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Freerefill

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**"Venetian Blind" Locking Mechanism**

First off, let me apologize if this thread is in the wrong location. Secondly, let me also say that I did search this forum and Google for quite some time before I posted. If I missed something, I apologize.

Anyway, brass tacks.

I've been thinking about a mechanical system I've been "designing" in my spare time. I say "designing" because it's mostly just an entertaining thought experiment, something I'm curious about just to see if it can be done. Of course, adhering to proper design methodology, I've broken it into its elements and I've been trying to take each piece one small bit at a time. The bit I'm currently stuck on involves a system which can withstand a high load under "normal" circumstances, however, release that load with only a very small applied force over a very small distance. Something akin to a quick-release mechanism. I'm sure I haven't considered all the concepts that are available to me, but as I said, I'm mainly doing this for fun. The problem I'm stuck on, whilst it may end up not being useful in any way whatsoever, has gotten me quite stuck, and quite curious, and I would hate to see this opportunity to learn something go to waste.

I drew up a diagram to give a better idea on what's going on, because I'm sure I'd just get all confused trying to explain it verbally. The easiest way to explain it is to think of a Venetian blind. You know how you pull the cord to pull the blind up, and release the cord to let it down? Well if you want to stop it mid-way, you move the cord to the side to engage a small movable gear. Releasing the cord from there pulls the gear up into a wedge, forcing the gear to push against the cord, which tightens the cords grip on the gear, which ensures that the gear (and the cord, and the gear, and the cord, and so on) stays put. Supposing for a moment that this circumstance was achievable not with a gear, but with a smooth bearing in a smooth track, and it was simply friction that held it in place. You can see this sort of effect in the attached diagram; a force Fa is applied to a freely rolling bar B1 which, by means of the friction between it and B2, rotates B2. B2 will naturally try to rotate itself into B1, which will cause a large compressive (normal) force between the two, which will increase the of friction between the two.

I know that, by applying a greater force Fa, B2 will want to rotate more into B1, which will create a greater normal force between the two, which in turn will create a larger frictional force between the two. What I want to know is, given the coefficient of friction (I can look that up), the applied force (which is basically my variable) and the dimensions of the system (I'll modify these to tweak the system), how would I create a model to determine what force (F*, in the diagram) I would need to apply in order to free the system and allow B1 to move?

My problem lies here: Every time I get to modeling it (free-body diagram, summing the forces/moments, et cetera.. nothing fancy..), I get stuck in some sort of recursive loop. Let me try to explain my approach (which may be completely wrong. If it is, please tell me!):

Determine all the static forces and moments on the system.

Fa is the applied force

Ff is the friction force

Fn is the normal force

Fm is the force opposing the normal force

Ma is the moment due to the applied force

Mr is the moment opposing the applied moment

F* is a variable force

M* is a moment applied by F*

The goal, I believe, is to apply a force F* such that the normal force Fn is reduced, thus the (static) frictional force Ff is reduced below the applied force Fa:

Fa > Ff

The applied force is a given, so it follows to determine what the static frictional force is. This should be easy enough, it should be just the normal force Fn times the coefficient of static friction u

Ff = Fn*u

It follows, then, to determine Fn, which should be a function of the applied force Fa and the variable force F*. This is right around where I get lost. I tried summing the moments caused by the three forces and, for the sake of simplifying the algebra, assuming that the distances ra and rb were equal and that the angle theta was 45 degrees, thus the distance terms would cancel out and:

Fn + F* = Fa

Which means:

Fn = Fa - F*

Plugging this into the inequality,

Fa > (Fa - F*)u

Solving for F* yields:

F* > Fa(1 - 1/u)

Which initially struck me as perfectly reasonable, in that the variable force F* would definitely be a function of the applied force Fa and the coefficient of friction u, assuming the distances were equal. However, when I tested this with a real number, using 0.5 for the coefficient of friction, it claims that:

F* > -Fa

Which doesn't seem to make much physical sense. Clearly I've done something wrong.

Any help would be appreciated. :)