Question

An offset slider-crank mechanism is shown in the figure at an instant. Conventionally, the Quick Return Ratio (QRR) is considered to be greater than one. The value of QRR is

Answer 1

Length of connecting rod : $I_r=40mm$
Crank radius : $r=20mm$
Eccentricity : $e=10mm$
$\varphi =co{s}^{-1}\left(\frac{e}{I+r}\right)-co{s}^{-1}\left(\frac{e}{I-r}\right)$
$=co{s}^{-1}\left(\frac{1}{6}\right)-co{s}^{-1}\left(\frac{1}{2}\right)={20.4}^o$
$QRR=\frac{Timeofadvancestroke}{Timeofreturnstroke}$
$=\left(\frac{{\theta }_c}{2\pi N}\right)\left(\frac{2\pi N}{{\theta }_R}\right)$
$QRR=\frac{{\theta }_c}{{\theta }_R}=\frac{{180}^o+\varphi }{{180}^o-\varphi }$
$=\frac{{180}^o+{20.4}^o}{{180}^o-{20.4}^o}=1.25$