Setting up kinematics for my Ballscrew articulated B-axis

Hi everyone,

So I have my B-axis articulated by a ballscrew, as you might have guessed, and I am having some trouble understanding kinematics and how to set this up in LinuxCNC. Below is a picture of my design, followed by a drawing of the geometry. My trouble isn't with getting the math correct, so you can ignore the math if you wish. I need help understanding how to input this into LinuxCNC. So far I have followed this tutorial,  but I have got stuck with the kinematics part. 

And the geometry

So to describe the drawing

• Line CD is a connecting rod where point C travels along the ballscrew path AB, and the path is perpendicular to the Z-axis
• Point H is a point along the path AB that is directly above point E, that is, angle BHE will always be 90 deg and the distance HE is 120mm and AH is 217mm
• Point E is the centre of the B-axis rotation 
• Point D represents where the connecting rod is connected to the B-axis assembly
• Line FG is the spindle where G is the tool tip.
• CD = 125mm
• DE = 127mm
• EG = 120mm
• HE = 120
• Angle DEF = 30.579 deg

So to find the angle of the spindle  FEH we must first find DEH and subtract DEF from it.
DEH

So if I were to write a function to find the angle of the spindle(FEH) relative to the Z-axis based on the length of AC, it would be as follows
So first, we will calculate the length CE based on the length CH
CE = sqrt(CH2 +HE2) where HE = 120
CE = sqrt(CH2 +1202)
CE = sqrt(CH2 + 14400)

Now we can calculate angle DEC and subtract angle DEF to get the angle of the spindle

COS(DEC) = (1272 + CE2 - 1252)/(2*127*CE)
COS(DEC) = (1272 + CH2 + 14400 - 1252)/(2*127*sqrt(CH2 + 14400))
COS(DEC) = (CH2 - 14904) / (254*sqrt(CH2 + 14400))                  
where CH = AC - AH = AC-217

If you are not interested in the math, please continue reading here
So if COS(DEC) = (CH2 - 14904) / (254*sqrt(CH2 + 14400))  - DEF describes the relation of the ballscrew moving to the rotation of the B-axis how do I set this up in LinuxCNC? Also, do I need to calculate the formula for the tool tip change in X-axis and Z axis based on the B-axis rotating as well, before inputting this into LinuxCNC or is this sufficient? Thank you for your help and patience

Your image links don't work.

You can attach a file or use something like mega.nz or GitHub.

Picture is fine.
linuxcnc.org/docs/html/motion/kinematics.html is a starting point if you haven't been there already.