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



1
Expert's answer
2021-06-01T03:46:10-0400

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


"\\dfrac{W_D}{W_C} \u00d7\\dfrac{W_C}{W_B}\u00d7 \\dfrac{W_B}{W_A} =\\dfrac{T_C}{T_D} \u00d7\\dfrac{T_B}{T_C}\u00d7 \\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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