## 1 Introduction
In [23], part deviations and fixture deviations are combined based on the influence coefficient method to study their propagation characteristics in multi-stage assembly systems, and a method to assess the propagation of dimensional changes in multi-station flexible transfer systems is proposed based on the linear elasticity theory and the state space method. In [24], it is pointed out that most assembly deviation prediction methods at the present stage focus on the product design and assembly stages, while ignoring the hazards caused by assembly deviations in the product service stage, and, therefore, a method is proposed for predicting assembly quality based on observable combined deviations. However, the deviation transfer model based on the state space method is mostly limited to two-dimensional rigid parts and does not consider the flexible deformation of weakly rigid parts in three-dimensional space. In addition, the dimensionality of the observation equations will be greatly increased in the face of complex 3D assembly systems, and the observation vectors of the observation equations are difficult to unify. In [25], on the basis of the mainstream assembly quality prediction models, the comprehensive deformation of a part under the simultaneous influence of manufacturing errors and assembly loads was studied, not only considering the initial manufacturing errors of the part, but also using the flush coordinate transformation method to accurately establish a prediction model for the surface assembly accuracy of the part to be assembled. In [26], a non-linear state space is used to simulate the accumulation of deviations from one assembly station to the next by station with the objective of minimizing the sum of squares of the standard deviations of the critical products as well, and genetic algorithms are used to optimize the assembly quality problem in the multi-station assembly (MSA) of an automotive body. [PERSON] et al. [27] investigate the impact of machine tool assembly deviations on tooling, consider components in an unassembled state, establish a method for pre-adjustment in the assembly design phase, and characterize the propagation of deviations during machine tool assembly by means of a state space approach. On the basis of the above research, based on the linear elasticity theory and the state space method, a three-dimensional weakly rigid part multi-level assembly deviation transmission model is established for an assembly system containing multiple assembly stations, and a deviation state equation containing part rigidity and flexibility deviations, fixture deviations and assembly contact deviations is defined. Considering the problem of inconsistent observation vectors in the assembly system, a Jacobi-spinor method is used to represent the deviation propagation in three-dimensional space by means of the infinitesimal modelling of open kinematic chains in robot kinematics, and the part coordinate system is correlated with the assembly (observation) coordinate system to obtain a unified observation vector and a concise equation of state. Finally, the computational procedure of the proposed method is presented with an aircraft engine nacelle as an example, and finite element simulation tests are carried out to verify the accuracy of the mathematical model of assembly deviation transmission.