Answer to Question #154858 in Mechanical Engineering for Pranav Gaikwad

Question

In a crank and slotted lever mechanism, the length of crank is 560 mm and the

ratio of time of working stroke to return stroke is 2.8. Determine (a) distance

between the fixed centres, and (b) the length of the slotted lever, if length of

stroke is 250 mm.

Answer 1

$\frac{180-\beta}{\beta} = \frac{1}{QPR}=\frac{1}{2.8}$

$\frac{180-\beta}{\beta} = 2.8 \implies \beta= 2.8 \times180 -2.8\beta$

$\beta=\frac{180\times2.8}{3.8}=\implies \frac{\beta}{2}=\frac{90\times2.8}{3.8}$

$cos(\frac{\beta}{2})=\frac{AB_1}{AC}$

$cos(\frac{90\times2.8}{3.8})=\frac{560}{AC}$

$AC = 1394 mm$

$Stroke =2\times CD \times\frac{AB_1}{AC}$

$250 =2\times CD \times\frac{500}{1394}$

$CD=\frac{250 \times 1394}{2 \times 500}=348.5 mm$