Mechanical advantage of a pneumatic piston bellcrank system

[Otibix]

Hi all,

I've really been struggling to come to determine a formula which calculates the mechanical advantage of a system.

The system is a vertical pneumatic piston which actuates a connecting rod, pushing a bell crank to push against a wall.

I need to determine the mechanical advantage (wall force / piston force) based on the changing geometry. I've derived an equation which states that the mechanical advantage is proportional to tan(q). The piston can actuate up to a connecting rod angle of 88 Deg based on the distance of the crank to the wall. I don't know where his is going wrong. I've attached my derrivation.

 

[GregLocock]

At theta =90 degrees Fw will be zero.

Cheers

Greg Locock


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[Otibix]

Hi Greg, thanks for your input. Why do you think this? Is there a relationship between the Fp and the FS term that I have missed?

My derivation suggests that the wall force would tend to infinity which obviously cannot be true?

Thanks

O

 

[MintJulep]

You seem to have forgotten half of your toggle linkage.

 

[GregLocock]

And at theta = 0 it will be P*A*Lx/Ly (there's an error in your first diagram)

Cheers

Greg Locock


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[GregLocock]

Simple logic, if you push on the end of a link at 90 degrees tot he link you can't generate an axial force.

Cheers

Greg Locock


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[MintJulep]

You're missing a moment reaction at the cylinder bushing, and a horizontal reaction of the piston against the cylinder wall.

Anyways, mostly what this machine will do is destroy pneumatic cylinders.

 

[GregLocock]

It won't even move unless the cylinder can move laterally..

Cheers

Greg Locock


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[Otibix]

The assembly is mounted inside a unit. The point of the assembly is to push the unit laterally away from the wall. This is the entire assembly and has been shown to work in practice. Annoyingly I need to define the ratio in a formula to allow us to assess the rest of the part. There is a fixed pivot is ridgedly attached to the piston.

 

[Otibix]

Thanks Greg, I agree that the at theta = 0 it will be P*A*Lx/Ly does this not align to my diagram? At theta 0 FS=0. I'm not sure what mistake you are referring to?

 

[Otibix]

That's a good point MintJulep, I hadn't considered the moment provided by the guided support. I believe that the addition would make this case statically indeterminate? Or do I misunderstand

 

[Otibix]

The questions boil down to can I get an equation for the mechanical advantage for all angles, if not what is the maximum mechanical advantage of the system.

 

[MintJulep]

There is a fixed pivot is rigidly attached to the piston.

Depending on how I imagine that statement, it might (mostly) allow the cylinder to act only axially.

 

[Otibix]

Sorry if I'm not clear. The bellcrank pivot is ridgedly attached to the piston cylinder by a plate.