Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_3

⚡ Mecademy AIENG정역학 · ch7  Problem Statement For a given force determine the angle for equilibrium. Neglect the mass of the links. Problem 7/3 (a) Determination of the equilibrium angle To determine the equilibrium position of the mechanism, we apply the Principle of Virtual Work. We consider a small virtual change in the configuration defined by the coordinate , denoted as . 1. Formula: For a system in equilibrium, the total virtual work done by all active external forces during a virtual displacement must be zero: The active forces in this problem are the applied horizontal force and the gravitational force (weight) of the platform of mass , which is . 2. Substitution: Let the pivot of the left link be at the origin . We express the positions of the points where forces are applied in terms of : Force : It is applied at the top end of the left link, which has a total length of . The coordinates of this point are . The force vector is . The virtual displacement of this point is . The virtual work done by is: Weight : The platform of mass rests on the horizontal link . The vertical position (height) of this link is . The weight vector is . The virtual vertical displacement is . The virtual work done by gravity is: Pθ θ θ δθ δU δU=F ⋅ ∑ i δr = i 0 P mW=mg (0,0) θ P 2b(x ,y )= BB (2bcosθ,2bsinθ) P=−Piδr = B δ(2bcosθ)i+δ(2bsinθ)j=(−2bsinθδθ)i+(2bcosθδθ)j P δU = P P⋅δr = B (−P)(−2bsinθδθ)=2Pbsinθδθ W=mgmAC y = m bsinθ W=−mgjδy = m δ(bsinθ)= bcosθδθ δU = W W⋅δr = m (−mg)(bcosθδθ)=