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A fast numerical algorithm for the forward kinematics optimization of 3—RPS parallel manipulator was presented. Through numerical optimization methods, the problem of forward kinematics of parallel robot was inverted to minimization problem. According to the optimization of forward kinematics for 3—RPS parallel manipulator, the forward kinematic functions, which were the multi-objective nonlinear equations with constraint, were built based on numerical method. The fitness function was established to achieve the optimization of single objective, and the minimum optimization was solved based on the global-best artificial bee colony algorithm. The information carried by employed bees was exchanged among the neighboring bees. The position information was exchanged randomly and the neighborhood bees were chosen randomly as the standard artificial bee colony algorithm. In addition, for the global-best artificial bee colony algorithm, the global best bee which carried the best position information would guide all bees to move to the better position, and convergence fast to the best position. As the simulation result of 3—RPS forward numerical kinematics showed, compared with continuous ant colony algorithm and standard artificial bee colony algorithm, the global-best artificial bee colony algorithm was an effective way, which with high precision and high speed, to solve forward kinematics of parallel manipulators.