Answer to Question #200268 in Mechanical Engineering for Muhammad Idrees

Question #200268

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

Expert's answer

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

Velocity ratio;

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

WA = 20

TA = 150

TD = 40

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

WD = 275 rpm (ccw)

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