**Rigidity Analysis**

- Perform a rigidity analysis at the pinion location for the input shaft using the following procedure:

The deflection at the pinion, in the y-direction can be found using the following equation:

Note: If

a=b, first simplify the equation before solving by usinga=b=l/2where:

yis the deflection in the y-direction at the pinion location (B)_{B}

W_{t}is the tangential force acting on the pinion

ais the distance between points A & B

bis the distance between points B & C

Eis the Young's Modulus of Elasticity for the material of the shaft (Carbon Steel)

Iis the 2^{nd}moment of area of theshaft at the location of the pinion= p d^{4}/64

lis the total distance between points A & CSimilarly, find the deflection (

z) at B (pinion location), in the z-direction using_{B}Winstead of_{r}W, and calculate the_{t}total deflectionat the pinion using the following equation: