Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_107

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the force in the hydraulic cylinder AB and the magnitude of the pin reaction at O for the position shown. The bucket and its load have a combined weight of 4000 lb with center of gravity at G. You may neglect the effect of the weights of the other members. Problem 4/107 (a) Force in the hydraulic cylinder AB ● Calculation Process 1. Identify Geometry and Coordinates: We set the origin of our coordinate system at the main pivot pin . Based on the provided dimensions: The center of gravity of the bucket and its load is located 100 inches to the left of the vertical through (from ). Thus, in. Pin on the loader arm is located 50 inches to the left of and 13 inches below (from the vertical dimension). Thus, in. Pin on the chassis is located 6 inches to the right of and 11 inches below . Thus, in. 2. Moment Equilibrium Equation: To find the force in the cylinder , we take the sum of moments about the pivot for the entire arm assembly. where lb is the weight and is the force from the cylinder on the arm at . 3. Substitute Values and Calculate Moments: Moment of weight: (Counter-clockwise). Vector (direction of cylinder force): in. O(0,0) G O50"+50"x = G −100 AO OA=(−50,−13) BOO B=(6,−11) AB O M = ∑ O 0⟹ ×r OG W+ ×r OA F = AB 0 W=−4000jF AB A M = W x ⋅ G (−W)=(−100 in)⋅(−4000 lb)= +400,000 lb-in BA = BAA−B=(−50− 6,−13−(−11))=(−56,−2) Length of cylinder: . Force vector . Moment of cylinder force: . 4. Final Calculation: ● Final C