Answer to Question #200268 in Mechanical Engineering for Muhammad Idrees

Question

An epicyclic gear train, as shown in Fig. 13.35, is composed of a fixed annular wheel A having 150 teeth. The wheel A is meshing with wheel B which drives wheel D through an idle wheel C, D being concentric with A. The wheels B and C are carried on an arm which revolves clockwise at 100 r.p.m.

about the axis of A and D. If the wheels B and D have 25 teeth and 40 teeth respectively, find the number of teeth on C and the speed and sense of rotation of C

Answer 1

Velocity ratio (not considering arms speed, i.e W_arm = 0)

$\dfrac{W_D}{W_C} ×\dfrac{W_C}{W_B}× \dfrac{W_B}{W_A} =\dfrac{T_C}{T_D} ×\dfrac{T_B}{T_C}× \dfrac{T_A}{T_B}$

$\dfrac{W_D}{W_A}= \dfrac{T_A}{T_D}$

Now consider the arm speed (W_arm)

Velocity ratio;

$\dfrac{W_D-W_{arm}}{W_A-W_{arm}} =\dfrac{T_A}{T_D}$

W_A = 20

T_A = 150

T_D = 40

$\dfrac{W_D+100}{100} =\dfrac{150}{40}$

W_D = 275 rpm (ccw)