Question

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 ω2. Length of different links are :

O2O4 = O2A = L,

AB = O4B = √(2)L.

The magnitude of the angular speed of the output link 4 is ω4 at the instant when link 2 makes an angle of 90° with O2O4 as shown. The ratio ω4is __________ (round off to two decimal places).

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Answer :

0.79


O2A = O2O4 = L

AB = O4B =  √2L


I24 I12 ω2 = I24 I41 ω4

I24 I12 = L tan 75° (from  le I24 I12 I23 )

I24 I41 =  L + L tan 75°

ω42 = I24I12 / I24I41  = L tan 75°/ (L + Ltan 75°) = 0.788

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