Determination of Stability Correction Parameters for Dynamic Equations of Constrained Multibody Systems

When analyzing mechanical systems with numerical simulation by the Udwadia and Kalaba method, numerical integral results of dynamic equations will gradually deviate from requirements of constraint equations and eventually lead to constraint violation. It is a common method to solve the constraint violation by using constraint stability to modify the constraint equation. Selection of stability parameters is critical in the particular form of the corrected equation. In this paper, the method of selecting and determining of stability parameters is given, and these parameters will be used to correct the Udwadia-Kalaba basic equation by the Baumgarte constraint stability method. The selection domain of stability parameters is further reduced in view of the singularity of the constraint matrix during the integration procedure based on the selection domain which is obtained by the system stability analysis method. Errors of velocity violation and position violation are defined in the workspace, so as to determine the parameter values. Finally, the 3-link spatial manipulator is used to verify stability parameters of the proposed method. Numerical simulation results verify the effectiveness of the proposed method.