A planar four bar mechanism with all revolute joints has link lengths AB = 30  m, BC = 120 mm, CD = 100 mm and AD = 80 mm. The link to be fixed to obtain a double crank mechanism is

Correct option is A

​$$\begin{aligned}&\text{To determine which link must be fixed to get a \textbf{double crank mechanism}, we apply the \textbf{Grashof’s Criterion}:} \\[1em]&\textbf{Grashof’s condition:} \quad L + S \leq P + Q \\[1em]&\text{Where:} \\&\quad \bullet \ L = \text{Longest link} \\&\quad \bullet \ S = \text{Shortest link} \\&\quad \bullet \ P, Q = \text{The other two links (intermediate lengths)}\end{aligned}$$

$$\begin{aligned}&\bullet \ S = AB = 30\, \text{mm} \\&\bullet \ L = BC = 120\, \text{mm} \\&\bullet \ P = CD = 100\, \text{mm} \\&\bullet \ Q = AD = 80\, \text{mm} \\[1em]&\text{Now check Grashof's inequality:} \\&S + L = 30 + 120 = 150 \\&P + Q = 100 + 80 = 180 \\[1em]&\text{Since:} \\&S + L = 150 < 180 = P + Q \\[1em]&\boxed{\text{Grashof's condition is satisfied, so at least one link can make a full rotation.}}\end{aligned}$$​​​