A method to escape Painlevé paradox in a two-link robotic manipulator

When the tip of the second link of a two-link robotic manipulator is sliding on a dry rough surface, the motion could go through a range of inconsistency or indeterminacy known as the Painlevé paradox. In this research a new method for eliminating the Painlevé paradox is proposed. A paradox index is specified and for any specific distance between the fixed pivot and the contact surface, the index changes along a specific curve during the motion. Calculating and monitoring the index specifies how close is the robot from the paradox zone. Whenever the robot is closed enough to the paradox zone the distance between the fixed pivot and the contact surface instantaneously decreases. Hence, the robot goes away from the paradox and the index follows another curve during the subsequent motion. The same action will be repeated till the system reaches the critical height of the pivot height at which the system leaves the surface just before the paradox starts.