In the field of autonomous mobile robotics, optimal geometric trajectory planning is a key step to ensure precise and efficient robot navigation. This paper presents a fast and straight forward method for generating an optimal trajectory between an initial and a final position in environments free of obstacles. The proposed approach accounts for the kinematic constraints of the robot, thereby guaranteeing the feasibility of the generated paths. By modeling the trajectory using straight-line segments and circular arcs, the method achieves low computational complexity, making it suitable for real-time applications. Simulation results demonstrate the effectiveness of the proposed solution and highlight its advantages over existing approaches, particularly in terms of trajectory length and adherence to realistic kinematic behavior.