## 1 Introduction  
Shaft-hole fit is a common form of fitting in rotating mechanical products. Dimension error, geometric shape error, and fit error of shafts and holes are important sources of assembly error [1; 2; 3]. They directly affect the assembly accuracy, kinematic accuracy and service life of products, for example, the rotation accuracy of a machine tool spindle, gear transmission error, and service life of the bearing [4]. Therefore, it is necessary to discuss the relationship between assembly system performance and geometric and fit error of the shaft-hole. Historically, scholars have conducted extensive research work on this issue. However, most studies have focused on the tolerance analysis of assembly systems, including the Direct Linearization Method [5], Matrix method [6], Unified Jacobian-Torsor method [7], and the Small Displacement Torsor method [8]. Assembly error with clearance fit is mainly studied by equivalent substitution. For example, [PERSON] et al. [9] proposed the Matrix method to view shaft-hole clearance fit into coaxiality tolerance. [PERSON] et al. [5] regarded different fit states in all kinds of kinematic pairs according to the Direct Linearization Method. [PERSON] et al. [7] expressed the contact and kinematic relationship between fitting parts by the Torsor method. They established error propagation models based on the dimension chain, which regard the tolerance value and clearance value as constrained boundaries for variation in the tolerance feature (TF) through an optimization method or conducting statistical analysis with the tolerance domain being the boundary, so as to realize error analysis of the assembly system [10]. Tolerance analysis models like the Matrix method and the Small Displacement Torsor method give a range of 12 ultimate values for TF from the angle of six degrees of freedom (DOF). Influenced by the principle of the algorithm itself, the search for the limiting state of TF by the optimization method is probably formed by multiple uncertain combinations of deviations on multiple DOF, but it does not determined the limit deviation from the expected DOF. Therefore, when the limiting situation or statistical situation for all kinds of product performances with errors such as the kinematics and dynamical properties, is carried out in the product design phase, input parameters may not be accurate enough and will affect the accuracy of the analysis results. Therefore, before performance analysis of products with errors, pose (position and orientation [11]) decoupling on six spatial DOF must be implemented for TF so that the actual deviations of TF on all DOF are obtained [12; 13]. In this way, the error range of the target feature can be more accurately obtained and this range should be smaller than error ranges given by the Matrix method and the Small Displacement Torsor method, etc. Moreover, explicit analytic expression of target feature error can be obtained, especially when ultimate error is not solved through optimized mathematical iteration method. Thus, explicit solutions for six DOF at arbitrary positions, including the limiting position of TF, can be realized. Currently, when prediction and analysis of the mechanical properties of assembly systems with errors is conducted in the product design phase, the error value is usually manually set [14], and it is not derived from tolerance values given by designers. Therefore, in order to explore a method which establishes the relation between tolerance of part of the dimension chain and performance of the assembly system, TF of shaft-hole fit-axis TF [15] was taken as an example in this paper, to examine a pose decoupling model. Inspiration for this method came from the Tolerance-Map (T-Map) model proposed by [PERSON] et al. [16] and the Deviation-Domain model proposed by [PERSON] et al. [15]. The two methods are still essentially tolerance analysis methods.