Investigation of Painlevé's paradox and dynamic jamming during mechanism sliding motion

The paradox of Painlevé occurs when the dynamics of a sliding rigid body has solution inconsistency. When approaching a configuration of inconsistency, the contact forces and accelerations may grow unbounded in finite time, a scenario which is called dynamic jamming. Painlevé's paradox was originally formulated for a sliding rod with uniform mass distribution, for which inconsistency occurs only under unrealistically high contact friction conditions. This paper shows that when the sliding rod is replaced by a sliding mechanism, the dynamic jamming predicted by Painlevé's paradox can occur under relatively low friction. The paper proposes a particular mechanism, called IPOS, which consists of an inverted pendulum hinged to a plate that slides on an inclined plane (IPOS = Inverted Pendulum On a Slider). The IPOS mechanism can reach solution inconsistency under practical friction conditions, and can thus be used to experimentally validate the theoretical predictions. The conditions under which dynamic jamming occurs in the IPOS mechanism dynamics are explicitly derived, and numerical simulations illustrate the feasibility of dynamic jamming experiments.