Deflection angle for idle gear development
When I develop the machine, I used to use some formulars in textbook which I studied at my university. I used the Castigliano's theorems so often and several cases were already solved so I just needed to apply it to my real case. But below case was not in my textbook, which I needed this case for my idle gear development so I made it by myself. M A B = − M ′ − F a c l M B C = − M ′ + F ( c − l − a ) M_{AB} = -M' - \frac{F a c}{l} \qquad M_{BC} = -M' + F(c - l - a) ∂ M A B ∂ M ′ = − 1 ∂ M B C ∂ M ′ = − 1 \frac{\partial M_{AB}}{\partial M'} = -1 \qquad \frac{\partial M_{BC}}{\partial M'} = -1 θ A = ∫ 0 l + a M ( ∂ M ∂ M ′ ) d c E I , (where M ′ = 0) \theta_A = \int_0^{l+a} M \left( \frac{\partial M}{\partial M'} \right) \frac{dc}{EI} \quad,\quad 2M' = 0 = ∫ 0 l − F a c l ( − 1 ) d c E I + ∫ l l + a F ( x − l − a ) ( − 1 ) d c E I = \int_0^l -\frac{F a c}{l} (-1) \frac{dc}{EI} \;+\; \int_l^{l+a} F(x - l - a)(-1)\frac{dc}{EI} = F a E I ∫ 0 l x l d ...
