Experimental Investigation of the Painleve ́ Paradox in a Robotic System

This paper aims at experimentally investigating the dynamical behaviors when a system of rigid bodies undergoes so-called paradoxical situations. An experimen-tal setup corresponding to the analytical model presented in our prior work [28] is developed, in which a two-link robotic system comes into contact with a moving rail. The experimental results clearly show that a tangential impact does exist at the contact point and takes a peculiar property well coinciding with the maximum dissipation principle stated in [11] by Moreau; the relative tangential velocity of the contact point must immediately approach zero once a Painleve ́ 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 in [28] to determine the post-impact velocities of the system, and use an event-driven algo-rithm 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 Painleve ́ paradox, but can also find its applications in better understanding the instability phenomena appearing in robotic systems. Keyworsds: Painleve ́ paradox; robotic system; instability phenomenon; impulsive dynamics