Dynamic Modeling of Three Links Robot Manipulator (Open Chain) with Spherical Wrist

Dynamic modeling of a robot manipulator is a central problem in an accurate robot control. In this paper; the dynamic equations of motion were derived by using Eular-Lagrange method for a six degree of freedom articulated robot manipulator based on the geometrical jacobian construction for each link and actuator. In addition, friction effects beside the end effector forces that act the environment are considered. A Matlab Simulink plant is developed to embrace the theoretical work and simulate the dynamic response for a designed nonlinear controller Proportional Derivative plus Gravity (PD+G), also a modified controller is applied to reject the disturbances and the internal friction effect where the settling errors were 3.57E-6, 2.09E-7, -3.63E-6, 8.84E-6, -5.39E-8 and -4.39E-5 (deg) for joints one to six respectively. The presented approach can be applicable to solve the dynamic problem of other n-link robot manipulators and achieve a suitable solution for tracking trajectories.