The influence of mechanical errors on fiber positioners of LAMOST

Large-scale spectroscopic surveys are revolutionizing our comprehension of the universe. By analyzing the spectra emitted or absorbed by celestial bodies, scientists can obtain important information such as their properties, composition and distribution. The key for obtaining numerous spectra within a reasonable time is the use of fiber positioner arrays. To guarantee no blind area, positioners are hexagonally distributed with overlapped patrol areas, introducing issues such as fiber assignment and collision avoidance. These issues are heavily affected by the precision of positioners. However, errors are inevitable. The machining of components and the engagement of gears may result in discrepancies between the actual and theoretical data regarding arm length and rotation angles. The central shaft deviation caused by assembly will result in the arm being unable to reach the expected position after rotation. The lack of precision in controlling the gear reduction ratio can impact results as well. The research focus of the paper is to explore the impact of various factors on system accuracy through simulations. The kinematic model of theta-phi positioners has been established based on geometry and Denavit-Hartenberg (D-H) method. The factors are analyzed and their impacts are simulated through the method of controlled variables. Through error analysis, the influence of various factors can be reduced by adjusting parameters before manufacturing the positioners, or to screen for positioners that require repair during maintenance. This study provides a reference for the design, calibration, and control of positioners.