This study focuses on the theoretical design of a lightweight screw extruder for robotic additive manufacturing (AM). The primary objective is to enhance material flow control, minimize extruder weight for seamless robotic integration, and improve thermal efficiency. A mathematical model is used to analyze material transport, pressure distribution, and extrusion rate stability. Key design parameters, including screw geometry, barrel dimensions, motor torque, and heating efficiency, are calculated. The proposed extruder ensures precise and reliable material deposition, making it suitable for industrial AM applications. The findings provide a foundation for further development of efficient extrusion systems in robotic additive manufacturing printing.