Spatial Robotic Systems Subjected to Impact with Friction

Hesham A. Elkaranshawy


Impact with friction, multibody systems, spatial robots, human robot interaction.


A precise and effective approach for modeling and simulation of impact with friction in spatial robotic systems is presented. Assuming single contact point and coulomb’s friction, the nonlinear equations of motion are developed considering normal impulse at the contact point as the time-like independent variable. The derived equations show that the sliding direction continuously swerves. Hence routh’s incremental method is employed to distinguish between different modes of sliding behavior, namely: continuous sliding, sticking, and discontinuous sliding. The discontinuity encountered when the sliding velocity instantaneously vanishes is considered, mathematically solved, and the new sliding direction is specified. The end of contact is specified using the coefficient of restitution. A numerical procedure is proposed and the flowchart of the procedure is given using an energetic coefficient of restitution and substitutions are established to transform to either Poisson’s coefficient or Newton’s coefficient. The proposed method is applied to four degrees of freedom spatial robot that collides with a rough surface. The dynamical behaviors are exhibited and the friction influence is investigated. The results show that the present methodology not only offers a powerful tool for modeling and simulating such practical problems but also in understanding the behavior of these systems in such situations.

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