Lower Limb Joint Kinematic Calculation Based on 3D Marked Inverse Kinematic Gait Model

In rehabilitation medicine and bipedal robotic gait simulation, human lower limb joint angles serve as crucial biomechanical parameters. This study proposes a human joint angle calculation framework utilizing relative rotation matrices. By integrating dynamic and static marker data to establish local coordinate systems, we derive adjacent segmental relative rotation matrices and resolve joint angles using Z-X-Y Euler angles. To address ankle joint kinematic redundancy, a quaternion representation coupled with gradient descent optimization is introduced. Experiments using motion capture data constructed a multi-degree-of-freedom human model encompassing lumbar, hip, knee, and ankle joints. Results demonstrate angular root mean square error (RMSE) from OpenSim below 6.06 degree during walking experiments, with most joints controlled within 2.68 degree, while running experiments exhibited a maximum RMSE of 6.03 degree and maintained majority RMSEs between 1.62 degree and 4.33 degree. This methodology provides an efficient and generalizable solution for high-precision joint motion analysis, establishing theoretical foundations for rehabilitation assessment and robotic motion control.