Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_60

⚡ Mecademy AIENG정역학 · ch7  Problem Statement The cylinder of mass is held in the equilibrium configuration by means of three light links and a nonlinear spring near . The spring is uncompressed when link is vertical, and the potential energy in the spring is given by , where represents the amount of spring deformation from the uncompressed position and the constant is related to the stiffness of the spring. As increases, the rod, which is connected at , slides through the pivoted collar at and compresses the spring between the collar and the end of the rod. Determine the values of for system equilibrium over the range and state whether the system is stable or unstable in those positions for , , and . Assume no mechanical interference for the indicated range of motion. Problem 7/60 (a) Equilibrium and Stability Analysis 1. Formula: The total potential energy of the system is the sum of the gravitational potential energy and the elastic potential energy . The equilibrium positions are found where the first derivative of the potential energy with respect to is zero: The stability is determined by the sign of the second derivative at the equilibrium positions: - Stable if - Unstable if 2. Substitution: From the geometry of the mechanism: Coordinates of : (taking as the origin) Coordinates of : Spring deformation Height of mass : mθ EOA V = e kδ 3 δ k θAE θ 0≤θ≤90 ∘ k= 35 N/m 2 b=600 mmm=2 kg V V g V e V=V + g V e θ = dθ dV 0 dθ 2 dV 2 > dθ 2 dV 2 0 < dθ 2 dV 2 0 E(0,b)O A(bsinθ,