Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_108

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Consider the additional dimensional detail for the front-end loader of Prob. 4/107. Determine the force in the hydraulic cylinder CE. The weight of the bucket and its load is 4000 lb with center of gravity at G. You may ignore the effects of the weights of other members. Problem 4/108 (a) Analysis of the bucket and linkage system To determine the force in the hydraulic cylinder , we consider the entire bucket and tilt linkage assembly as a single system in equilibrium. This system is supported by the main lift arm at two points: the main pivot point and the hydraulic cylinder attachment point . By summing moments about the pivot point , we can isolate the effect of the cylinder force and the weight of the bucket . 1. Formula: Establish a coordinate system with the origin at point . The equilibrium condition for the moments about the pivot point is: 2. Substitution: Based on the provided dimensions, we identify the coordinates of the key points relative to : Center of Gravity: Main Pivot Point: Cylinder End (on arm): Weight of bucket: acting in the direction. The moment of the weight about : The moment of the cylinder force about : CE FE F F CE W C(0,0) F M = ∑ F 0 + M W/F = M F /F CE 0 C(0,0) G=(−16,0) in. F=(12,−15) in. E=(12+3,5+12)=(15,17) in. W=4000 lb−j F M = W/F W⋅(x − F x )= G 4000 lb⋅[12−(−16)] in.=4000⋅28=11 F CE F 3. Calculation: Set the sum of moments to zero: 4. Result: ● Final Conclusion: The magnitude of the force in