Errors Control of Constraint Violation in Dynamical Simulation for Constrained Mechanical Systems

Abstract

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.