## 1 Introduction  
During the phases of take-off and landing of the flight, the main task of a landing gear retraction mechanism is to extend the structure stably and precisely to the designated position [1, 2]. The stability and precision of a landing gear mechanism are strongly concerned with its robustness. Joint clearances are universal for landing gears, and they inevitably affect the kinematic accuracy and robustness of mechanisms. Due to the uncertainty and complexity of clearances, it is often challenging to model them in the kinematic analysis. And what is more, this situation results in the difficulty to estimate the joint clearance effects on the kinematic accuracy and robustness. Traditionally, the kinematic accuracy model is deduced from the kinematic equations, however, joint clearances are often omitted. There is a relative paucity of studies focusing specifically on the relations between clearance effects and kinematic accuracy. Meanwhile, no previous study has covered the robustness of a mechanism through the way of kinematic accuracy analysis. An intriguing question is raised, that is, how to establish the link among joint clearances, kinematic accuracy, and robustness. The answer in this paper is tolerance analysis. Regarding aircraft assemblies, dimensional chains are widely used in tolerance analysis. Basic theories are described in the literature written by [PERSON] [3]. Jacobian model is a novel method in tolerance theory, which was proposed by [PERSON] and [PERSON] [4; 5; 6]. In this model, Functional element (FE) pairs and functional requirement (FR) are used to represent the relationship between parts. Tolerance propagation functions are obtained by transform matrix of variations. The utilization of this model has been expanded in the past twenty years. [PERSON], [PERSON], and [PERSON] [7; 8; 9; 10; 11] modified the original Jacobian model and established Jacobian-Torsor model. Different joint types are represented by the displacement matrix in the model. Meanwhile, tolerance zones and propagation functions can be established by this model. Many studies [12; 13; 14; 15; 16; 17; 18; 19] have involved the application of these two jacobian models. In the manufacturing process, the study of [PERSON] [20] treated workpieces, fixtures, and machine tools as an assembly, and formulated the corresponding error propagation model using the Jacobian-Torsor theories. A group of constraints to variations were added to the Jacobian-Torsor model by [PERSON] [21; 22; 23]. The analysis of engine assemblies was performed by this modified model in his study. Concerning kinematic accuracy analysis, the small-displacement torsor model was used in the study conducted by [PERSON] [24]. However, the application was still bound up with the static assembly processing, which limits the use of tolerance theory. The Jacobian model is the ideal method to establish a kinematic accuracy model for mechanisms, however, efforts are lacking thus far. Robustness is the idea first proposed in the area of product quality and widely adopted in various industrial fields [25]. On the subject of mechanism design, several studies have tried to introduce robust theories into parameter analysis [26; 27; 28; 29; 30; 31; 32]. The target of robust analysis is to get high-quality design insensitive to unexpected errors and deviations. [PERSON] et al [33] proposed to adopt robust theories to find an appropriate robustness index, and then robust dimensions can be obtained. The Taguchi method in robust theory was utilized to obtain a set of robot parameters and to reduce performance variations by [PERSON] and [PERSON] [34]. In the study by [PERSON] et al [35], random and interval variables were considered and then performance deviations were minimized through the robust mechanism synthesis. Similarly, the study by [PERSON] et al [36] proposed to accommodate truncated random variables and clearance variables during robust design. The Taguchi method was improved especially for mechanisms by [PERSON] and [PERSON] [37; 38].