how did he get the reaction forces?

A double reduction gearbox design has developed to the point that the general layout and axial dimensions of the countershaft carrying two spur gears has been proposed, as shown in Fig. 7-10. The gears and bearings are located and supported by shoulders, and held in place by retaining rings. The gears transmit torque through keys. Gears have been specified as shown, allowing the tangential and radial fordes transmitted through the gears to the shaft to be dete where the superscripts + and r represent tangential and radial directions, respectively: and, the subscripts 23 and 54 represent the forces exerted by gears 2 and 5 (not shown) on gears 3 and 4 , respectively. EXAMPLE 7-2 Step I: Identify critical section W33=5401bfW54=2431lbr Solution Perform free body diagram analysis to get reaction forces at the bearings. RAz=115.0lbfRAy=356.7lbfRBz=1776.0lbfRBy=725.3lbf From Mx, find the torque the shaft between the gear: T=W23(d3/2)=540(12/2) 3240lbf in