GATE ME 2019 Set 2 — Question 49
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Theory of Machines & Vibrations → Mechanisms & Linkages → Four-Bar & Slider-Crank
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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 . Length of different links are:
,
.
The magnitude of the angular speed of the output link 4 is at the instant when link 2 makes an angle of with as shown. The ratio is ______ (round off to two decimal places).
,
.
The magnitude of the angular speed of the output link 4 is at the instant when link 2 makes an angle of with as shown. The ratio is ______ (round off to two decimal places).
Correct answer
0.78 to 0.8
Solution
We can use the instantaneous center (I-center) method. The ratio of angular velocities of links 2 and 4 is given by:where is the instantaneous center of link 4 relative to link 2. lies at the intersection of the line joining and (link 1) and the line joining and (link 3).
Let be at and be at .
At the given instant, link 2 is at , so is at .
Link 3 () has length and link 4 () has length .
Let be .
Subtracting the two equations gives .
Substituting into .
Solving for : .
So .
The line passes through and .
Slope .
Equation of line : .
is the intersection of and the -axis ():
.
.
Distances:
Ratio:Rounding to two decimal places, the ratio is .
Let be at and be at .
At the given instant, link 2 is at , so is at .
Link 3 () has length and link 4 () has length .
Let be .
Subtracting the two equations gives .
Substituting into .
Solving for : .
So .
The line passes through and .
Slope .
Equation of line : .
is the intersection of and the -axis ():
.
.
Distances:
Ratio:Rounding to two decimal places, the ratio is .
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