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.

考虑到多体系统的剧烈滑动，可以发现一系列不确定性或非唯一性解决方案，这称为：Painlevé悖论。如果发生这种情况，则会导致机器人操纵器的末端执行器与滑动表面之间发生意外分离。在这项研究工作中，指明了导致Painlevé悖论的条件。为了检查影响悖论的因素，对两个滑动操纵器进行了参数研究。Prismatic-Revolute机械手（PR）和Revolute-Prismatic（RP）机械手。这些参数研究研究了摩擦系数以及链节长度和惯性的影响。提出了逃避悖论区域的建议，包括通过重新布置机器人的关节来进行新颖的猜想。