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My Ender 3, and I think lots of printers, have 4 bed leveling adjusstments, one at each corner. It seems to me that having 4 points produces an over-determined system, making it confusing to get the leveling right - adjusting one of the four may have little or no effect, but then cause a later adjustment elsewhere to have effects that violate a least-surprise principle.

Would it be better to have only three points? Or is the fourth necessary/useful with non-completely-rigid bed structures to add rigidity?

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Similar reasoning as for question "3 vs 4 bearings for y axis travel"" holds. If you introduce a fourth point, it is more difficult to make a flat plane.

Provided that your bed is stiff, e.g. a flat piece of glass, or a thick metal plate is used, you do not need more than 3 screws. Both my custom built printers use pieces of glass on aluminium heated beds that use three screws for levelling.

If your bed is thin (e.g. thin heated bed with tape, so no glass) and flexible or warped, an extra screw might be handy to deform the bed to a more flat plane.

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    $\begingroup$ I'm in agreement with 0scar. I have a monoprice mini IIIP with a four point "leveling" system. I've added a piece of glass atop a silicone thermal transfer pad. The four-point system warps the thin aluminum bed very badly. I've since drilled a hole in the front to create a three-point level. No more bed warping! $\endgroup$ – fred_dot_u Jun 28 '19 at 18:13

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