Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_22

⚡ Mecademy AIENG정역학 · ch7  Problem Statement The portable work platform is elevated by means of the two hydraulic cylinders articulated at points . Each cylinder is under a hydraulic pressure and has a piston area . Determine the pressure required to support the platform and show that it is independent of . The platform, worker, and supplies have a combined mass , and the masses of the links may be neglected. Problem 7/22 (a) Determination of required hydraulic pressure 1. Formula: The principle of virtual work for equilibrium is given by: For this system, the active forces are the weight of the platform and the forces from the two hydraulic cylinders . The equation is: where is the vertical height of the platform and is the vertical height of the cylinder attachment points . 2. Substitution: Based on the geometry shown in the diagram: The scissor lift consists of two stages. In each stage, let the total length of a diagonal link be . From the labels, a full link is composed of two segments. For the lower links, the half-length to the center hinge is (since there are two segments between the ground pin and ). Thus, . The total height of the platform supported by two such stages is . The cylinders are articulated at points . According to the labels, point is at a distance of from the ground pin along the link. Therefore, the height of point is . CpA pθ m p δU=F ⋅ ∑ i δr = i 0 W=mg F = cyl pA δU=−mgδy + P 2(pA)δy = C 0 y P y C C L Bbb/2 BL=2b y = P 2× (2bsinθ)=4bsinθ CC b/2C y