Constrained Multibody Dynamics

Abstract

This paper presents some techniques that may be used to obtain more efficient and general computer-based dynamics modeling and simulation algorithms with potential real-time applications. Constrained equations of motion are first formulated in an augmented differential-algebraic form using spatial Cartesian and joint coordinates. Spatial algebra and graph theoretic methods allow separation of system topology, kinematic, and inertia properties to obtain generic equation representations. Numerical stability is improved by employing coordinate partitioning or singular value decomposition to define suitable sets of independent variables. Substantial matrix operations during run-time are avoided by employing equation preprocessing to generate explicit expressions for all dependent variables, and coefficients of their first and second time derivatives. The velocity and acceleration coefficients allow explicit elimination of all spatial and dependent joint coordinates yielding a minimal system of highly coupled differential equations. A symbolic recursive algorithm that simultaneously decouples the reduced equations of motion as they are generated, was developed to maximize algorithm parallelism.