Project ForgeIn a slider-crank mechanism, the lengths of the crank and the connecting rod are 100 mm and 160 mm, respectively. The crank is rotating with an angular velocity of 10 radian/s counter-clockwise. The magnitude of linear velocity (in m/s) of the piston at the instant corresponding to the configuration shown in the figure (crank perpendicular to the line of stroke) is __________.
Explanation
With the crank AB perpendicular to the line of stroke AC, place A at the origin, B=(0,r) with r=0.1 m. Differentiating the loop-closure equation x_c(θ)=r cosθ+√(l²−r²sin²θ) with respect to θ and evaluating at θ=90° (sinθ=1, cosθ=0), the connecting-rod coupling term vanishes exactly, leaving dx_c/dt = −ωr = −(10)(0.1) = −1 m/s. So the piston speed is exactly ωr = 1.0 m/s at this instant, independent of the connecting-rod length.
Source: GATE ME 2017 Session 2 (ME-2) (2017)
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