Solution to Three-Dimensional Indeterminate Contact and Impact With Friction Using Rigid Body Constraints

This work analyzes three-dimensional multibody systems undergoing indeterminate contact and impact in the presence of Coulomb friction. A discrete approach is used to analyze the impact behavior upon detection of the impact events during simulation. During an impact event, the velocities of the impact points describe the systems state and can be studied to characterize the nature of impact and determine the post-impact behavior of the system. The velocities of the impact points during an impact event can be described in terms of the impulses at those points. This work uses Amontons-Coulombs law of friction and rigid body constraints to develop a technique for reducing the number of impulses required to compute the velocities of the impact point during the impact event. Indeterminacies associated with slip direction arise, when Coulombs friction is considered. Therefore, a numerical approach is used to evolve the slip direction along with the slip velocity, with respect to a normal impulse. The work-energy theorem is used to detect the end of the impact event, and determine the post-impact velocities of the system. Examples of a three-dimensional rocking block and a sphere impacting a corner are analyzed to demonstrate the proposed methodology.</jats:p>