Discussion
In a crank and slotted lever quick return mechanism, the distance between the fixed centres is 400 mm and the length of the crank is 200 mm. If the length of the slotted bar is 2000 mm, what is the Ratio of time of cutting stroke to time of return stroke.
Answer: C
The ratio of cutting time to return time is 2.
In the crank and slotted lever mechanism, the extreme positions of the slotted lever occur when it is tangent to the crank circle, which makes a right angle between the crank and the lever. If the return stroke takes a crank angle \(\beta\), then
\[ \begin{aligned} \cos\frac{\beta}{2} &= \frac{\text{crank}}{\text{centre distance}} = \frac{200}{400} = 0.5 \\ \frac{\beta}{2} &= 60^{\circ}, \quad \beta = 120^{\circ} \end{aligned} \]
The cutting stroke takes the rest of the turn, \(360^{\circ} - 120^{\circ} = 240^{\circ}\). At uniform crank speed, the time ratio is \(\frac{240}{120} = 2\). The 2000 mm length of the slotted bar affects the length of the stroke, not the time ratio, so it is not needed here.
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