Design a Crank Mechanism: Solutions & Equations

[TheRedDevil18]

I want to design a crank mechanism. I found this page on Wikipedia
https://en.wikipedia.org/wiki/Piston_motion_equations

Relating from this diagram, is x the max stroke of the piston ?, or is it PO-(max stroke of piston) ?

And why is l^2 = r^2 + x^2 - 2*r*x*cos(A)

Shouldn't it be, l^2 = r^2 + OP^2 - 2*r*OP*cos(A) ?

 

[OldYat47]

Total stroke is 2*r. There are a couple of ways to calculate piston position (the position of the center of the piston wrist pin, to be more precise). A common one is to use a perpendicular from the stroke line to form two right triangles. The length of that perpendicular is r*sin A. So the piston is at (r*cos A) + [l^2-(r*sin a)^2]^0.5. When angle A is zero the position is (l+x). When angle A is 180 deg the position is (l-x).

If you look further down in the Wikipedia article you will find the equation above.