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A 4-bar mechanism with all revolute pairs has link lengths lf = 20 mm, lin = 40 mm, lco = 50 mm and lout = 60 mm. The suffixes 'f', 'in', 'co' and 'out' denote the fixed link, the input link, the coupler and output link respectively. Which one of the following statements is true about the input and output links?

A 4-bar mechanism with all revolute pairs has link lengths lf = 20 mm, lin = 40 mm, lco = 50 mm and lout = 60 mm. The suffixes 'f', 'in', 'co' and 'out' denote the fixed link, the input link, the coupler and output link respectively. Which one of the following statements is true about the input and output links? Correct Answer Both links can execute full circular motion

Concept:

Grashof’s law:

It states that for a planar four-bar mechanism the sum of shortest and longest link length can’t be greater than the sum of remaining two link length if there has to be continuous relative motion between them.

L + S ≤ P + Q  (first check this condition then proceed further)

∴ for continuous relative motion, this relation should be satisfied.

Inversions (arrangement of links) of planar four-bar mechanism.

Case 1: L + S < P + Q

  • When the shortest link is fixed → Double crank mechanism, it means both input and output link can do the complete circular motion.
  • When link adjacent to shorter link is fixed → Crank rocker mechanism, it means one of the links can do complete circular motion and other can partially circular motion (oscillates)
  • When shortest is coupler → Double rocker mechanism, it means both links cannot do complete circular motion ( they can only oscillate).

Case 2: L + S = P + Q

  • All the inversions are similar to case 1.

Case 3: L + S > P + Q

All the inversions result in double rocker mechanism.

Calculation:

Given:

S = 20 mm, L = 60 mm, P= 40 mm, Q = 50 mm and S is fixed.

First, check if there is continuous motion or not i.e. relation L + S ≤ P + Q is satisfied or not.

L + S = 20 + 60 = 80 mm and P + Q = 40 + 50 = 90 mm

As, L + S < P + Q 

∴ Continous motion is possible.

Now as the shortest link is fixed, so there will be a double crank mechanism which means both input and output link can do the complete circular motion.

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