Try to design a worm$-$gear mesh with one of FOS $($contact$,$ wear, or bending$)$ to connect an induction motor to a centrifugal pump. The motor speed is $1125re\frac{v}{m}in,$ and the velocity ratio is to be $11$:$1.$ The input power requirement is $15$ hp $.$ For this service $K_{a}1\mathrm{.}1$ is appropriate. Additionally, a design factor $n_d$ of $1\mathrm{.}1$ is to be included to address other unquantifiable risks. Materials are High test cast iron for worm and cast bronze for the worm gear. Worm axial pitch $=1\mathrm{.}75$ in$.$