Abstract: It is necessary to know the adaptive ability of robot operating or dexterity within its reachable workspace in the applying field.Service angle,dexterity,and line with an equivalent extent pitch are put forward as performance index.At first,the structure feature and freedom of EMR system robot are analyzed,and the service angle is determined as performance index of system dexterity.Then,several methods of solving robotics service angle are presented,and the decomposing method is discussed in detail.This method can be adapted to control online with little computer time.