Question about play tolerance on linear shafts

Greetings Reprap community,

I was looking for some help researching a design I'm working on for a 3d printer. Currently, I'm having an internal debate about the "play" on linear shaft bearings, to determine the most optimal way to reduce unwanted movement along the axis. For vertical movement, a lot of designs tend to use two rods with a screw, and four pillow block bearings (two on each rod). For horizontal, I've seen two rods again with a belt, and three pillow block bearings, two on one side and one on the other (the side with two having them the maximum distance apart).

Where would I go about finding information (other than physically making it myself) about the pros & cons of these two styles of design? The one I'm working on I'm trying to make as cost effective as possible, so reducing the number of pillow bearings would be ideal, however, if the ends justify the means, I will "go all out" with the bearings.

My question is mainly for vertical movement, with two rods on each side and one of the two sets of rods having a screw in the middle. Hopefully the picture below can help shed some light on my question. I know the bearing/casing size has a lot to do with the play involved on the shaft, but this is just a general question looking for some more information. (each side on the picture between the bar is a different setup)

Hello,
Just my $0.02 thoughts on the subject.

First thing, imho you should conceptually separate the two functions: linear guidance and linear motion.

1) Belts and screws are for linear motion. The play you should be concerned with here is along the axis of motion and is generally called backlash. Whether you are using belts or screws, there are ways to eliminate or minimize backslash issues.

2) The smooth rods and linear bearings provide linear guidance. Using proper diameter rods and good quality bearings generally results in very little to no play at all (perpendicular to the axis of motion). Using three or four linear bearings is a matter of how carefully you can align them (incorrect alignment results in excessive friction), and how much play your application can tolerate. The Prusa i3 originally used three LM8UU bearings for each of the X and Y axis. But I have built a few P3Steel's (a Prusa i3 variant) with four LM8UU bearings for each of the X and Y axis, and I can confirm there is a little less play and a little more friction with this arrangement. However, the quality of the prints of these P3Steel's is the same as with a well-built Prusa i3 with three LM8UU bearings for each of the X and Y axis. So the jury is still out.

Actually there is a term you can google: over constrained axis

It isnt about the alignment of the bearings. It has to do with how and where the load is attached.

For example. The Y axis on a cartesian printer such as the Prusa. Some bottom plates have four bearings some have three. The common denominator is the load eg the belt is attached in the middle. In that arrangement four bearings is good. Three allows lateral play in the bearings to twist the bed.

With three bearings it is better to have the load closer to the lead bearings which are two on one axis and one on the follower side.

Im not an expert but that is what i have read on mechanical design sites.

I agree with thetazzbot.
Belt attached in the center of the bearings allows the table to wobble. ( Even with four bearings ).
There will always be differences in friction while the table moves along the rods. Those can make the table wobble.

three bearings => belt attached on the dual bearing side
four bearings => two belts / steppers (one on each side )
-Olaf