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The gear train transmits power from a motor to a machine at $E.$ The motor turns at $1970$ rpm $.$ The diameter of solid shaft $(1)$ is $1\mathrm{.}74$ in$.,$ the diameter of solid shaft $(2)$ is $2\mathrm{.}42$ in$.,$ and the allowable shear stress for each shaft is $6\mathrm{.}7$ ksi $.$ Assume $N_A=23$ teeth, $N_B=73$ teeth, $N_C=21$ teeth, $N_D=52$ teeth. Determine:

$($a$)$ the maximum power $P$ that can be transmitted by the gear train.

$($b$)$ the torque $T_E$ provided at gear $E.$

$($c$)$ the rotation speed ${}_E$ of gear $E.$

Answers:

$($a$)P=q,$ hp$.$

$($b$)T_E=$ lb$-$ft$.$

$($c$){}_E=$ rpm$.$