GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

Question : 41 of 65

Marks: +1, -0

The sun (S) and the planet (P) of an epicyclic gear train shown in the figure have identicalnumber of teeth.

If the sun (S) and the outer ring (R) gears are rotated in the same direction with angular speed

ω_{5}

and

ω_{k}

, respectively, then angular speed of the arm

A B

Solution:

Arm	sum	Planet	ring
0	$+x$	$-x$	$- {x}(\;{T_{ {p}}}/{T_{ {R}}})$
0	$+x$	$-x$	$-x/3$
Y	$y+x$	$y-x$	$y-x/3$

{y}- {x} {/} 3=ω_{ {r}} ⇒ 3 {y}- {x}=3 ω_{ {r}}

{y}+ {x}=ω {s}

{y}+ {x}=ω_{ {s}}

4 {y}=3 ω_{ {r}}+ω_{ {s}}

y=\;{3}/{4} ω_{r}+\;{1}/{4} ω _s

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