Engineering Statics

A-16


The input and output torques from a gear box are shown. Determine the magnitude and direction of the resulatant torque. (Note the altered axis positions.)

The first thing we do is draw a free body diagram of just the 
torque or moment vectors.
We note that the moment vector M1 is 750 in the i-direction.
We note that the moment vector M2 is 200 in the j-direction.
Similarly, we see that the moment vector M3 is 
150 times the cosine of 45° in the j-direction, and 
150 times the cosine of 45° in the k-direction.
The moment vector M4 is 125 in the k-direction.
We sum the moments in vector form...
We can see the componets of the vector.
The magnitude can be determined using the Pythagorean theorm.
Note that the units are in Nm.