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Question

The configuration of a mechanism is shown in the figure, where the link AB is collinear with link AD and both are horizontal. The link DC is vertical. The link AB has an instantaneous angular velocity of 3 rad/sec in CCW direction. AB = l 0 cm, BC = 50 cm, CD = 30 cm, AD = 50 cm. The angular velocity of link DC is


A
3/4 rad/sec CCW
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B
4/3 rad/sec CW
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C
3/4 rad/sec CW
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D
4/3 rad/sec CCW
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Solution

The correct option is C 3/4 rad/sec CW

Given date:

AB=10cm

BC=50cm

CD=30cm

ω2=3rad/sec(CCW)

From Kennedy theorem, we know that

ω2(I23I12)=ω3(I23I13)

I13 isnot knownso we locate itusing Kennedy theorem as shown in figure

It lies at I41

I23I12=AB=10 cm,

I23I13=BD=40 cm,

3×10=ω3×40

ω3=34rad (CW)

Direction is CW because I12 & I23 lie opposite to I23

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