A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link 2 is rotating anti-clockwise with a constant angular speed \omega_{2}. Length of different links are : O_{2} O_{4}=O_{2} A=L A B=O_{4} B=\sqrt{2 L} The magnitude of the angular speed of the output link 4 is \omega_{4} at the instant when link 2 makes an angle of 90^{\circ} with {O}_{2} {O}_{4} as shown. The ratio {\omega_{4}}/{\omega_{2}} is________________ (round off to two decimal places).

GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper

Question : 48 of 65

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A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link 2 is rotating anti-clockwise with a constant angular speed

ω_{2}

. Length of different links are :

O_{2} O_{4}=O_{2} A=L

A B=O_{4} B=√{2 L}

The magnitude of the angular speed of the output link 4 is

ω_{4}

at the instant when link 2 makes an angle of

90^{∘}

with

{O}_{2} {O}_{4}

as shown. The ratio

\;{ω_{4}}/{ω_{2}}

is________________ (round off to two decimal places).

Your Answer:

Validate

Solution:

Using Instantaneous center method

I_{24} l_{12} ω_{2}=I_{24} I_{41} ω_{4}

I_{24} I_{12}=L \tan 75^{∘}(\;\text " from "\; ∆ I_{12} I_{23} I_{24})

I_{24} I_{41}=L+L \tan 75^{∘}

∴ \;{ω_{4}}/{ω_{2}}=\;{I_{24} I_{12}}/{I_{24} I_{41}}=\;{L \tan 75^{∘}}/{L+L \tan 75^{∘}}=0.788

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