SD4 - why does the bed move?

put your printer info in your signature like others (see mandatory signature topic) have to help get better replies. from other posts it seems you added a glass bed plate which requires mod to the Z switch adjuster (like done on SD2 & SD3). but dont tighten springs down tight as that is for allowing movement from extruder bumps or when removing prints etc. thats far as I can help with no SD4 exp

I'm not sure what glass bed you added but mine is about 4mm high I just tightened my level screws a little without adjusting the z height limit switch. if your head is banging against the print you either haven't calibrated the height and/or your level is off. My procedure is to use a single edge razor & I take off the safety end so I have a very flat surface. A single edge razor is a precision instrument with a height of about 0.22 mm. I home my Z axis then adjust the back screw so the razor smoothly glides underneath, then I adjust the left & right front screws, I repeat the process just in case. Finally I set my slicr3 z offset to .19 this allows some give for the hot filament. but your adjustment depends on your desired extrusion width... I always get very accurate prints and very rarely have failed prints.

If you can get your hands on a dial gauge, and put the lawsy/adrian firmware on the board (which has the hysteresis fix), you can measure backlash in the z axis and have the board compensate for it with M99 in your start code. This made a huge difference to my first couple of layers (mine dragged quite badly). I'd see it as one of the more effective solutions for z backlash - even given I'm a mechanical engineer and appreciate a good mechanical solution!

Re wobbling - yup, it's in the design, and it's pretty annoying... I've been meaning to stabilise the front of the bed for a while now, i'm pretty sure most of the ghosting on my prints is the bed moving. It's not affecting my overall accuracy by much though, it's just ugly in the wrong lighting!

Your distortion due to backlash is in the x-y right? You can consider the hysteresis fix method to improve this too if you don't want to get too crazy with the mechanical mods. I went all-out mechanically: bearings on all the driveshafts and bearing idlers, direct-drive y axis (motor sticks waaay out the left of the case), GT2 belts - the result is I can press skate bearings into a 22mm circular hole kind of perfectly (I haven't actually measured the residual backlash recently), but looking back I have a sinking feeling I could have got here just with a firmware tweak...

That's my plan - people already seem to build things that run up and down the sides of the case, but I figured I could just redesign the y idler brackets to fit a vertical 8mm shaft, and do one on each side, with a brace that connects them to the middle of the front of the bed. Bottom end would be a printed spigot bolted to the bottom of the case (so I can adjust them to be parallel; don't trust my ability to spot a hole in the SM accurately enough! ).

I had exactly the same - they hadn't loosened I think, they were like that when I got it. Drilling them out and replacing with bolts did help a lot. I'd recommend it to anyone if you notice the joints are loose as you describe; although a lot of disassembly is required to get the bed out to drill out those rivets.

There's still quite a lot of wobble in the flexing of the z rods that I'd like to get rid of!