For right-circular cylindrical shafts made up of different materials with an individual cylinder length Li and torque Ti. The angular deflection θ can be estimated accurately by the equation:

1
\(\theta = \sum \theta_i=\sum \frac{T_iL_i}{G_iJ_i}\)
2
\(\theta = \sum \theta_i=\sum \frac{T_iL_i}{G_l}\)
3
\(\theta = \sum \theta_i=\frac{T}{G}\sum \frac{L_i}{J_i}\)
4
\(\theta = \sum \theta_i=\sum \frac{T_i}{G_lJ_l}\)

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