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Question

A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link 2 is rotating anticlockwise with a constant angular speed ω2. Length of different links are:
O2O4=O2A=L,AB=O4B=2L
The magnitude of the angular speed of the output link 4 is ω4at the instant when link 2 makes an angle of 90o with O2O4 as shown. The ratio ω4ω2is (round off to two decimal places).

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Solution



According to Arnold's Kennedy theorem,
tan75o=(I24I12)(L)
(I24I12)=(L tan 75o)=3.732 L
(I24I14)=4.732 L
ω2×(I24I12)=ω4(I24I14)
ω4ω2=I24I12I24I14
ω4ω2=(3.7324.732)=0.7886

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