Stabilization of Multiple Constraints in Multibody Dynamics Using Optimization and a Pseudo-inverse Matrix

An approach for solving the forward dynamics problem for mechanical systems with many closed kinematic chains is presented. The dynamic model takes the form of Differential-Algebraic Equations. An optimization method for stabilization of kinematic constraints using the pseudo-inverse mass matrix of the dynamic equations is suggested. The stabilization algorithm provides minimal deviations of the parameters and their velocities with respect to the solution of the differential equations. Estimation of independent coordinates is not required. The forward and inverse dynamic problems of a spatial mechanism and a spatial moving platform with many closed chains are solved. The effectiveness of the algorithm is analyzed.