Industry 4.0 factories now use more robots to replace human power. To make sure the robot is adaptive to the dynamic working environment, the end effector absolute accuracy needs to be greater than the mechanical tolerance involved in the robot missions. For example, if a robot arm is to place a part to a hole with a tolerance of 1 mm, the mission is very likely to fail for end effector accuracy higher than 1 mm. This paper introduces how three-dimensional (3D) positioning of end effector absolute position and nonlinear parametric modeling of end effector errors can play an important role of improving the end effector absolute accuracy and enhancing the success rate of robot missions. This paper presents the experimental setup and the results of the said end effector positioning and error correction. The 3D end effector positioning can be done by either trilateration or multilateration with more than 3 cable encoders. The proposed method can improve the accuracy from millimeters to less than 0.5 mm. The greatest advantage of the introduced modeling method is that it is suitable for any kind of end effectors.