The D-H parameter method has found extensive application in the analysis of manipulator motion. However, it primarily describes motions along the x and z axes, neglecting the y-axis motion. To address this limitation, the screw theory method was emploied to represent the manipulator's position and orientation as a screw, conducting an in-depth analysis of its kinematics and dynamics. In contrast to the traditional D-H approach for forward kinematics, screw theory offers a holistic depiction of the robot arm's motion, eliminating the necessity for an intermediate reference system with explicit geometric significance. To tackle the inverse kinematic problem of the elbow robotic arm, the Paden-Kahan subproblem was applied, resulting in the computation of an inverse kinematics solution. Leveraging screw theory and Lie group-Lie algebra, the Newton-Euler approach was employed to construct an efficient recursive dynamic model. Ultimately, the manipulator's inverse kinematic solution derived through the screw theory was subjected to simulation and verification, with its workspace calculation revealing that the screw theory method offers a more concise, accurate, and effective approach.