Novel methods to escape Painlevé paradox for sliding multi-body systems

Abstract

Considering rough sliding of multi-body systems, a range of uncertainty or non-uniqueness of solution could be found, which is termed: Painlevé paradox. If occurs, it leads to undesired detachments between the end effector of a robotic manipulator and the sliding surface. In this research work, the condition leading to Painlevé paradox is specified. To examine the factors affecting the paradox, parametric studies are performed for two sliding manipulators; Prismatic-Revolute manipulator (P-R), and Revolute-Prismatic (R-P) manipulator. These parametric studies investigate the effect of the coefficient of friction and links' lengths and inertia. Recommendations to escape the paradox zone are proposed including a novel conjecture through rearranging the joints of the robot.