Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_27

⚡ Mecademy AIENG정역학 · ch7  Problem Statement Express the compression in the hydraulic cylinder of the car hoist in terms of the angle . The mass of the hoist is negligible compared with the mass of the vehicle. Problem 7/27 (a) Expression for the compression force in the hydraulic cylinder 1. Formula: The principle of virtual work states that for a system in equilibrium, the total virtual work done by all active forces during a virtual displacement is zero: In this problem, the active forces are the weight of the vehicle and the compressive force in the hydraulic cylinder. 2. Substitution: Let the platform be supported by parallel links of length (as indicated by the label parallel to the middle link). The platform remains horizontal at a height . Thus, the vertical position of the vehicle's center of mass is: The virtual displacement of the center of mass is: The hydraulic cylinder is connected between a fixed ground pivot and the top joint of one of the links. Let be the length of the cylinder. From the geometry of the triangle formed by the link base, the cylinder base, and the top joint, we use the law of cosines: Differentiating both sides with respect to : 3. Calculation: The virtual work done by the weight is negative as the height increases: . The virtual work done by the internal compressive force as the cylinder expands is positive: . Applying the equilibrium Cθ m C δW=F ⋅ ∑ i δr + i M ⋅ ∑ j δθ = j 0 W=mg C b b y=bsinθ y = G bsinθ+constant δy = G δθ = dθ dy G bcosθ