The Rigid-Flexible Two Link Manipulator with Joint Friction and Different Number of Modes for the Flexible Link Discretization

Abstract

A Rigid-Flexibletwo Link Rotatingmanipulator Likesystem is Mathematically Modeled Usinglagrange’s Equations. Two Different Approaches are Considered for the Flexible Linkdiscretization:(a) only the First Flexuralmode is Considered and (b) Two Flexural Modes are Considered. the Mainidea here is to Investigate the Participation of the Second Flexural Mode in the System Dynamics Forslow and Fast Maneuversin the Presence of Friction Forces. Nonlinearity Arises in this Problem Fromthe Coupling between the Variable Representing the Angular Velocity of the Rotating Axis Connected Tothe Flexible Link and the Variable Representing the Vibration of the Flexible Link. Sufficiently Largeangular Velocities are Considered in Order to the System to Undergo Sufficiently Strongnonlinearbehavior.Coulomb Friction Isconsidered on both Joints.For Position/velocity of both Rotating Axesand Elimination of Vibration in the Flexible Link the Nonlinear Control Technique Named Statedependent Riccati Equation (SDRE) is Applied. Theresults for the Different Mathematicaldescriptions of the System are Compared and Discussed