GATE ME 2015 Set 2 — Question 19
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Theory of Machines & Vibrations → Cams, Gears & Gear Trains → Kinematic Pairs, Chains & DOF
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Question
The number of degrees of freedom of the planetary gear train shown in the figure is
Correct answer
(C) 2
Solution
For a planetary gear train, the degrees of freedom (DOF) can be calculated using Kutzbach's criterion: .
In a standard planetary gear train consisting of a sun gear, a planet gear, an arm, and a ring gear (assuming the frame is the 5th link if none are fixed):
(Frame, Sun, Planet, Ring, Arm)
(Revolute joints: Frame-Sun, Frame-Ring, Frame-Arm, Arm-Planet)
(Higher pairs/gear meshes: Sun-Planet, Planet-Ring)
.
Alternatively, for a planetary gear train, we need two inputs (e.g., speeds of any two members) to uniquely determine the speeds of all other members. Thus, .
In a standard planetary gear train consisting of a sun gear, a planet gear, an arm, and a ring gear (assuming the frame is the 5th link if none are fixed):
(Frame, Sun, Planet, Ring, Arm)
(Revolute joints: Frame-Sun, Frame-Ring, Frame-Arm, Arm-Planet)
(Higher pairs/gear meshes: Sun-Planet, Planet-Ring)
.
Alternatively, for a planetary gear train, we need two inputs (e.g., speeds of any two members) to uniquely determine the speeds of all other members. Thus, .
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