Linear Motion Stage with Offset Loading Problem

Question

I'm currently developing a linear motion system which will have to withstand a large offset load (see image below). There will be two rails, each with a carriage on, which will be connected by a beam/stage (see yellow beam); and a 1,000 kg load will hang 1 m away from the front carriage.

I'm trying to calculate the rolling moment that the carriages will experience due to the offset load. After doing a free body diagram of the system I believe the front carriage will experience a moment of:

M = 1 m * 1,000 kg * 9.81 m/s^2 = 9,810 Nm

And the back carriage will experience 0 Nm moment.

Therefore, I believe I will need some carriages which can withstand a rolling moment of at least 9,810 Nm.

However, I spoke to a linear motion supplier and their engineer stated that they didn't believe the front carriage would experience any moment loading at all, and so they quoted me for a carriage which could handle 1,000 kg of compressive load, but fell really short on it's moment roll load capacity; which was about 600 Nm. The only explanation they have given so far is that the back rail would highly reduce the moment experienced by the front carriage... but I disagree.

How much moment do you think the front and back carriages will experience and why?

Thanks in advance, James

Answer 1

I don't know what you mean by rolling moment. A 3d sketch of the rails and the beam would help.

As it is this is a basic cantilever beam. Ignoring the weight of the beam:

equating sum of the moments about the left rail =0:

$\Sigma M_{rail}=0 \quad -1000*1.5+R{carriage}*0.5=0$

$R{carriage}=1500*2=3000kg. \uparrow$

$R{rail}=3000-1000=2000kg\downarrow$

you should multiply these reactions by a factor of safety of 3 or whatever is your usage requires.