Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_44

⚡ Mecademy AIENG정역학 · ch7  Problem Statement In the figure is shown a small industrial lift with a foot release. There are four identical springs, two on each side of the central shaft. The stiffness of each pair of springs is 2k. In designing the lift, specify the value of k which will ensure stable equilibrium when the lift supports a load (weight) L in the position where with no force P on the pedal. The springs are equally precompressed initially and may be assumed to act in the horizontal direction at all times. Problem 7/44 (a) Stability Analysis of the Industrial Lift ● Calculation Process 1. Present Final Formula: The total potential energy of the system is the sum of the gravitational potential energy of the load and the elastic potential energy of the springs. We define the datum for gravitational potential at the base of the mechanism. For a single link of length , the vertical height is and the horizontal displacement of the roller is . With a total vertical load and two identical symmetric links, the total gravitational energy is: There are four identical springs total, organized into two pairs (one pair for each side/link). The problem states each pair has a stiffness of . For a symmetric precompressed setup that maintains equilibrium at , the total horizontal stiffness acting on the mechanism as it spreads is the sum of the stiffnesses of the pairs. The total elastic energy is: (Note: Precompression in a symmetric opposing setup does not affect the stiffness o