Effect of Friction on the Dynamical Analysis of Three-Link Planar Robot Arm by Using Lagrange Approach


The dynamic analysis of Three-Link planar robot arm and control system with (PID) are presented and investigated. The dynamic analysis is very important in the design and control of the robot. The difference between the actual dynamic analysis and ideal dynamic analysis is the presence of friction in the robot joints. In this work, the frictional effect in the joints of three-link planar robot is inserting in the dynamic equations and that makes the dynamic analysis is more reality and difficult. The mathematical model that represent the friction consist of two types of friction (Coulomb and viscous friction). A Lagrange method is used and applied to evaluate the generalized forces in the two cases (without and with the effect of friction). Control system with (PID) controller is presented with Simulink block set to evaluate and show the dynamic response of each link in two cases (without and with friction). MATLAB software is used for programing and simulation the equations. In addition, with that, error signals are presented and analyzed for each link. It is concluded from the results that the values of generalized forces in case of presence of friction are more about (12%) than the values of the forces in case of without friction and the behaviors of the dynamic response is linear in case of without friction while the behavior become (non-linear) by inserting the frictional effect in the robot joints. The results indicate that the effect of friction is very important and must be not neglected.