To address the requirements of dynamic tracking tasks demanding extensive motion range， high stiffness， and rapid response， this study examines a coaxial 3-RRR spherical parallel mechanism for optical dynamic tracking applications. Initially， the mechanism's forward and inverse kinematics are analyzed using a geometric vector method. Vector projection is employed to identify the unique inverse kinematic solution corresponding to the actual configuration from eight analytical candidates. Subsequently， a singular forward kinematic solution is determined from up to eight closed-form solutions by applying the proposed inverse kinematics algorithm. Furthermore， integrating the forward and inverse kinematic algorithms with a motion singularity index and a collision avoidance strategy， the reachable Cartesian and configuration spaces are systematically characterized under singularity-free and collision-free conditions. A unit quaternion-based spherical interpolation method is introduced to guarantee smooth orientation transitions of the moving platform within the workspace. Both computational and experimental results demonstrate that the analytical forward kinematics solution enhances computation speed by 94% compared to conventional constraint-based iterative methods， while reducing numerical error to the order of 10⁻¹⁴ and obviating the need for initial value estimates. Workspace analysis reveals that the mechanism achieves a pitch range from 48.42° to 138.42° and a full azimuthal range of -180° to 180°， maintaining the rolling degree of freedom about the pointing axis within this domain. Theoretical and experimental findings confirm that the proposed coaxial spherical parallel tracking mechanism exhibits superior motion performance， fully meeting the demands of optical dynamic tracking applications.