expanding flakes: nut vs. cam?

brenta wrote: That's exactly it. The point is that the outward force is not the sum of the forces at the two sides. And there's no more reason to go to the lab to test this than there is to write a proposal to get some time on the supercomputers at Oak Ridge National Labs to settle the dispute as to whether three plus three equals six or twelve.

I don't think you get how forces work yet. If the coefficient of friction is 0.25, and you only have twice the load in compression, your cam would be slipping.

If you look at the contact point of your cam, you need to have four times the load being exerted in order to resist pull, do you agree with that? Where you are going wrong is that you add 2 times on one side, and then add 2 times on the other side and say that adds to four times. This is the completely wrong part.

The forces are a force pair that create compression on the cam. You don't treat them individually. If you took one away, the cam would go zooming off into space.

If instead of a cam, suppose you had just a block of aluminium against a flat rock face. How hard would you have to push it against the wall to keep it from slipping? You would need to apply a force equal to four times it's weight correct? But by your logic, you are actually pushing it with eight times it's weight, because you apply four times on one side, and the wall applies four times against it in the other direction. Do you see where your logic has gone askew?

As for the original question, it depends on the taper angle. A very high taper (like you get on a hex) will exert less force than a cam. A very small taper less than something around 8 deg will in theory exert more outwards force than a cam, but this will depend on the coefficient of friction.

brenta wrote:And there's no more reason to go to the lab to test this than there is to write a proposal to get some time on the supercomputers at Oak Ridge National Labs to settle the dispute as to whether three plus three equals six or twelve.

Then again, a couple minutes in the lab would have easily prevented several pages of arguing about it. Seems worthwhile to me, but YMMV.

David Horgan wrote: That's what the Greeks said about all matter being composed of four elements.

No, they didn't.

While Sicily is currently part of Italy, in 490BC was actually part of Greece. The significance of this is that Sicily is the birthplace of Empedocles, who was the first to posit the 4 element theory that was held as true for the next thousand or so years in the Western world.

(/tangent)

brenta wrote: No, they didn't.

I'm sure you're correct, I'm no historian, and was just kind of fooling around. And I certainly don't know how to say "Oak Ridge supercomputer" in Ancient Greek.

But the point behind the fooling around, which I will definitely stand by, is that there are a whole lot of examples in which very sensible applications of idealized scientific principles turned out to be incorrect when measured experimentally.

DannyUncanny wrote: Your nit picking is incorrect. Friction force adds up to load force, normal force adds up to 4 x friction force, you can add it any way you want, it's still 4 times.

Not correct. Draw yourself a free body diagram (or check out the awesome MS Paint one I drew below), you have the downward force "F" on the cam, and you have 2 forces "f" from the rock onto the cam lobes. Now the vertical components of the 2 "f" forces have to add up to the total downward force "F", and the horizontal component of the force "f" is the force causing the flake to expand. Now we can create equations for the sum of the forces equal to zero in both the horizontal and vertical dirrections, but lets just worry about the vertical since there are only the two horizontal components of the two "f" forces that will just cancel each other out. So in the vertical dirrection we have:

0 = f sin (theta) + f sin (theta) - F

Now we want to solve for "f" since the horizontal component is the expansion force:

f = F / (2 sin (theta))

Now we pick a random cam angle for thata, lets say 15 degrees to make it simple and we get:

f = 1.932 F

Now the expansion force is the horizontal component of "f", fx, which is found as "f" times the cos of theta:

fx = 1.866 F

so for a cam angle of 15 degrees and neglecting the friction between the cam lobe and the axel, the expansion force on the flake is 1.87 times the force of the fall. Of course as the cam angle decreases the expansion force will increase, but even a 13 degree cam angle only gives an expanding force of 2.17 F, nowhere near 4 times the downward force.

DannyUncanny wrote: I don't think you get how forces work yet.

Philosophus mansisses si tacuisses.

DannyUncanny wrote: If the coefficient of friction is 0.25, and you only have twice the load in compression, your cam would be slipping.

No. The relation between tangent of the cam angle and friction coefficient is easily derived as follows:

1. From the moment equation that says that the lobe is not rotating around the axle, we get that the ratio between friction force on one side and the normal force equals the tangent of the cam angle.

2. It is this ratio that must be less than the coefficient of friction lest the cam should start slipping. We are applying Coulomb's Law here. It follows that as long as the tangent of the cam angle is less than the coefficient of friction, enough friction will be available to avoid slipping.

DannyUncanny wrote: If you look at the contact point of your cam, you need to have four times the load being exerted in order to resist pull, do you agree with that?

No, for the above reason.

DannyUncanny wrote: Where you are going wrong is that you add 2 times on one side, and then add 2 times on the other side and say that adds to four times. This is the completely wrong part.

Whatever it is you're trying to describe, it's not what I'm doing. Let's write the translational and rotational balance equations and solve them: it's easy-peasy. Let F be one frictional force, L the load, N the normal force and beta the cam angle:

1. 2F = L
2. F cos(beta) = N sin(beta)

whence N = F/tan(beta) = L/(2 tan(beta)).

DannyUncanny wrote: The forces are a force pair that create compression on the cam. You don't treat them individually. If you took one away, the cam would go zooming off into space.

Obviously.

DannyUncanny wrote: If instead of a cam, suppose you had just a block of aluminium against a flat rock face. How hard would you have to push it against the wall to keep it from slipping? You would need to apply a force equal to four times it's weight correct?

You are ignoring the friction between the block and whatever you use to push the block against the wall. If you used a frictionless device, like a roller, to push the block, then you'd be right, but the lobes of a cam don't work like that.

DannyUncanny wrote: But by your logic, you are actually pushing it with eight times it's weight, because you apply four times on one side, and the wall applies four times against it in the other direction. Do you see where your logic has gone askew?

I hope by now you see how nonsensical this is.

David Horgan wrote:That's what the Greeks said about all matter being composed of four elements.

.

Brenta wrote:No, they didn't.

.

David Horgan wrote: I'm sure you're correct, I'm no historian, and was just kind of fooling around.

Actually, he's not; see post above re: Empedocles. As for the cam/nut thing, I'd rather see someone put it to rest by measuring something rather than continue watching this turn into RC.

i don't want to distract from the original question but i was wondering...

would a thin dyneema sling slung around a dead, rotting tree exert more force than a fat nylon sling? and, please, no speculation. we need to be discussing in terms of quantitative analysis. this is important stuff.

Aric Datesman wrote: . . Actually, he's not; see post above re: Empedocles. As for the cam/nut thing, I'd rather see someone put it to rest by measuring something rather than continue watching this turn into RC.

Don't you miss RC even just a little Aric? ;)

I'd also love to see someone measure something, unfortunately, you're the only person I know of who has that ability currently. If you do get time to do some measurements, make sure the plates are textured where the nut contacts them because I'm sure that the frictional forces will keep the nut from expanding the flake (or plates in this case) nearly as much as the cam would.

Ok, I concede now, I was wrong.

Aric Datesman wrote: Actually, he's not; see post above re: Empedocles.

Aric, no one disputes that Empedocles put forth the four-element theory and that it held sway for a couple of millennia. What is incorrect and naive is to believe that the Greek had no interest in measurements. Look no further than at Eratosthenes' measurement of the circumference of the Earth. It is also incorrect to conclude from the uselessness of one experiment the uselessness of the experimental method.

Aric Datesman wrote: As for the cam/nut thing, I'd rather see someone put it to rest by measuring something rather than continue watching this turn into RC.

It's much easier to question one's experimental setup than a mathematical derivation. The kind of person who is not convinced by the mathematical derivation may, for instance, argue that you only measured half the force. Another may believe that your load cell is defective, that rock flakes do not behave like your metal plates, and so on.

kennoyce wrote: Don't you miss RC even just a little Aric? ;)

Not really. Too much of a time suck.

kennoyce wrote: I'd also love to see someone measure something, unfortunately, you're the only person I know of who has that ability currently. If you do get time to do some measurements, make sure the plates are textured where the nut contacts them because I'm sure that the frictional forces will keep the nut from expanding the flake (or plates in this case) nearly as much as the cam would.

That's the beauty of fixturing it like that.... No special equipment needed. All you need are some nuts, bolts and some metal stock from Home Depot, along with something heavy and a way to measure accurately. Were it not for needing to finish the project I'm working on (and 2weeks late with) I'd do it, but alas, I can not.

brenta wrote: Aric, no one disputes that Empedocles put forth the four-element theory and that it held sway for a couple of millennia.

Not to argue with you Brenta, but you did just a couple posts ago. As for the rest, as an objective observer of this discussion it's clear that there's several people putting forth theories for how it works based on their understanding of the subject. The easiest way to sort the wheat from the chaff is to get some empirical evidence to test the theories rather than each standing there proclaiming themselves to be the only one who really understands the problem.

Sooooooooo... Are we any closer to getting any form of answer to the OP's question (even if it's intuitive/based on anecdotal evidence) or are you guys going to continue displacing large amounts of air by tooting your own horns?

brenta wrote: Aric, no one disputes that Empedocles put forth the four-element theory and that it held sway for a couple of millennia. What is incorrect and naive is to believe that the Greek had no interest in measurements. Look no further than at Eratosthenes' measurement of the circumference of the Earth. It is also incorrect to conclude from the uselessness of one experiment the uselessness of the experimental method. It's much easier to question one's experimental setup than a mathematical derivation. The kind of person who is not convinced by the mathematical derivation may, for instance, argue that you only measured half the force. Another may believe that your load cell is defective, that rock flakes do not behave like your metal plates, and so on.

Actually, I'd accept the lab data over the math as at least a starting point toward an actual comparison between nuts and cams. Then I'd accept objections about the lab setup as a way toward making a better setup.

But for a START I'd even accept some math which actually answered my question, which was nuts VERSUS cams, not cams cams cams cams cams, which is where this discussion is heading.

So are people willing to accept the logic that cams and nuts work on the same mechanical principle, and since nuts have the smaller angle, they have the greater expansion force?

Again, to be clear, I'm not asserting this myself, because I don't understand mechanics well enough. But among those that do understand it well enough, is there agreement on this point?

Boissal wrote:Sooooooooo... Are we any closer to getting any form of answer to the OP's question (even if it's intuitive/based on anecdotal evidence) or are you guys going to continue displacing large amounts of air by tooting your own horns?

Wow, that's great! Way better than any of that Icanhazcheezburger stuff. (the pic, I mean, although the comment is good too.)

Aric Datesman wrote: Not to argue with you Brenta, but you did just a couple posts ago.

No, I did not. Please, read more carefully. If you still think so, please, explain how you came to that conclusion.

well, this is fun,isn't it? the internet has pictures of lions!

I think there are two cases that should be treated separately:

1. an flake that you're worried about breaking with outward force

and

2. an (big) flake that isn't going to break from being flexed a little bit.

in the first case, you might focus on trying passive pro in hopes of getting some protection without as much outward force- maybe a hex that really hangs up on a feature in the crack and would pull down on the flake instead of outward in the case of a fall.

in the second case, use a cam, because it will still provide an outward force (and friction) as the flake flexes beyond the size of the chock you're using.

If you have a situation where your nut isn't going to pull through even with the flex, then get back on MP and push this one to page 4.

brenta wrote: No, I did not. Please, read more carefully. If you still think so, please, explain how you came to that conclusion.

Ah, I see. My apologies. Upon a quick reading it appeared you were responding to David's comment re: the Greeks and their 4 elements. I will say in that case I don't quite follow your response to how David's point that the Greeks were incorrect on this belief, but frankly I don't have a horse in this race and have more important things to do at the moment.