4-6 axis feed rate

[robomechs]

It is necessary to check the consistency of the feed rate on the 3,4,5,6 axis.
It is necessary to understand how the speed should be calculated on more than 3 axes. And check how it is calculated on 3 axes.

[siy]

For 3 axes this is quite straightforward - speed is calculated as length of speed vector in 3D space, i.e. square root of sum of squares of speeds by each axis. For remaining axes situation is much more complicated, usually for 4th and 5th axes some base coordinate system is chosen, for example tied to workpiece. Then it's transformed back to machine coordinates to obtain resulting speeds for each axe. I never saw mention of 6-axis, so I can only guess that it can be calculated in similar way. In fact, I think that there are no big sense to worry about speed calculation for remaining axes in case of GRBL. By design 4+ axes are synchronized with 3 main axes. The only issue is that commanded movement may exceed physical limits of the machine. But this can be handled by trial-and-error for particular machine and case. After all, we're talking about GRBL which is not designed to handle complex setups like machines with 4+ axes and uses some specific optimizations for 3 axes. If you really interested in proper handling of such hardware, I may share some (well, a lot) research papers dedicated to this problem, but you should be prepared to write firmware from scratch, GRBL for several reasons is not suitable as a base for such project.