I’ve been observing the dynamics of the print bed on my 3D printer which is a Prusa i3 style Cartesian printer. The bed has 3 linear bearings that rid along two smooth rods. The bearings are arranged in a triangular pattern, with the drive belt down the center line. I have noticed that with some bearings, that have play or are loose, I get wiggle in the bed. I believe it is due to the following:
I’ve surmised that because the bearings have play, the motor applies a force on the bed which the single bearing receives as force across the horizontal axis in this picture, which is opposite (accros) the belt. This allows a “wobble” or slight rotation of the bed in the center point of the triangle. Because of the unreliable specs of the bearings, each has a different tolerance and even the smooth bars may not be manufactured to any type of specification. If the bearings aren’t fitting on the bar with minimal play, then you will get inconsistent layers, and your walls will not be smooth/straight.
For beds arranged like this, the situation is different and maybe non-existent:
Three bearing designs are great for machines that have expensive, tight tolerance components. For RepRap printers, four bearings are probably better over all.
The following approach would minimize the problem for three bearing designs:
The reason for this is that in three bearing designs, you typically have “leaders” and “followers”. The Leaders are the drive bearings. The follower is a supporting bearing.
These are my theories based only few hours of observation and non-scientific brain-storming. I’m not an engineer, just a mechanically inquisitive person who was raised in a junk yard.