Treatment of Constraints in Complex Multibody Systems. Part I: Methods of Constrained Dynamics

The objective of this investigation is to discuss the use of several nonlinear dynamic formulations for modeling constraints in large-scale multibody systems in general, and tracked vehicles in particular. Among the formulations discussed in this article are the augmented method, the nonpartitioning augmented method, the recursive method, and the penalty method. In the augmented formulation, the vehicle kinematic constraints that describe mechanical joints and specified motion trajectories are augmented to the system dynamic equations using the technique of Lagrange multipliers. A Newton-Raphson algorithm and a coordinate partitioning scheme are used to ensure that the kinematic constraint equations are satisfied at the position level. In the nonpartitioning augmented formulation, no check is made to satisfy the kinematic constraint equations and, as a consequence, no coordinate partitioning is required. In the recursive formulation, the system kinematic equations are expressed in terms of the joint degrees of freedom. This formulation allows for modeling spherical, revolute, prismatic, and cylindrical joints. Using this formulation, closed loop chains are modeled using the recursive joint formulation, and cuts are made at selected secondary joints in order to avoid the singular configurations. In the penalty formulation, mechanical joints are modeled using elastic force elements that have assumed stiffness and damping coefficients. These above-mentioned four formulations are discussed in this article. Results of the computer simulations of a large-scale bulldozer model are presented in Part H of this two-part article.