Hi,
note that the above were for a machine where the two rotational axes are coincident, namely the trunnion (A) axis is in the same plane as the platter (C) axis.
Therefore some terms drop out of the matrix formulation, i.e. the above matrix math is as simple as it gets.

I have attached a picture of my trunnion/platter. Note that the true machine center where the A axis and C axis intersect is a small (20.045mm by my measurement) distance
above the platter, but vertically above the center of the platter. i.e. D_z=20.0245mm

The same document outlines the matrix formulation for a machine where the center point is displaced by both Z and Y axes, D_z and D_y.
This is actually more realistic of my machine, its just that in my case D_y=0mm, and allows a minor simplification of the matrix formulation.

Craig

while I'm not particularly up on the specific, I'd imagine it has to do with the fact that a rotational axis (and you shouldn't think round here) has at least two ways of getting to a single point.  I ran into something like this with a SCARA robot.. you need to watch and make sure you tell it how to bend and articulate its horizontal... otherwise you will either smack into something or crash in the next move. So how you approach a specific point in space depends on where you are beforehand and how you got there.
I would imagine that if Linux/CNC is already doing kinematics on the fly, then the equations are already in place. So why don't you simply switch over?   

Hi,

I'd imagine it has to do with the fact that a rotational axis (and you shouldn't think round here) has at least two ways of getting to a single point.  I ran into something like this with a SCARA robot.. you need to watch and make sure you tell it how to bend and articulate its horizontal... otherwise you will either smack into something or crash in the next move. So how you approach a specific point in space depends on where you are beforehand and how you got there.

Yes, that it it exactly. Further I understand it is very much the concern of robots. Five axis CNC machines are less difficult, but that does not make it easy either.
The matrix formulations I have excerpted do not resolve that issue, and there is I believe yet more to learn about the resolution of those conflicts.

I would imagine that if Linux/CNC is already doing kinematics on the fly, then the equations are already in place. So why don't you simply switch over?

That is a very good question....and the only real answer is momentum. I have been using Mach4 for ten years and daily for at least five years in business. 99.99% of all of that is three axis,
and for that purpose Mach4 has been excellent. My preference would be that Mach4 has RTCP natively, and that would allow seamless extension of my machine to four and five axis tool paths.
I do have twenty or thirty toolpaths that are four and five axis, so its not like Mach4 cannot do simultaneous four and five axis, but it requires a very specific set-up of your material in the machine
in absence of RTCP. RTCP would mean a easier migration to more complex parts, not that its absence precludes those tool paths.

Like any decent free loader/bludger/sloth.....I would like someone to do the heavy lifting for me!

I have plenty of projects on the go already, adding coding my own RTCP module for Mach4 is appealing, but is unrealistic at the moment.

Craig

yes, I was confusing RTCP as it references CNC with something else.... yes, RTCP does what you are looking for ... that is calculate the required axis translations on the fly.. and that requires an OS with a deterministic operation. Its already been done in Linux/CNC so the modules are already available. I doubt that many hobbyists or even general users would require it. And it should be only utilized with a real closed loop setup.. not a 'closed loop servo' as the cpu doesn't know if the servo is actually where its supposed to be in real time. So there goes 99.8% of your users... its most likely too small a target group for that much effort and cost. 

and I would add... I've determined that Mach4 has some very basic flaws... and the programmers aren't even interested in correcting those... more colors and new screen development tools sell ... fixing problems doesn't but still costs $$ they can't recover.  sounds like mach4 does a good job for you however. 

Hi,

that is calculate the required axis translations on the fly.. and that requires an OS with a deterministic operation.

No it doesn't. It can be calculated in exactly the same manner as the trajectory is, and that is used to fill the motion controllers buffer. It does not require deterministic behaviour
any more than three axis Mach does.

And it should be only utilized with a real closed loop setup..

No it does not. As I've already posted Mach4 does a perfectly excellent job of five axis tool paths, to whit I have several of them myself. WITHOUT RTCP it means that I have to place the material
in strict coincidence with the machine center point about which the Gcode was composed. It does not require closed loop (not just closed loop drives) servos any more than it requires closed
loop servo for three axis.

RTCP is solely to allow you to place the material and/or work holding in a convenient location in the machine and yet still have the tool path run AS IF the material had been placed
in strict coincidence with the assumed machine center.

Without RTCP, you could if you wish, you could translate the machine center in your CAM program to reflect the position of the material/workholding and then re-generate
the Gcode then post and run the Gcode as normal.

To date I've always placed my material carefully to be coincident with the machine center, save having to shag around with Fusion Machining Extensions all the time.

I've determined that Mach4 has some very basic flaws... and the programmers aren't even interested in correcting those... more colors and new screen development tools sell ...

Quite frankly, I think that stuff is a red-herring. Sure you can make it look nice, or maybe more convenient to operate, but Mach will go no faster, nor more accurately, nor anything else that
improves the parts coming out of the machine. RTCP would make five axis more convenient, and that would be nice, nice enough that I'd pay a $500/year subscription for it.

Can't really be bothered with cosmetic changes, what really counts for me is operational capability.....everything else is just 'gilding the lily'.

Craig