The robotic arm of the Wentian module can complete tasks such as supporting astronauts' extravehicular activities, installing and maintaining payloads, and inspecting the space station. The 7-joint SSRMS manipulator is critical for space missions. This study aims to build its kinematic model via screw theory. It simplifies SSRMS to right-angle rods, defines joint screw axes, twist coordinates, and initial pose matrix. Using PoE formula, the 7-DOF forward kinematics equation is derived. Besides, it derives fixed joint angle for inverse kinematics, including analytical solutions and numerical solutions. It elaborates analytical solutions for fixing joints 1/7 and 2/6 and numerical solutions for fixing joints 3/4/5,solves all joint angles via kinematic decoupling, and addresses special cases. Experiments with China’s space station small arm parameters show The probability of meeting the accuracy threshold of 10−4 is 99.79%,verifying model effectiveness, while noting singularity-related weak solving areas. This provides a reliable basis for subsequent inverse kinematics optimization.