The 6-branch chain parallel platform has complex positional constraints and is prone to damage to the mechanical structure when the control algorithm fails. Therefore, this paper analyses the kinematic operability and workspace of a 3UPU-UP parallel platform. Firstly, the kinematic model of the 3UPU-UP parallel platform is derived through the analysis of vector method and kinematics, based on which, the evaluation index of the operability of the tandem robotic arm is firstly combined with the characteristics of the mechanism structure of the 3UPU-UP parallel platform. The operability of the 3UPU-UP parallel platform is computed, analyzed, and visualized. The Monte Carlo method is combined with the orthogonal kinematics to analyze the workspace of the 3UPU-UP parallel platform. The Monte Carlo method and positive kinematics are combined to calculate, analyze, and visualize the workspace of the parallel platform. The workspace of the parallel platform can be expressed more intuitively and completely. These studies provide the theoretical basis for the design of the 3UPU-UP parallel platform and confirm its theoretical feasibility.