Dynamics and control of Robot manipulators

In the present work, the Newton - Euler dynamic modeling ofsix degrees of freedom robot manipulator is introduced. Themodeling is based on the approach utilizing the kinematicparameterization of a manipulator, as an open kinematic chain,using Rodrigues formula of finite rotation. Complete analysis ofthis approach is presented. The advantage of this method overthe Denavit Hartenberg kinemaics is discussed. A computerpackage has been prepared herein to calculate the manipulatorsdynamic model based on Newton - Euler formulation andRodrigues’ parameterization. The output of this package is thedriving forces / torques at each joint of the robot manipulatorassociated with every point on the manipulator trajectory. Thispackage can be used in such away that the effect of friction onthe movement of the manipulator joints is investigated fordifferent values of coefficients for both viscous and coulombfriction.. The validity of the techniques used as well as of thecomputer package has been checked. Identical results have beenrecognized.Case study is presented for the robot manipulator (PUMA 560).The objective of this study is to demonstrate the applicability ofthe proposed method and check its validation. In this studya proposed procedures for tracking error evaluation is presented.A time based end effector trajectory is assumed. This assumedtrajectory is defined as desired trajectory. The inverse kinematicproblem (IKP) , the inverse dynamic problem (IDP), the directdynamic problem (DDP) and the direct kinematic problem(DKP) have been solved. The output of solving these problemsis a calculated time based end effector trajectory. Thecomparison between the desired trajectory and the calculatedone showed that the tracking error is quite satisfactory. Thisresult proves the applicability of the developed package.