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GATE 2022 ME (ME1) – Question 38

Theory of Machines · Displacement, velocity and acceleration analysis of plane mechanisms · 2 marks · Multiple choice

A planar four-bar linkage mechanism with 3 revolute kinematic pairs and 1 prismatic kinematic pair is shown in the figure, where AB ⊥ CE and FD ⊥ CE. The T-shaped link CDEF is constructed such that the slider B can cross the point D, and CE is sufficiently long. For the given lengths as shown, the mechanism is

a ground link FG of length 3 cm. A link AG of length 5 cm pivoted at G, with a rigid arm AB of length 3 cm perpendicular to the line CE ending in a slider B on the line CE. The T-shaped link CDEF is pivoted at F, with FD = 1.5 cm perpendicular to the line CE.
  1. a Grashof chain with links AG, AB, and CDEF completely rotatable about the ground link FG
  2. a non-Grashof chain with all oscillating links
  3. a Grashof chain with AB completely rotatable about the ground link FG, and oscillatory links AG and CDEF
  4. on the border of Grashof and non-Grashof chains with uncertain configuration(s)

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Show answer and explanation

Correct answer: (B) a non-Grashof chain with all oscillating links

Explanation

The point A is always at the distance 3 cm from the line CE, while the pivot F is at the distance 1.5 cm from that line, on the same or the opposite side as the slider crosses D. So the distance FA can only be between $|3 - 1.5| = 1.5$ and $3 + 1.5 = 4.5$ cm. The point A moves on a circle of radius 5 cm around G, with $FG = 3$ cm, and the distance FA of that circle ranges from 2 to 8 cm. Since 8 > 4.5, the link AG cannot make a full turn, and then neither can the others. All the moving links only oscillate, so the chain is non-Grashof.