Dynamic analysis of an n-revolute planar serial manipulator and sensitivity analysis based on Sobol's method

Abstract

In this paper, dynamic modeling and dynamic sensitivity analysis of an n-revolute planar serial robot are investigated. First, a dynamic modeling algorithm is proposed which is based on the concept of the so-called Natural Orthogonal Complement. The main goal of this algorithm consists in deriving the corresponding dynamic equations of a planar serial manipulator systematically. As a comparison study, 3-DOF a planar serial manipulator is modeled and the results of the proposed algorithm is compared with other methods, i.e., Newton-Euler, Lagrange-Euler, Adams software and an Open Dynamics Engine, the so-called MatODE. Then, in order to develop a dynamic sensitivity analysis scheme, Sobol's method is employed. By the use of inverse kinematics analysis of the robots for a predefined trajectory of end-effector, the joint coordinates, angular velocities and angular accelerations are founded for a given period of time. Then the sensitivity of delivering torques to joint coordinates, angular velocities and angular accelerations are analyzed. The sensitivity analysis is developed for two planar serial robots, 2-R and 3-R. The results reveal that actuating torques are more sensitive to joint coordinates with respect to angular velocities and accelerations.