After reading your example, I see that I mis spoke in my last post. Mach doesn't always accelerate at the set rate. It will not, however, ever exceed it. Which answers your question I think.

OK, then I think I will be pretty safe for the time being. I'm quite familiar with calculations for pick 'n place robots but CNC is so much different with the constant interpolation. If necessary I can reduce the gear ratio to slow down the top speed as this is a hobby machine, not needing full scale production speeds. Thanks Gerry and Rich too.

PS. Obviously there was a typo in my previous post, should of course have read dx/dt and dy/dt.

You dont need to gear to limit your top speed, whatever velocity you set in motor tuning will be the max you will ever get.

Hood

If necessary I can reduce the gear ratio to slow down the top speed as this is a hobby machine, not needing full scale production speeds. Thanks Gerry and Rich too.

No need to gear anything. Rapid speeds are set in software. If your talking about slowing down cutting speeds, just change them in your code or use the Feedrate override to slow it down. There's also a separate rapid feed override.

Edit: Damn, a hair too slow.

Uh guys, are you serious, I thought you knew the physics;-)

There's a difference between slowing down because you want to and slowing down because you need to.