Calculate Resultant Couple from 3 Couples in 3D

[wannawin]

Homework Statement

Replace the three couples with a single resultant couple. Specify its magnitude and direction of its axis using angles to the positive x, y, and z axes.

Homework Equations

M = r x F (r cross F)

The Attempt at a Solution

I'm pretty sure I want to resolve the moments into their force components, but to do that I would need to set an r. But since I have no measurements other than the angle of inclines I don't see how I can do that.

 

[PhanthomJay]

Homework Statement

Replace the three couples with a single resultant couple. Specify its magnitude and direction of its axis using angles to the positive x, y, and z axes.

Homework Equations

M = r x F (r cross F)

The Attempt at a Solution

I'm pretty sure I want to resolve the moments into their force components, but to do that I would need to set an r. But since I have no measurements other than the angle of inclines I don't see how I can do that.

The nice thing about couples is that they are independent of 'r'...the moment of a couple about any point is the couple itself. The couple can be represented by a vector pointing perpendicular to the plane of the couple, following the right hand rule method for its direction (+ or - ) perpendicular to the plane. Then solve the resultant couple as a vector located anywhere on the plane, but with a certain magnitude and direction.

 

[wannawin]

Then I guess this question isn't that complicated at all. If you number the couples 1-3 going from left to right:
M_1x=0
M_1y=1.5cos20
M_1z=1.5sin20

M_2x=0
M_2y=1.5
M_2z=0

M_3x=0
M_3y=1.75cos25
M_3y=-1.75sin25

Therefore M_Rx=0
M_Ry=4.496
M_Rz=-0.2265

M_R has a magnitude of 4.5012

And the angles are 0 with the +x axis, 2.91 with the +y axis, and 87.1 with the -z axis (using simple trig)

Barring any issues with significant digits, I think that makes some sense since the resultant is almost vertical.

 

[PhanthomJay]

You may have your plus/- signs mixed...the y component points down, are you calling that the positive y axis? Otherwise, your work is very good.

 

[wannawin]

You may have your plus/- signs mixed...the y component points down, are you calling that the positive y axis? Otherwise, your work is very good.

I did. Good catch and thanks a lot