Abstract: It is important to select resonable linkage tolerances of an industrial robot with design accuracy.This paper deals with optimum accuracy design,i.e.,error synthesis.Aftcr error probability analysis being made,a mathematic model for the optimumaccuracy design of robot linkage is established with the linkage tolerances as designvariables and the linkage tolerance cost as objective function.At last,a 15-DOF industrial robot with a closed loop is taken as an illustiative example,and optimum results under several kinds of accuracy requirements and probability levels are given.