In the double-reduction gear train shown, shaft a is driven by a motor attached by a flexible coupling attached to the overhang. The motor provides a torque of 2500 lbf in at a speed of 1200 rpm. The gears have 20° pressure angles, with diameters shown in the figure. Use an AISI 1020 cold-drawn steel. Design shaft a with a design factor of 1.5 by performing the following tasks. Given; Se = 24.5kpsi, Sut = 68kpsi, Sy =37.5kpsi, Ma = 2178 lbf-in, Tm 2500 lbf-in and Mm = Ta=0, kf 1.9, kfs =2.6. a) Sketch a general shaft layout, including means to locate the gears and bearings, and to transmit the torque. b) Perform a force analysis to find the bearing reaction forces, and generate shear and bending moment diagrams. c) Determine potential critical locations for stress design. d) Determine critical minimum diameters of the shaft based on fatigue DE-criterions, and check yielding of the shaft using static stresses at the critical locations. e) Make any other dimensional decisions necessary to specify all diameters and axial dimensions. Note: Dimensions are given in inches