Mechanical Engineering > GATE 2025 > Kinematics of Mechanisms
An offset slider-crank mechanism is shown in the figure below. The length of the stroke of the slider is ______ mm (rounded off to nearest integer).

Correct : 62.05 ≈ 62 mm

The correct stroke length of the slider is 62 mm.
From the figure: crank radius r = 30 mm, connecting rod length l = 50 mm, and offset e = 10 mm.
For an offset slider-crank mechanism, the slider reaches its two extreme positions when the crank and connecting rod are fully collinear — once stretched out (Inner Dead Centre) and once folded back (Outer Dead Centre).
The stroke length formula is:
Stroke = √((r + l)2 − e2) − √((l − r)2 − e2)
At Inner Dead Centre (IDC) — crank and rod both point toward the slider:
x1 = √((30 + 50)2 − 102) = √(6400 − 100) = √6300 = 79.37 mm
At Outer Dead Centre (ODC) — crank folds back against the rod:
x2 = √((50 − 30)2 − 102) = √(400 − 100) = √300 = 17.32 mm
Stroke = 79.37 − 17.32 = 62.05 ≈ 62 mm

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