Kinematic and kinetic derivatives in multibody system analysis

摘要

Analytical formulas for kinematic and kinetic derivatives needed in multibody system analyses are derived. A broad spectrum of problems, including implicit numerical integration, dynamic sensitivity analysis, and kinematic workspace analysis, require evaluation of first derivatives of generalized inertia and force expressions and at least three derivatives of algebraic constraint functions. In the setting of a formulation based on Cartesian generalized coordinates with Euler parameters for orientation, basic identities are developed that enable practical and efficient computation of all derivatives required for a large number of multibody mechanical system analyses. The formulation is verified through application to a spatial slider crank mechanism and a 14 body vehicle model. Efficiency of computation using the expressions derived is compared with results obtained employing finite differences, showing significant computational advantage using the analytically derived expressions. [References: 23]