This paper proposes a new solution to the problem of torque minimization of the medical device SurgiScope ® by connecting to the initial structure a secondary mechanical system, which generates a vertical constant force on the platform of the robotized device. The conditions for optimization are formulated by the minimization of the root-mean-square values of the input torques of the studied device. The positioning errors of the unbalanced and balanced robots are provided. A significant reduction of these errors is achieved by using the suggested balancing mechanism. The efficiency of the developed approach is illustrated by numerical simulations.