Shaft design, deflection consideration, linear and angular deflection

Deflection analysis at a single point of interest requires complete geometry information for the entire shaft.
For this reason, a common approach is to size critical locations for stress, then fill in reasonable size estimates for other locations, then perform deflection analysis.
Deflection of the shaft, both linear and angular, should be checked at gears and bearings.
There is a distinction between deformation and deflection. Deformation is dealing with the extension or compression of the beam/shaft, however, deflection is addressing the transverse displacement of the shaft.
Curvature Equation:
𝑦^′′ (𝑥)=𝑀(𝑥)/𝐼𝐸
Deflection Equation:
𝑦(𝑥)=∫∫𝑀(𝑥)/𝐼𝐸 𝑑𝑥
Angular deflection must be considered in addition to linear deflection. Large slope at bearings would cause increase in wear, friction and vibration