Robust critical inverse condition number for a 3RRR robot using failure maps

Abstract

Industrial manipulators must be robust with regard to manufacturing tolerances and uncertainties. This paper presents a study of the effects of geometrical uncertainties of a planar parallel manipulator on its kinematic performance and robustness, regarding possible failures. The parallel manipulator under study is a 3RRR, which is composed of a single end-effector connected to the ground by three identical kinematic chains. Each kinematic chain is composed of two passive and one active revolute joints. Among others, parallel manipulators may suffer from two important failures: when the end-effector reaches (i) the workspace’s limitation and (ii) a singular region. Both failures can be assessed by calculating the inverse of the condition number of the Jacobian matrix. In order to evaluate geometrical uncertainties, a Monte Carlo simulation is performed to estimate the probability of both types of failures. Failure Maps are depicted by plotting the probability of failure on the workspace, exhibiting the most affected regions. Based on this information, a robust inverse critical condition number is proposed. This information can be exploited for robustifying the control design and the motion planning of parallel manipulators.