# Piston angle

1. Oct 12, 2009

### 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 cant 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 dont know how I can find an expression for theta that doesnt invlove a very nasty re-arrange..

#### Attached Files:

• ###### piston.jpg
File size:
8.2 KB
Views:
97
2. Oct 12, 2009

### Mech_Engineer

3. Oct 13, 2009

### 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 dont have to show a derivation, use the wiki link.

4. Oct 13, 2009