include a sketch of your stepped cylindrical shaft, showing all diameters, fillet radii, and keyways. also note where bearings will be placed. use the failure criteria in chapter 7 to determine the minimum diameters at the critical locations on the shaft. design keys to transmit torque between the two gears and the shaft. shaft design constraints: the intermediate shaft must be designed as a solid shaft of length no larger than 300 mm. the shaft will be supported by two 15 mm wide ball bearings (you are not required to specify the bearings). minimum distance between the bearings and the next installed part on the shaft must be 20 mm, to facilitate good lubrication and cooling of the components within the gear box. distance between the two gears should be between 80 mm and 140 mm. clearly indicate how the two gears will be installed on the intermediate shaft and create a shaft layout before moving to the next step. you are to perform static and fatigue analysis for the shaft. for the fatigue analysis assume a reliability of 99%, a minimum required life of 107 cycles and light-shock loading. use appropriate materials for the shaft and indicate if heat treatments are required for any regions of the shaft. the minimum design factor for any region of the shaft should be 1.2.