LAMOST requires fast and accurate alignment of 4000 optical fiber units on a 1.75m-diameter convex focal plane to simultaneously observe 4000 targets, and the positioning accuracy of the unit is very demanding. But in fact there are a variety of factors such as motor motion error, machining error, assembly error, etc. which may lead to great positioning error. Moreover gear meshing transmission at the eccentric shaft and the anti-backlash spring may also cause greater positioning accuracy error. Besides,the inevitable gap between the center shaft and the bearing leads to motion error of the rotation mechanism, which also affects the precise positioning of the optical fiber. Therefore, in this paper, model and simulate the eccentric shaft basing on virtual prototype ADAMS set parameters and change the axial restraint of the gear, then obtain the axial movement curve. Design 9 groups of comparative tests through orthogonal experimental design.The results in case that: (1) The maximal movement of the gear at the eccentric shaft is within the allowable range, and has little effect on the unit positioning accuracy; (2) The overall error of the unit shaft clearance is in the range of -0.06deg/s -0.2deg/s, which leads to low positioning accuracy that may not meet the observation requirement. This research provides a theoretical basis for the design of a new generation high-precision positioning unit in the future.