Project ForgeA slider crank mechanism has crank length 30 mm and connecting rod length 70 mm. At the instant when the crank angle is 45°, a force of 40 N acts towards the left on the slider. Ignoring the effect of gravity, friction and inertial forces, the magnitude of the crankshaft torque (in N·m) needed to keep the mechanism in equilibrium is _________ (correct to two decimal places).
Explanation
By the virtual-work/instantaneous-power method, T = F·(dx/dθ), where x(θ)=r cosθ+√(l²−r²sin²θ). At θ=45°, r=30, l=70: r sinθ≈21.21, r²sin²θ=450, √(l²−r²sin²θ)=√4450≈66.71, r cosθ≈21.21. dx/dθ = −r sinθ[1+(r cosθ)/√(l²−r²sin²θ)] ≈ −21.21×[1+21.21/66.71] ≈ −21.21×1.318 ≈ −27.96 mm/rad. |T| = |F·dx/dθ| = 40×27.96/1000 ≈ 1.12 N·m.
Source: GATE ME 2018 Session 1 (Set 1) (2018)
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