Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_42

⚡ Mecademy AIENG정역학 · ch7  Problem Statement In the mechanism shown, rod AC slides through the pivoted collar at B and compresses the spring when the couple M is applied to link DE. The spring has a stiffness k and is uncompressed for the position . Determine the angle for equilibrium. The masses of the parts are negligible. Problem 7/42 (a) Determination of the equilibrium angle ● Calculation Process 1. Identify the Geometry and Kinematics: From the diagram, the mechanism consists of a fixed vertical axis containing points and . Link of length is pivoted at and makes an angle with the vertical. Link of length is connected to and . Rod is pivoted at and slides through a pivoted collar at . The vertical distance between and is given by the segments of length and , so . Due to the parallelogram configuration, link remains parallel to the vertical line . Let's set a coordinate system with at the origin . Then: Coordinates of : Coordinates of : Coordinates of : Since is vertical and has length , 2. Determine Spring Compression: The spring is on rod , and its compression is related to the distance between and the fixed collar . Since the spring is uncompressed when , and at , , the compression is simply the distance . θ=0θ θ DBDEa DθEAbE AACAB DBabBD= a+bEA BDD(0,0) B(0,a+b) E(asinθ,acosθ) AEAbA= (asinθ,acosθ+b) ACδ AB θ=0θ=0A=(0,a+b)=B AB δ=AB= (x −x )+(y −y ) AB 2 AB 2 δ= = (asinθ−0)+(acosθ+b−(a+b)) 22 asinθ+a(cosθ 2 2 2 3. Apply the Principle of Virtual Work: The active forces