Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_20

⚡ Mecademy AIENG정역학 · ch7  Problem Statement The elevation of the platform of mass supported by the four identical links is controlled by the hydraulic cylinders and which are pivoted at point . Determine the compression in each of the cylinders required to support the platform for a specified angle . Problem 7/20 (a) Determination of cylinder compression force 1. Formula: The principle of virtual work for a system in equilibrium is given by: For this mechanism, the active forces are the weight of the platform and the compressive forces in each of the two hydraulic cylinders. The equation becomes: where is the vertical height of the platform and is the length of each cylinder. 2. Substitution: From the geometry of the symmetric linkage with four links of length and bottom pivot points at a fixed horizontal distance from the center: The vertical height of the platform is . The coordinates of joint relative to bottom pivot are . The length of cylinder is . Taking the virtual variations with respect to : Substituting these into the virtual work equation: m ABACA Pθ P δU= F⋅ ∑δr+ M⋅ ∑δθ=0 W=mg P δU=−mgδy+2PδL=0 yL bb y=2bsinθ BA(0,0)(−b+ bcosθ,bsinθ) ABL= = (−b+bcosθ)+(bsinθ) 22 b = 2−2cosθ2bsin(θ/2) θ δy= (2bsin θ ) δθ = dθ d 2bcosθδθ δL= (2bsin( θ /2)) δθ = dθ d bcos(θ/2)δθ −mg(2bcosθδθ)+2P(bcos(θ/2)δθ)=0 3. Calculation: Simplify the equation by canceling common terms : Solve for : Using the double-angle identity , we can also express this as: 4. Result: The magnitude of the c