OK dayglo, here we go.

Here's a picture to go with the formuals:


Variables:

R = length of conrod in [mm]
D = Stroke/2 in [mm]
P = piston position relative to center of crank in [mm]
X = crank pin postition relative to center of crank in [mm]
alpha = crank angle in [deg]


Formulas:

In the picture we can see that:

P = X + T

where

X = D x cos(alpha).

To calculate T we need the help of phytagoras formula that says:

R^2 = T^2 + T2^2

Solve for T and we get:

T = SQRT(R^2 - T2^2)

T2 can also be expressed as:

T2 = D x sin(alpha)

which gives us:

T = SQRT(R^2 - (D x sin(alpha))^2

Finally we get the expression for P as a function of crank angle alpha:

P = D x cos(alpha) + SQRT(R^2 - (D x sin(alpha))^2)

Now you can insert: D = Stroke/2 (but I won't do that, it makes it cluttered to read)

Hope this helps.