In order to solve the limitations of the existing bridge pier damage detection equipment, a rope-driven bridge pier damage detection robot (RDBPDR) is proposed. Firstly, the composition of the RDBPDR system was introduced. Secondly, the kinematical and dynamical model of the RDBPDR was established, and the optimization model of rope tension was given. Based on the dynamic model, the evaluation method and index of the stability of the RDBPDR were given. Finally, the distribution of the stability evaluation index of the RDBPDR in the workspace was clarified with an example calculation and analysis. The results show that the stability of the RDBPR gradually decreases from the geometric center to the boundary area in the horizontal section. With the increase in the height of the damage detection platform, the stability of the RDBPDR gradually increases in the vertical direction, but this change is not significant. It provides a basis for detection task planning, overall structure configuration, and prototype testing in the future.