Finding Expression for Theta with Flywheel and Piston Movement

[a.mlw.walker]

Hi I am struglling to work out the expression for theta=f(x) for a piston, that moves linearly by a distance of x along the inside of the cylinder, and is attached to a conrod of length l, whose other end is at a radius r on a fly wheel. I want an expression for the angle theta that the fly wheel moves through, when the piston moves back a distance x. I think I am over complicating things but I just can't seem to find the expression.

I have attached a basic drawing.

cos(theta)=a/r

sin(theta)=h/r

both a and b change when x changes, and so I don't know how I can find an expression for theta that doesn't invlove a very nasty re-arrange..

 

[Mech_Engineer]

Perhaps the piston motion equations will help you, they are easy to find with a quick google search.

http://en.wikipedia.org/wiki/Piston_motion_equations

 

[xxChrisxx]

You have to have one of those nasty rearranges I'm afraid.

Your problem stems from the fact that to describe the postion, the crank angle and conrod angles are changing. You can rewrite the equations to show displacement in terms of theta only but that will involve comopound angle formulas.

If you don't have to show a derivation, use the wiki link.

 

[a.mlw.walker]

Thanks guys, but the wiki link reminded me of the cosine rule, which i felt stupid to have forgotten, but I finally came up with a relationship over at this post if you want to have a look:
https://www.physicsforums.com/showthread.php?t=345319