Project ForgeA quick return mechanism has a crank OS driven at 2 rev/s counter-clockwise, with the slotted-lever pivot O positioned 500 mm from the crank center O. If the quick return ratio is 1:2, then the length of the crank in mm is
- 250
- B250√3
- C500
- D500√3
Explanation
At the mechanism's dead centers, the crank OS is tangent to (perpendicular to) the line from the crank pin to the lever pivot, giving cos(φ)=r/d where d=500mm is the distance between the fixed pivots and φ is the half-angle (at the crank center) of the smaller (return) stroke's swept arc. With return:forward angle ratio 1:2, the return sweep is 2φ and forward is (360°−2φ), so 2φ/(360−2φ)=1/2, giving φ=60°. Then r=d·cos(60°)=500×0.5=250 mm.
Source: GATE ME 2007 (2007)
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