This paper describes the mathematical model, control and simulation of 3DoF (Degrees of Freedom) robot manipulator moving in a three-dimensions Cartesian coordinate frame. The four Denavit-Hartenberg (D-H) parameters are used to determine the homogenous transformations matrices of the links of the robot and express the robot’s forward kinematics. Both link position and orientation are embedded in the homogeneous transformation matrix. The geometric solution approach based on the decomposing of the spatial geometry of the robot into several plane geometry is applied to determine the inverse kinematic problem of the robot. Dynamic equations of the robot are important studies to provide an understanding of the behavior of robot moving in a three-dimensional coordinate frame. The Newton-Euler formulation is utilized to recursively derive the dynamic equation of each link of the robotic manipulator, and it is used to analyze the robot by treating the system into separate parts. The forward recursion is used to derive the generalized forces working from the end link to the base of the manipulator, and backward recursion of the velocities and accelerations working from the base of the manipulator to the end link. The end result is to determine the mathematical model of the robot in an explicit form and use that explicit equation to simulate the whole system. The mathematical models of the kinematic and dynamic equations of the robot are derived, and the validity of the model is proved by numerical simulation in conjuction with control systems.