Abstract: For a rigid body sliding on a rough surface, a range of
uncertainty or non-uniqueness of solution could be found, which is
termed: Painlevé paradox. Painlevé paradox is the reason of a wide
range of bouncing motion, observed during sliding of robotic
manipulators on rough surfaces. In this research work, the existence
of the paradox zone during the sliding motion of a two-link (P-R)
robotic manipulator with a unilateral constraint is investigated.
Parametric study is performed to investigate the effect of friction,
link-length ratio, total height and link-mass ratio on the paradox zone.
Abstract: The system of ordinary nonlinear differential
equations describing sliding velocity during impact with friction for a
three-dimensional rigid-multibody system is developed. No analytical
solutions have been obtained before for this highly nonlinear system.
Hence, a power series solution is proposed. Since the validity of this
solution is limited to its convergence zone, a suitable time step is
chosen and at the end of it a new series solution is constructed. For a
case study, the trajectory of the sliding velocity using the proposed
method is built using 6 time steps, which coincides with a Runge-
Kutta solution using 38 time steps.