 In this video, I want to briefly talk about shafts. So shafts are probably the most common component that we would encounter in a machine. Really, they're a structural component that serve to provide support for other things that we might talk about, gears, pulleys, any sort of transmission device, power transmission device. Shafts then take in torque, output torque, and are used as part of the power transfer system. So we talk about shafts in a variety of contexts, and shafts have already been covered when we talk about fatigue or just static loading, beam loading, things like that. So shafts can take a lot of different types of loads. They might be subject to axial loads, torsion loads, bending loads, and any combination thereof. So we might put together all of those different loads at the same time. And we have to know how to handle that from a stress calculation standpoint. So with that in mind, there's kind of two special considerations that I want to think about or talk about beyond that basic stress calculation that we would normally do. And the first is that we have to remember that shafts have rotational inertia themselves. So as a shaft is rotating, that shaft has mass, and that means that there is inertia behind that rotation, especially when we're talking about high speed rotations. So there's something called critical speeds, and that is when a shaft is rotating about its rotation center, but its mass center is not necessarily in the exact alignment with the rotation center. And that could be due to the components that are mounted to it, the shaft manufacturing or just being slightly out of balance, things like that. So that means that because that those two things are not perfectly aligned, and they pretty much never will be, that there is likely to be a speed at which the small perturbations in that motion of that shaft as it rotates are exacerbated, made much larger. And we're familiar with this idea from the concept of a natural frequency. We know that when we pluck something, or we vibrate something at its natural frequency, we get much larger motion out than at other frequencies. And the same thing is true of shafts. If we were to rotate that shaft at this natural frequency, where there is a critical situation, we can cause it to go unstable and cause large deflections. And we want to try to avoid that. So we'll talk about that in another video. We also want to think about how things are mounted to the shaft. So gears and other components can be mounted to shafts using a variety of methods. We could use keys, we could use set screws, snap rings, splines, and just press fitting. So each of these methods, probably with the exception of press fitting, involves some sort of modification of the shaft. And anytime we're modifying that geometry or doing something to the shaft, we're likely introducing stress concentrations and changing the overall size of the shaft and therefore likely weakening it in some way. So those considerations need to be brought forward as we think about shaft design as well. Thanks.