Project ForgeAn offset slider-crank mechanism has crank length 20 mm, connecting rod length 40 mm, and an offset of 10 mm between the crank pivot and the line of stroke. Conventionally, the Quick Return Ratio (QRR) is considered to be greater than one. The value of QRR is __________.
Explanation
The slider's extreme (dead-center) positions occur exactly when the crank pivot O, crank pin A, and slider P are collinear, i.e. OP = r+l (extended) or OP = l−r (folded). With r=20, l=40, offset e=10: for OP=r+l=60, the point P on the offset line (distance e=10 from O) has x=√(60²−10²)=59.16, giving crank angle ≈−9.62° (≡350.38°). For OP=l−r=20, x=√(20²−10²)=17.32, giving OP direction −30°, and since A lies opposite P from O in this folded case, crank angle=−30°+180°=150°. The crank sweeps 159.62° between these angles going one way and 200.38° the other way (summing to 360°). QRR = larger arc/smaller arc = 200.38/159.62 ≈ 1.255.
Source: GATE ME 2014 (Session 1 / Set-1) (2014)
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