1250 x 1250 cnc router (from scratch)

[D.C.]

Assuming your z-axis can reach just below the top of the bed for surfacing it for doing flatsheets then that will be the lower limit of your z-axis travel. But for doing fourth axis work the lowest limit you need is the centre of the spindle, any material lower than that gets rotated upwards towards the cutting head.

So if you have the 4th-axis centred on the the z-axis limit of travel, you can cut 6 inch radius stock with 6 inches of z-axis travel. If you move the centre of the 4th axis up 2 inches this means you can only cut 4 inch radius stock with 6 inches of z-axis travel because the 2 inches you have below the centre will never be used for doing 4th axis work but your z-axis still needs to be travel that far to reach the bed when doing flat sheet work on the rest of the table.

Putting the centre at the same height as the bed results in the shortest required z-axis.

In reality you can position the 4th axis centre slightly lower than the top of the bed because your z axis will reach down that low for surfacing the bed and you never ever want to cut all the way through a piece of spinning wood that requires the support of two centres because it will fly off the machine at great speed doing a great deal of damage to any fleshy human type objects in it's path.

[JAZZCNC]

Putting the centre at the same height as the bed results in the shortest required z-axis.

No it doesn't it puts it at the longest Z extension. It will only be shortest when cutting at the outer radius and ever millimetre towards the centre the extension gets longer weaker and therefore the chatter will get worse.
I know what your saying but really it's down to the size of radius you want to cut or the size your most likely to do often. Why would you want the centre 7" away when your mostly turning 2" stock.? You wouldn't set your rest 7" away from centre on a Manual lathe if you where turning 2" stock so why would you in this case.? . . .That would just be creating a weaker machine for the Odd occasion when you want to turn larger diameter.!

The ideal would be an adjustable position and that's what I'd probably do in reality.! . . BUT.!!. . . . Like I said it's only a mock up and if you wanted 6" from the floor then go for it. But this was drawn just to show the principle with simple Leg or spindle turning in mind so that's why it landed there. . . Oh and it's 4.5" away there so thats 9" Diameter which is more than enough for most 4th axis work.!!