwise.

Perhaps I'm missing something.

CS

 

[DaveC426913]

How exactly would this not move? If F1 = F2 then the torque at the fulcrum from one direction would be double that from the other direction since the distance from the fulcrum and the points of applied force is double. The rotation would be counter-clockwise.

Perhaps I'm missing something.

CS

The spring on F₂ would absorb half of the force, balancing it with the force from F₁. It's not meant to be the solution, merely to demonstrate that, in principle, there are ways to modify the forces.

 

[russ_watters]

But that's the thing: in principle the internal forces are irrelevant. It is the extrenal forces on the system that make the lever arm move or not move. You cannot absorb/redirect forces like this, it's a violation of conservation law. This is how perpetual motion crackpots are made - they look for ways to do exactly what is being looked at in this thread.

 

[Dale]

FURTHER EXPLANATION: Just FYI, another way to explain what I am needing is this... I need a lever-arm with say 1 lb of force acting on the arm at 6 inches, and a second 1 lb force acting on the arm at 12 inches, but in the opposite direction. My problem is finding an arrangement in which these forces are balanced so that they cancel each other out and the arm doesn't move due to either force.

Am I correct in thinking that I could achieve the scenario above if the force acting on the arm at 12 inches was arranged so as to point in a 45 degree angle to the arm, thus halving the 'active' force acting on the arm?

OK, if you want to keep a lever arm from rotating you need to balance http://en.wikipedia.org/wiki/Torque" (r x f = |r| |f| sin(a)). As you said, if you angle the force with the longer r you can get a smaller torque, but you need a sharp 30º angle, not just 45º. The other thing you could do is add a third torque, e.g. add an electric motor at the fulcrum to provide the extra torque you need. Since you are keeping everything stationary there are no concerns about violating conservation laws, no work is being done.

 

[stewartcs]

The spring on F₂ would absorb half of the force, balancing it with the force from F₁. It's not meant to be the solution, merely to demonstrate that, in principle, there are ways to modify the forces.

The spring still has an equal reaction force against the lever, regardless of the spring's displacement. For example, place a scale on a table top, then place a spring on the scale, then place a 1 lbf weight on top of the spring. The scale will still read 1 lbf (ignoring the spring's weight in this case). The normal force on the scale is unchanged (with or without the spring) even though the spring "absorbs" the force.

CS

 

[stewartcs]

OK, if you want to keep a lever arm from rotating you need to balance http://en.wikipedia.org/wiki/Torque" (r x f = |r| |f| sin(a)). As you said, if you angle the force with the longer r you can get a smaller torque, but you need a sharp 30º angle, not just 45º. The other thing you could do is add a third torque, e.g. add an electric motor at the fulcrum to provide the extra torque you need. Since you are keeping everything stationary there are no concerns about violating conservation laws, no work is being done.

Exactly, as long as the system stays in equilibrium, it won't move!

That idea sounds feasible though.

CS

 

[DaveC426913]

But that's the thing: in principle the internal forces are irrelevant. It is the extrenal forces on the system that make the lever arm move or not move. You cannot absorb/redirect forces like this, it's a violation of conservation law. This is how perpetual motion crackpots are made - they look for ways to do exactly what is being looked at in this thread.

So where does the spring idea fail?

 

[stewartcs]

So where does the spring idea fail?

Take a look at post #21. When the spring has a force applied to it, the opposite end of the spring (where the lever is in your drawing) has a reaction force equal to the applied force. The spring's displacement (length) is just reduced. The magnitude of the applied force is still seen at the lever (i.e. the other side of spring). So nothing is gained from it.

CS

 

[DaveC426913]

Take a look at post #21...

Sorry. Somehow I got behind a post or two. I wouldn't have asked if I'd read that.

 

[russ_watters]

After discussion in the mentor's forum, we've decided this thread doesn't go anywhere good. The concept is just plain wrong and the flaw has been explained, so there is nothing to be gained by pursuing it further.