Time integration of the equations of motion in mechanism analysis

The formulation of time integration algorithms for mechanism analysis problems is discussed. Particular aspects to be considered are the treatment of constraints and of the finite rotation associated terms. It is shown that in order to time integrate constrained systems, the algorithmic damping at infinite frequency is of utmost importance. It is demonstrated that the Newmark trapezoidal rule is unconditionally unstable in the presence of constraints. The use of second order accurate dissipative algorithms like the Hilber-Hughes-Taylor scheme is recommended. Finally, the integration of finite rotation associated terms is performed by projecting the equations onto the tangent space to the rotation group. In this way, well-known results of accuracy and convergence can be applied. Several examples illustrating the covered topics are presented.