Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_81

⚡ Mecademy AIENG정역학 · ch4  Problem Statement The dual-grip clamp shown in the figure is used to provide added clamping force with a positive action. If the vertical screw is tightened to produce a clamping force of 3 kN and then the horizontal screw is tightened until the force in the screw at A is doubled, find the total reaction R on the pin at B. Problem 4/81 (a) Calculation of the total reaction at pin B To find the total reaction at pin , we analyze the equilibrium of the lever arm (the internal movable part of the clamp). We first determine the initial state when only the vertical screw is tightened, and then the final state after the horizontal screw force at is doubled. 1. Initial Equilibrium of the Lever Arm: When the vertical screw is tightened to produce a clamping force , the workpiece exerts an equal and opposite downward force on the lever arm jaw. For the lever arm to be in equilibrium, the horizontal screw at must exert a balancing force . Summing moments about the pin : 2. Final State Analysis: The horizontal screw is further tightened until the force at is doubled. Let be the new force in the horizontal screw and be the new clamping force. Maintaining the moment equilibrium about for the new state: B A C=3 kN A F A B M = ∑ B 0⟹C⋅d − jaw F ⋅ A d = A 0 3 kN⋅75 mm−F ⋅ A 125 mm=0 F = A 3⋅ = 125 75 1.8 kN AF A ′ C ′ F = A ′ 2⋅F = A 2⋅1.8 kN=3.6 kN B C⋅ ′ 75 mm=F ⋅ A ′ 125 mm C= ′ 3.6⋅ = 75 125 6 kN 3. Calculation of Pin Reaction Components: From the force equili