Experimental Investigation of the Painlevé Paradox in a Robotic System

摘要

This paper aims at experimentally investigating the dynamical behaviors when a system of rigid bodies undergoes so-called paradoxical situations. An experimental setup corresponding to the analytical model presented in our prior work Liu et al. [2007, “The Bouncing Motion Appearing in a Robotic System With Unilateral Constraint,” Nonlinear Dyn., 49(1–2), 217–232] is developed, in which a two-link robotic system comes into contact with a moving rail. The experimental results show that a tangential impact exists at the contact point and takes a peculiar property that well coincides with the maximum dissipation principle stated in the work of Moreau [1988, “Unilateral Contact and Dry Friction in Finite Freedom Dynamics,” Nonsmooth Mechanics and Applications, Springer-Verlag, Vienna, pp. 1–82] the relative tangential velocity of the contact point must immediately approach zero once a Painlevé paradox occurs. After the tangential impact, a bouncing motion may be excited and is influenced by the speed of the moving rail. We adopt the tangential impact rule presented by Liu et al. to determine the postimpact velocities of the system, and use an event-driven algorithm to perform numerical simulations. The qualitative comparisons between the numerical and experimental results are carried out and show good agreements. This study not only presents an experimental support for the shock assumption related to the problem of the Painlevé paradox, but can also find its applications in better understanding the instability phenomena appearing in robotic systems.