Chapter 2.10, Problem 174P

The directions of rotation of the input shaft A and output shaft B of the worm-gear reducer are indicated by the curved dashed arrows. An input torque (couple) of $80\text{N}\cdot \text{m}$ is applied to shaft A in the direction of rotation. The output shaft B supplies a torque of $320\text{N}\cdot \text{m}$ to the machine which it drives (not shown). The shaft of the driven machine exerts an equal and opposite reacting torque on the output shaft of the reducer. Determine the resultant M of the two couples which act on the reducer unit and calculate the direction cosine of M with respect to the x-axis.