Kinematics for XYZAB mill

Turns out all those sin² and cos² might cancel out.
Would be great if somebody could look that over (still doesn't fix the kinematic though): 



Andy, my motivation is to understand how those kinematics were derived in the first place. Would be nice to be able to create a proper kinematic instead of trying to fiddle around with something that doesn't quite fit the requirements.
Although I have to admit I'm not exactly crushing this, yet.

Aciera,

Awesome thank you. Your interpretation of the machine is perfect!
It looks like the A axis is rotating the wrong way as shown here. I bet thats just not as easy to fix as changing the sign!

 

I started with the B axis at the bottom (eg arm vertical) with the spindle touching one of the white lines on the B axis table.
Jogging A generated the current tool path.

I think the B axis is OK as I can scribe a circle when the arm is horizontal.
 

@Dewey, thanks for the succinct summary. I was thinking more along the lines of having this included in KINS so it could be installed in the same way as XYZAC-trt et al but I guess that can be discussed after its debugged.

Its been very awesome work by a great team

Hey Rod, do you have this machine, the mira6? Ive had my eye on this company for a while because they are local(ish) and they are a distributor of the spindles I use, and make machines similar to mine. If you do have this machine, share your thoughts or comments?

cakeslob wrote:

Hey Rod, do you have this machine, the mira6? Ive had my eye on this company for a while because they are local(ish) and they are a distributor of the spindles I use, and make machines similar to mine. If you do have this machine, share your thoughts or comments?

Sorry no I don't.  They asked me if I could help them with linuxnc. I thought that would be straightforward until The XYZAB kinematics sunk in. I did not want to take it on until we had the kinematics sorted as I thought it would  be a nice contribution to the cause!

They do look pretty impressive and have some amazing examples on their web site..

So from what I can see the error is in the original term AAP because the signs of the sines have not been inverted as mentioned in the original model at the top of  page 5

rodw wrote:

So from what I can see the error is in the original term AAP because the signs of the sines have not been inverted as mentioned in the original model at the top of  page 5

I went through this all for my own benefit. (25) changes some signs around and becomes I think that makes sense because any term that includes  Sa inverts the sign
I don't yet understand how to get to 26 but you could follow the same logic and chane the sign of terms containing Sa I guess.