Resolving Moments in 3D

Seven7

1. The problem statement, all variables and given/known data

At a particular stage of the manufacturing process, a robotic arm has the position and loading shown in the figure;



Calculate the direct stresses due to bending and the shear stresses due to torsion.

2. Relevant equations

M = r x F

3. The attempt at a solution

First, I took the applied force and resolved the moments about point A as follows (assuming the applied force is travelling parallel to the z-axis);


M = r x F = i(1-0) -j(2-0) = i - 2j

I am fairly sure that the next step in the problem is resolving these moments about the x and y axes into a moment along the figure (a torsional moment) and a moment parallel to the BC section; please refer to the following diagram;



However I'm not exactly sure how to do this. A tutor told me it's ok to treat the moments as if they were forces but i can't get my head around the idea.

Any advice or help would be appreciated.

elbarto

I haven't had a great deal to do with moment vectors to this extent, but if your tutor has told you to treat the moments like forces maybe he is implying that to find the moment about the axis paralell to AB (I the moment producing the torsion in that member), then my guess would be to find the dot product of the moment you have found with the unit vector or dirrectional vector (what ever you like to call it of AB)

That is,
Mab=(i-2j) dot (0.6i+0.8j)=(0.6+1.6)=2.2
Mbc could be found in the same way?

Sorry I couldn't be of more help, might be something for you to have a look at anyway.

Elbarto

Seven7

i've had a look at something from one of last year's courses and i think you're right... cheers elbarto... very helpful