Question

Consider a slider crank mechanism with given crank length (r) and connecting rod length (l) as the two sides and the line of stroke as base of a triangle. If the maximum area of triangle is obtained when the crank angle is ${75}^{\circ }$, then $l/r$ ratio will be

• A. 3
• B. 3.73
• C. 4.73
• D. 4

Answer 1

The correct option is B 3.73


$\text{Area}=\frac{1}{2}r\times \ell \times \sin \alpha$

$\text{For maximum area}\alpha ={90}^{\circ }$

$\varphi =90-75=15$

$r\sin 75=l\sin 15$

$\frac{\ell }{r}=\frac{\sin 75}{\sin 15}=\frac{1}{\tan 15}=3.73$