Robots are now commonly utilized to perform tasks more efficiently, accurately, and consistently than humans. Robotic manipulators are complex nonlinear systems characterized by strong interdependencies between multiple inputs and outputs, along with uncertainties and dynamic capabilities that change significantly over time. These factors contribute to the difficulties associated with controlling the trajectory of a robotic manipulator. To achieve optimal performance, the controller must address these issues. Sliding Mode Control (SMC) is a widely used method for such systems as it can effectively handle uncertainties and disturbances. However, designing an SMC system effectively requires precise knowledge of the extent of these uncertainties and disturbances, which can be difficult to obtain for complex robots with numerous degrees of freedom. The thesis develops a mathematical model for the robot manipulator's movement and torque using the well-known Euler-Lagrange equation to describe its dynamics. And also presents a controller design for a 3-DOF robotic manipulator that aims to achieve both accurate movement and robustness in the face of challenges. To ensure smooth operation and accurate positioning, the system's stability is analyzed using Lyapunov's stability criterion, which mathematically verifies if the robot's errors will dissipate over time. The thesis investigates the ability of a robot arm to follow various paths using a fuzzy sliding mode controller (FSMC), focusing on the controller's robustness in handling unexpected challenges. The simulation Result shows that the proposed controller is strong and effectively tracks trajectories, maintaining manipulator joint angle errors at approximately 10-3(rad) at steady state. Additionally, it has reduced Integral Time Absolute Error (ITAE). Furthermore, the fuzzy sliding mode controller (FSMC) has been observed to have lower control input torques compared to the Sliding Mode Controller (SMC), and it eliminates the chattering effect. Keywords: Three degree of freedom robotic manipulator, Trajectory tracking, sliding surface, Sliding mode control, fuzzy sliding mode control,