A Methodology to Detect the Precise Instant of Contact in Multibody Dynamics

The main purpose of this work is to present a general and comprehensive approach to automatically adjust the time step for the contact and non contact periods in multibody dynamics. The basic idea of the described methodology is to ensure that the first impact within a multibody system does not occur with a large value for relative bodies’ penetration in order to avoid the artificially large contact forces associated. The detection of the instant of contact takes place when the distance between two bodies change the sign between two discrete moments in time. In fact, in theory, the contact starts when this distance is zero, or a very small value to prevent the round-off errors. Thus, during the numerical solution of the system equations of motion if the first penetration is below this small value previously specified, then the current time is taken as the impact time. On the other hand, if the first penetration is larger than the specified tolerance, then the current time step is beyond the impact time. In this case, integration algorithm is forced to go back and take a smaller time step until a step can be taken within the acceptable tolerance. The main features of this approach are the easiness to implement and the good computational efficiency. In addition, it can easily deal with the transitions between non contact and contact cases in multibody dynamics. Finally, results obtained from dynamic simulations are presented and discussed to study the validity of the methodology proposed in this work.