The effectiveness of a Computer Numerical Control (CNC) machine tool to produce high precision products is significantly dependent on the contouring accuracy of the individual axes. The motion accuracy of such machines is influenced by the StickSlip Friction (SSF) between two sliding bodies. In this study, a contact force model employing relative coordinate systems for Multi-Body Dynamic (MBD) systems is used to model and simulate contact conditions at the sliding surfaces of CNC machine tools. MBD formulations and smooth SSF force model parameters in MBD are first explored. Then, computational simulations that combine MBD simulation and control system are performed on a three axes CNC machine tool model with a pure Proportional-Integral-Derivative (PID) controller to illustrate the proposed method. In the numerical simulations, the displacement of the moving part and the driving force of the controller are considered in cases of no friction, friction without stiction effect (sliding friction), and stick-slip friction. From these conditions, the influence of the friction on the sliding stability of the controller and the motion accuracy of the machine tool are analyzed and predicted. The results show that the controller must produce a higher driving force to control the MBD model when stiction occurs. The performances of the machine under different working conditions are also implemented to prove the use of embedding the smooth SSF model in co-simulate an MBD model with the control system. Hence, the main purpose of this research paper is to propose a computational co-simulation tool that can help the R&D engineers or scholars in considering SSF characteristics when analyzing and designing a machine tool.