Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_28

⚡ Mecademy AIENG정역학 · ch7  Problem Statement Determine the force between the jaws of the clamp in terms of a torque exerted on the handle of the adjusting screw. The screw has a lead (advancement per revolution) , and friction is to be neglected. Problem 7/28 (a) Determination of the clamping force ● Calculation Process 1. Present Final Formula: We use the principle of virtual work for a system in equilibrium. Neglecting friction, the virtual work done by all external forces and couples for an infinitesimal virtual displacement must be zero: where: is the applied torque. is the virtual rotation of the screw. is the clamping force between the jaws. is the virtual change in the separation distance between the jaw faces. 2. Substitute Values: The screw's lead defines the linear advancement of the screw joints for a given rotation : From the geometry of the symmetric linkage shown in Problem 7/28: The distance between the upper screw joints is . The distance between the vertical jaw faces is . By taking the differential with respect to : FM L F δU δU=Mδφ−Fδy=0 M δφ F δy Lδx δφ δx= δ φ⟹ 2π L δφ= δ x L 2π x=2bsinθ y=2(bsinθ−a) θ δx= (2bsin θ ) δθ = dθ d 2bcosθδθ 3. Partial Operations: Comparing the two expressions for virtual linear displacement: Now, substitute the expressions for and back into the virtual work equation: Since is a non-zero virtual displacement, we can divide it out: 4. Final Calculation: Solving for the clamping force : ● Final Conclusion: The force between the