GATE ME 2020 Set 1 — Question 18
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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 below.
For the mechanism to be a crank-rocker mechanism, the length of the link can be
Correct answer
(A) 80 mm
Solution
According to Grashof's law, for a four-bar mechanism to have at least one link capable of a full revolution, the sum of the shortest () and longest () link lengths must be less than or equal to the sum of the other two link lengths ( and ): . For a crank-rocker mechanism, the shortest link must be the crank (the link adjacent to the fixed link). In the given diagram, the fixed link is . Let be the crank.Given link lengths: , (fixed), , and .If is the shortest link ():Among the given options, only satisfies this condition. If , it is indeed the shortest link, and since it is adjacent to the fixed link, the mechanism will be a crank-rocker.
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