An EAST Articulated Maintenance Arm (EAMA), upgraded based on an articulated inspection arm (AIA), which was successfully operated in Tore Supra in 2008, was developed for the purpose of the inspection and maintenance of damaged internal components during plasma discharges without breaking the East Advanced Superconducting Tokamak (EAST) ultra-high vacuum condition. However, the coupling structure and high redundancy of the EAMA, due to the requirement of coverage ratio and the limitation of the EAST environment, produces a limited accuracy in positioning control. Therefore, the optimal design of the geometric parameters plays a vital role in the EAMA's performance. In this paper, the main characteristics of the EAMA system are investigated to formulate the optimization into a multi-objective problem. Furthermore, an approach based on the Monte Carlo method, integrated with a dedicated collision detection algorithm in the EAST environment, is elaborated on, which is utilized to calculate the collision-free workspace of the EAMA. With the knowledge of the workspace, the coverage ratio is obtained by a progressive meshing technique. Finally, several groups of geometric parameters are sampled to calculate the corresponding value of the objective functions, and the optimized combination of the geometric parameters is obtained by comparing the results.