CNC router occasionally makes jarring noise and home jumps when it does this. Help!!

[Jonathan]

So you could write G1 X100 Y1000 F1400 and actually cut at that speed.

I think you meant Y100 or X1000 there.

Otherwise, nicely summarised.

I think this means that if I stick a G0 move in at the top of my gcode file with a ridiculously fast F setting, then LinuxCNC will always give me the fastest rapids that preset max X and Y settings permit, but I should make sure that the F setting for g1 cuts is the actual cutting speed that I want.

The 'F' command does not affect G0 moves. By definition, G0 moves the machine as fast as permitted by the motor tuning, unless you've overridden it using the feedrate adjustment, in which case the speed would be lower.

As far as the original question is concerned, all this means is that you can look at max speed and accel along each axis independently in order to avoid missing steps and other nastiness, and actual speeds over the bed are just an accident of geometry and don't affect design and tuning parameters. If you are missing steps along X, say, during rapid feeds you might choose to reduce accel or max speed on that axis but you don't necessarily have to change Y if that is working fine with its current settings. However, if you get skipping during cuts, then it's a bit more complicated and you probably need to reduce the F cutting speed parameter just to reduce load as you can't tune this by axis.

Yes, that's correct.

And my apologies, guys - I was desperately trying to find an excuse for using nested integral signs and the odd greek symbol from the LaTeX library but just couldn't find a way to fit them in...

Here's an easy way to get some different symbols in... derive a formula to find the direction (angle) for which the machine can travel at the highest feedrate, for given X and Y rapid speeds.
It's just occurred to me that you could actually do something useful with that formula - potentially surface your bed faster by using a raster pass set to that angle.

[Neale]

Ooh, an excuse for some calculus! That'll get 'em rolling in the aisles...

Thanks for pointing out typo, Jonathan - correction made.

On the F setting and G0, though - my comment was based on my experience with LinuxCNC, and I wonder if I have misremembered or LCNC works a little differently to Mach 3 (which seems from casual observation on this forum to be much more popular). If I type G0 commands into LCNC to move the machine "manually", my recollection is that it bitches if it has not seen a previous F setting in a G0 context. I tend to have to type something like "G0 X100 Y100 F1200". Once I've done that, I don't need the F parameter for subsequent G0 commands. In other words, it doesn't seem to default to the max machine speeds. The way you describe it makes much more sense and I wish it worked like that on my system but it doesn't seem to. I'll have to experiment - I might have missed something subtle.

[Jonathan]

If I type G0 commands into LCNC to move the machine "manually", my recollection is that it bitches if it has not seen a previous F setting in a G0 context.

I don't remember... by all means check.
According to the definition here, it shouldn't be a problem:
G Codes

Also notice that they mention what we just discussed - 'The maximum rapid traverse rate can be higher than the individual axes MAX_VELOCITY setting during a coordinated move.'