Rigid-Body-Analysis

# Rigid-Body-Analysis - Rigid Body Analysis in a Plane The...

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Rigid Body Analysis in a Plane: The Most Common Machine Design Analysis General Case: Dynamic Translation and Rotation Special Case 1: Quasi-Static Translation and Rotation x y 1 F 2 F M 3 F Center of Mass (CM) Key Assumption: Accelerations are low enough to be neglected, and thus a and θ are negligible. x y 1 F 2 F M 3 F Arbitrary Point on Rigid Body A Governing Equations Governing Equations Translation Translation is evaluated at the Center of Mass (CM) Vector Notation CM a F Σ m = Scalar Notation in x and y x CM, x ma ΣF = y CM, y ma ΣF = Rotation The moments are calculated at the CM θ I ΣM CM CM = The Σ M includes moments from all forces and also applied pure moments. Translation Vector Notation 0 F Σ Scalar Notation 0 ΣF x 0 ΣF y Rotation The moments can be calculated about any point. 0 ΣM A The point “A” is any point on the rigid body. Since dynamic forces are negligible, the Center of Mass does not enter the governing equations. The proof of this is left as an exercise

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Rigid-Body-Analysis - Rigid Body Analysis in a Plane The...

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