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The purpose of the following work was to work out the dependency to allow for the determination of the repeatability positioning error value of the robot at any given point in its workspace, without the necessity of conducting time-consuming measurements while routing a precise surface of repeatability positioning.

The presented dependency permits for the possibility to determine, even at the planning phase, the optimal connection point in the workspace, ensuring the best parameters for the process of machine assembly, without needless overestimation of precision of the utilized equipment. To solve the task the sequential quadratic programming (SQP) method implemented in the MATLAB(R) environment was used. To verify the hypothesis of the compatibility of the empirical distribution with the hypothetical distribution of the robot’s positioning error, the Kolmogorov test was used.

In this paper, it has been demonstrated theoretically and experimentally that the industrial robot accuracy can vary over a very wide range in the workspace. This provides an additional opportunity to increase reliability of the assembly process through the appropriate choice of the point of parts joining. The methodology presented here allows the designer of assembly workstations to rapidly estimate the repeatability of robot positioning and to allocate at the design stage of assembly process the optimal position in the robot workspace to ensure the required precision, without unnecessarily high accuracy of equipment used and, therefore, without inflated costs.

An alternative solution to the stated problem can be the proposed method for determining the robot’s positioning errors, requiring a much smaller amount of measurements to be taken that would be necessary to determine the parameters of the random variable errors of the joint coordinates of the robot and for their verification by the repeatability of positioning in randomly selected points in the workspace. Additionally discussed in the study, the methodology of identifying connection place was designed for typical combinations of machine parts, most frequently encountered in assembly process and was taken into account, typical limitations occurring in actual manufacturing conditions.