Frictional impact analysis in open-loop multibody mechanical systems

Analysis of impact problems in the presence of any tangential component of impact velocity requires a friction model capable of correct detection of t he impact modes. This paper presents a formulation for the analysis of impa ct problems with friction in open-loop multibody mechanical systems. The fo rmulation recognizes the correct mode of impact; i.e., sliding, sticking, a nd reverse sliding. Poisson's hypothesis is used for the definition of the coefficient of restitution, and thus the energy gains inherent with the use of the Newton's hypothesis are avoided. The formulation is developed by us ing a canonical form of the system equations of motion using joint coordina tes and joint momenta. The canonical momentum-balance equations are solved for the change in joint momenta using Routh's graphical method. The velocit y jumps are calculated balancing the accumulated momenta of the system duri ng the impact process. The impact cases are classified based on the pre-imp act positions and velocities, and inertia properties of the impacting syste ms, and expressions for the normal and tangential impulse are derived for e ach impact case. The classical problem of impact of a falling rod with the ground (a single object impact) is solved with the developed formulation an d verified. Another classical problem of a double pendulum striking the gro und (a multibody system impact) is also presented The results obtained for the double pendulum problem confirms that the energy gain in impact analysi s can be avoided by considering the correct mode of impact and using the Po isson's instead of the Newton 's hypothesis.