Answer to Question #208089 in Mechanical Engineering for Sanajit

Question

An epicyclic reduction gear has a shaft A fixed to arm B.The arm B has a pin fixed to its outer end and two heard C and E which are rigidly fixed,revolve on this pin. Gear C meshes with annular wheel D and gear E with pinion F.G is the driver pulley and D is kept stationary.The number of teeth are:D=80,C=10,E=24 and F=18.If the pulley G runs at 200r.p .m,find the speed of shaft A.

Answer 1

Speed ratio

$\frac{N_F}{N_D}=\frac{N_F}{N_E}*\frac{N_C}{N_D}$

$\frac{N_F}{N_D}=\frac{T_E}{T_F}*\frac{T_D}{T_C}$

The relative velocity of gears with respect to the arm

$\frac{N_F -N_{arm}}{N_D-N_{arm}}=-\frac{T_E}{T_F}*\frac{T_D}{T_C}$

$\frac{200 -N_{A}}{0-N_{A}}=-\frac{24}{18}*\frac{80}{10}$

$\frac{200 -N_{A}}{N_{A}}=\frac{24}{18}*8$

$200-N_A=10.667 N_A$

$N_A=17.14 rpm$ same direction as gear F