Question

In a four-bar mechanism ABCD, the link lengths are given: AB = 800 mm, BC = 100 mm, CD = 400 mm, DA = 700 mm. If the mechanism is a double crank mechanism then the fixed link should be

• A. AB
• B. BC
• C. CD
• D. DA

Hint:

For a double crank mechanism, the fixed link must be the shortest, and Grashof’s law \( s + l<p + q \) must hold.

Answer 1

The Correct Option is B

Step 1: Understand the double crank mechanism.
A four-bar mechanism is a double crank (or crank-crank) mechanism if both the links adjacent to the fixed link can rotate fully (i.e., both are cranks). For a four-bar mechanism with links \( l \) (longest), \( s \) (shortest), \( p \), and \( q \), Grashof’s law states that the mechanism is a double crank if: \[ s + l<p + q, \] and the fixed link must be the shortest link for a double crank mechanism. Step 2: Identify the link lengths.
Given:
AB = 800 mm,
BC = 100 mm,
CD = 400 mm,
DA = 700 mm.
Sort the lengths:
Shortest (\( s \)): BC = 100 mm,
Longest (\( l \)): AB = 800 mm,
Others: DA = 700 mm (\( p \)), CD = 400 mm (\( q \)).
Step 3: Apply Grashof’s law.
Check the Grashof condition: \[ s + l<p + q, \] \[ 100 + 800<700 + 400, \] \[ 900<1100, \] which is true. The mechanism is Grashof, meaning it can have cranks. Step 4: Determine the fixed link for a double crank.
For a double crank mechanism, the fixed link must be the shortest link (BC = 100 mm). If BC is fixed:
Links AB and CD (adjacent to BC) become cranks and can rotate fully.
If any other link is fixed (e.g., AB, the longest), the mechanism becomes a crank-rocker or double rocker, not a double crank.
Step 5: Select the correct answer.
The fixed link must be BC (shortest link) for the mechanism to be a double crank, matching option (2).