3 bushing configuration formula

Hi,

I'm designing a small 3D printer and I want to use brass bushings and T2.5 timing belts for X, Y axis: 2 rods and 3 bushing per axis.

I saw in repRap and other designs that usually there are two bushing (or linear ball bearing) in the rod where the belt is clamped and the other bushing slides in the parallel rod, but shifted a litle with regards to the others ones. I tried some of these configurations and I saw that it's not so easy to move the guide smoothly if the bearings/bushings and belt forces are not in the correct position.

My question is: Does anybody know a formula to design this kind of linear systems? I mean, a formula to calculate the position of a 3 bushing (or linear ball bearings) + timing belt configuration.

Thanks in advance.

If the rods are spaced correctly and parallel, it shouldn't matter much where the belt is relative to the bushings. Near the rod with 2 bushings is best because it minimizes the loads on the bearings.

To avoid stick and slip effect and possible wear out due to exposed mass best would be as the busings and the belts fixation are in one plane which also intersects the center of mass of the moving parts!

the wider the busings are from ach other. the more tolerant is the system in case of exposed mass .. the closer.... ( perhaps you know that funny game woodpecker picking down a rod : same effect - just there it is wanted)

Also, the parallel rods shouldn't be too far apart. As a rule of thumb, the distance between the rods shouldn't exceed the distance between front and back bushing. Less is better.

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