This project deals with three dimensional collisions of rigid, kinematic chains with an external surface while in contact with other surfaces. We concentrate on a special class of kinematic chain problems where there are multiple contact points during the impact process. A differential formulation based algorithm is used to obtain solutions that utilize the kinematic, kinetic, and the energetic definitions of the coefficient of restitution. Planar and spatial collisions of a three-link chain with two contact points are numerically studied to compare the outcomes predicted by each approach. Particular emphasis is placed on the relation between the post and pre-impact energies, slippage and rebounds at the contact points, and differences among planar and nearly planar three dimensional solutions.
Schematic representation of the problem
Low velocity collisions of slender bars with external surfaces
An experimental analysis was conducted to study the rebound velocities of freely dropped bars on a large external surface. A high speed video system was used to capture the kinematic data. The number of contacts and the contact time were determined by using an electrical circuit and an oscilloscope. Tests were performed by using six bar lengths and varying the pre impact inclinations and the velocities of the bars. The experimental results were used to verify the applicability of Coulomb's law of friction and the invariance of the coefficient of restitution in the class of impacts considered in this study.
Computer animation of experimental data is available, please click here to watch.
The experimental setup
Solving Rocking Block Problem with Multiple Impacts
The objective of this study is to extend the method given in Ceanga and Hurmuzlu (2001) to solve the rocking block problem. Here, we consider a rigid block with two rocking ends on smooth surfaces that are set at arbitrary angles. First, using a compliant model we show that the Impulse Correlation Ratio concept is valid for the limiting cases. Then, we develop a solution method based on the rigid body approach and impulse momentum methods. We proceed by investigating the effect of geometry on the post impact bouncing patterns of the problem. Finally, we verify the approach by conducting a set of experiments, and comparing the theoretical outcomes with the experimental ones.
The experimental setup