Coupled forces, equivalent couple?

Question

The two shafts of a speed-reducer unit are subjected to couples of magnitude M1 = 18 N-m and M2 = 7.5 N-m. Replace the two couples with a single equivalent couple, specifying its magnitude and the direction of its axis.

Diagram:
http://i236.photobucket.com/albums/ff35/bugmenot_07/72.jpg

Answer 1

Mr = ((Mz)^2 + (Mx)^2)^0.5
Mr = (324 + 56.25)^0.5 = 19.5 N-m = the single equivalent couple

Cos z = Mz/Mr = 18/19.5 = .932307
so the angle which the resultant moment couple makes with the z axis is = 21.2 degrees
Cos x = Mx/Mr = 7.5/19.5 = .38461
so the angle which the resultant moment couple makes with
the x axis is = 67.4 degrees

Answer 2

If F1,F2,F3 are the three pairs of forces and C1,C2,C3 are the coressponding couples(2d of the forces approximately any ingredient),then C1=F1*X1,C2=F2*X2 and C3=F3*x3 the place X1,X2,X3 are the perpenduicular distances between each and each pairs of forces. ( X1 is the perpenduicular distances between the two F1 s. X2 is the perpenduicular distances between the two F2 s. X3 is the perpenduicular distances between the two F3 s. ) If F is the equivalent pair of forces and X is the equivalent perpenduicular distances between the two F3 s. Then, F1*X1+F2*X2+F3*x3 = F*X by using the above equation nonetheless we can not discover F and X one after the different we are in a position to discover the product F*x this is the equivalent couple (2d of the eqivalent tension approximately any ingredient). to discover F and X one after the different we would desire to seek for another equation. all of us comprehend F is the ensuing tension of the three forces. consequently F = F1+F2+F3 (be conscious that this may well be a vector addition and not asimple adition we would desire to take under consideration the direction. the easy way is to decide for each and all the forces into horizontal and vertical comoponents and the guidelines bieng the two vertical or horizontallthe undertaking may well be performed as uncomplicated sum) Having got here upon F, Xcan be solved from F1+F2+F3/ F