Rough collision in three-dimensional rigid multi-body systems

Abstract

In the current paper, single point rough collision in three-dimensional rigid multibody systems is modelled. Coulomb's friction law and infinite tangential stiffness are assumed. Routh's incremental model with energetic coefficient of restitution is used. Equations of motion are developed by means of Lagrangian formulation. The non-linear equations of motion show that the contact point could continuously change its sliding direction or the sliding could halt and the non-sliding persists or it could restart along a new direction. All these possible sliding behaviours during impact are identified, conditions leading to each behaviour are specified, and an appropriate numerical procedure is suggested. Normal impulse at the contact point is considered the independent variable, as time-like, to carry out the numerical integrations of the equations of motion. A case of a four-degrees-of-freedom spatial robot that collides with its environment is investigated. Solutions describing the variation of collision variables are obtained. It is recognized that qualitative changes to all the variables occur whenever sliding velocity reaches its minimum value. These critical spots are identified, the associated abrupt variations in the impact variables are explored and the friction influence is observed.