Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_45

⚡ Mecademy AIENG정역학 · ch7  Problem Statement The two uniform links, each of mass m, lie in a vertical plane and are connected and constrained as shown. Rod BD is connected to the roller at B and passes through a pivoted collar at A. At the position , the stop C rests against roller A and the spring is uncompressed. As force P is applied perpendicular to link AE, the angle increases and the spring of stiffness k is compressed. Determine the force P which will produce equilibrium at an arbitrary angle . Problem 7/45 (a) Determination of the required force P ● Calculation Process 1. Present Final Formula: We use the principle of virtual work, , where is the total potential energy (gravitational and elastic). 2. Geometry and Potential Energy: Set the origin at the fixed collar . Then, roller is at . The spring is connected between and , so its length is . The spring is uncompressed at , giving an unstretched length . The compression of the spring is . The elastic potential energy is . The center of mass for both uniform links of length and mass is at their common center pivot. The height of this pivot is . The total gravitational potential energy is . 3. Virtual Work of Force P: The force is applied at point , which is at the end of link . The position of is . θ=θ 0 θ θ>θ 0 δU=δW − P δV=0V δW = P δV + g δV e ABx = B 2bcosθ ABL=2bcosθ θ=θ 0 L = 0 2bcosθ 0 x=L − 0 L=2b(cosθ − 0 cosθ) V = e kx= 2 1 2 k[2b(cosθ − 2 1 0 cosθ)]= 2 2kb(cosθ − 2 0 cosθ) 2 2bm y = H bsinθ V = g (2m)gy =