Keys and pins are used to secure rotating elements such as gears, pulleys, etc. on a transmission shaft. Consider a shaft transmitting power P kW at N revolutions per minute using a gear. Describe in detail the design steps of selecting a suitable key to mount a gear on the shaft. Please note that keys transmit torque from the shaft to the gear, and in the process are subjected to both shear stress, and crushing stress. Your design steps should include a free body diagram of the key, identifying all the forces it is being subjected to, followed by stress calculation based on its assumed size/dimensions. You will also need to select appropriate failure criteria, along with design factor of safety to determine the size/dimensions of the key. You may assume any variable you may need in your design steps but please state all your assumptions.