Ratio Question With pics

I have a question about ratios since it came up in another thread, If the distance is the same from the center point to whatever it is thats pivoting thats a one to one ratio right? What if its like this and at the center point its bent at a 90 what would this be? heres a pic to help out
 

The other thread got me thinking about doing an entire tech piece on this subject, but I wouldn't even know where to start. From the simplest standpoint both diagrams are 1:1 leverage ratios, just for different drive angles. In the first pic, if the force is pushing up on the left side then the right side will move down an equal distance and force, but what happens when diagram two is pushed up? The lower point would move to the left an equal distance and force. So what if the left side of the first diagram had a rod attached to it that was driven by an A-arm? The rod would not push directly against the lever at a consistent 90o angle, so the ratio would then change and because the rod would be following the path of the a-arm at the bottom and the path of the lever at the top, the "driven" leverage ratio would be constantly changing. This would also be the case on the opposite side of the lever, constanly changing based on the angle(s) of the "driving" and "driven" parts. The shorter the parts, the more drastic the angle change, thus the more inconsistent the leverage ratios. Are we completely confused yet?

yup yup

so the ratio of the canti or bell crank piece itself IS determined by the distance from the center to each points BUT, it would change from how its driven correct? So it would be ok to say  you had a 2:1 canti setup if thats how everything measured out on your actual canti piece? Im just wondering how people get these figures is all! I understand that how its driven changes the force etc.!

---------------------------------------------Originally posted by BioMaxThe other thread got me thinking about doing an entire tech piece on this subject, but I wouldn't even know where to start. From the simplest standpoint both diagrams are 1:1 leverage ratios, just for different drive angles. In the first pic, if the force is pushing up on the left side then the right side will move down an equal distance and force, but what happens when diagram two is pushed up? The lower point would move to the left an equal distance and force. So what if the left side of the first diagram had a rod attached to it that was driven by an A-arm? The rod would not push directly against the lever at a consistent 90o angle, so the ratio would then change and because the rod would be following the path of the a-arm at the bottom and the path of the lever at the top, the "driven" leverage ratio would be constantly changing. This would also be the case on the opposite side of the lever, constanly changing based on the angle(s) of the "driving" and "driven" parts. The shorter the parts, the more drastic the angle change, thus the more inconsistent the leverage ratios. Are we completely confused yet?---------------------------------------------That's why when I draw out "canti" arm setups I find the complete arc the arm will travel, then setup so that halfway through that arc it's perpindicular to the direction of travel.  That way you don't lose any linear lift to the circular path.  You will still have the slight change in leverage for the force though, it's unavoidable when travelling through an arc.

^^^ That's how I do it too. Good call!

---------------------------------------------Originally posted by teckn9neSo it would be ok to say  you had a 2:1 canti setup if thats how everything measured out on your actual canti piece?---------------------------------------------You can call it anything you want, but the leverage should be considered exactly what it is, not what the lever or bellcrank measures out. I'm sure that there is a formula to calculate it out, but I don't know what that is. If there are any math majors out there I'd love to know.

If you have a cantilever setup drawn out, you can cycle it, take measurements, then plot in Excel.  This will give you the motion ratio at all points. The angle of the pushrod and bag also makes a difference, it's not just the rocker (belcrank) arm lengths.  You can get rising rates or diminishing rates by changing the rocker angles or pushrod angles, since what really matters is the perpendicular distance from the pushrod axis (or airbag axis) to the pivot. 

lol i should go chat with some of the mechanical engineers and physics professors on campus and see what they can give me.

Now you're talkin!