Function realization of mechanical systems can be considered as a series of constrained motions with the governing equations of mechanical systems constructed as the dynamic equations at the acceleration level. In the process of solving the dynamic equation, small numerical errors may appear on each integration step, and the errors accumulated might result in constraint violation, leading to difficulties in satisfying constraint at the velocity level and position level. Currently, constraint violation errors stabilization can be implemented through correcting acceleration or velocity equation; however, it is difficult to have an accurate control of the violation error threshold with these methods. On the basis of constraint direct correction method, this paper provides a control method of constraint violation errors, which can limit the constraint violation errors within a specific threshold range required by specific numerical simulation accuracy for the mechanical system. A dynamic model of a three-dimensional (3D) RRR (R, rotating) manipulator is constructed, followed by the implementation of dynamic simulation based on Udwadia–Kalaba method. A comparison between the previous methods and the current one is then made to analyze the control of the constraint violation errors in simulations, and the results show that the proposed method is effective in reducing violation errors to a specified range.

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.