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This paper aims to carry out assembly variation analysis for mechanisms with compliant joints by considering deformations induced by manufactured deviations. Such an analysis procedure extends the application area of direct linearization method (DLM) to compliant mechanisms and also illustrates the dimensional interaction within multi-loop compliant structures.

By applying DLM to both geometrical equations and Lagrange’s equations of the second kind, an analytical deviation modeling method for mechanisms with compliant joints are proposed and further used for statistical assembly variation analysis. The precision of this method is verified by comparing it with finite element simulation and traditional DLM.

A new modeling method is proposed to represent kinematic relationships between joint deformations and parts/components deviations. Based on a case evaluation, the computational efficiency is improved greatly while the modeling accuracy is maintained at more than 94% rate comparing with the benchmark finite element simulation.

The Equilibrium Equations of Incremental Forces derived from Lagrange’s equations are proposed to quantitatively represent the relationships between manufactured deviations and assembly deformations. The present method extends the application area of DLM to compliant structures, such as automobile suspension systems and some Micro-Electro-Mechanical-Systems.

The purpose of this paper is to focus on optimal sensor placement for the fixture variation diagnosis of compliant sheet metal assembly process. Fixture variations are the main sources for complex automotive body dimensional failures. An effective measurement strategy can help exactly and timely diagnose these fixture variations. Research on sensor placement strategy of compliant sheet metal assembly process is not much stated formerly.

The impact principle of fixture variations is analyzed to set up the relationship between the assembly variation and fixture variations applying the method of influence coefficients and the effective independence (EI) method is used to find the optimal sensor positions based on the impact principle analysis of fixture variations.

The obtained fixture variation sensitivity matrix describes the influence of fixture variations to compliant sheet metal assembly variation and can be used for diagnosing fixture variations. The EI method can effectively solve the optimal sensor positions for compliant sheet metal assembly by a case demonstration.

The proposed method can solve the sensor placement of online assembly station for diagnosing fixture variations. It takes the compliant characteristics of sheet metal parts into account and the sensor information has much greater diagnosability than that from applying other methods.

The purpose of this paper is to design a new method to realize automatic assembly of aircraft components with large shafts such as canard and vertical tail. The assembly structure of component with large shaft and fuselage is a mating assembly structure, and it is a challenge to satisfy the precision and assembly requirement.

According to the assembly structure features and process requirements of an aircraft component with large shaft, the operating principle of precise assembly system for shaft-hole mating is analyzed in this paper. The model of compliant assembly for shaft-hole mating is constructed, and force condition analysis of the compliant assembly is performed. An automatic precise shaft-hole assembly method for aircraft assembly using 5 degrees of freedom spatial mechanism, compliance technology and servo feeding system is put forward based on the analysis. A 5 degrees of freedom passive compliant experimental equipment has been developed.

Application test results of the 5 degrees of freedom passive compliant experimental equipment show that the simulated canard can be mated automatically and accurately through this method with high efficiency and high quality as long as the tip of shaft enters into the range of hole’s chamfer.

This method has been used in an aircraft assembly project. The practical results show that the aircraft components with large shafts can be mated automatically and accurately through this method with high efficiency and high quality.

This paper presents a new method and designs a new assembly system to realize the assembly of the aircraft components with large shafts. The research will promote the automation of fuselage assembly.

Large gear components widely exist in the transmission system of helicopters, ships, etc. Due to the small assembly clearance of large gear components, using an automatic docking system based on position control will lead to forced assembly. The purpose of this paper is to reduce the assembly stress of large gear components by an active compliant docking technology based on distributed force sensors.

Firstly, aiming at the noise interference in three-dimensional force sensor (TDFS), Kalman filter and Savitzky–Golay filter are used to process the sensor’s output signal. Secondly, the active compliant docking control model is constructed according to the principle of impedance control. Thirdly, the contact force is calculated based on the Euler equation, and the impedance control parameters are tuned by the particle swarm optimization algorithm. Finally, an active compliant docking system of a large gear structure based on distributed force sensor is built in the laboratory to verify the proposed method.

The experimental results show that the contact force and contact torque gradually decrease in all directions and are always in the safe range during the docking process. The feasibility of this method in practical application is preliminarily demonstrated.

The distributed TDFSs are used to replace the traditional six-dimensional force sensor in the active compliant docking system of gear components, which solves the problem of the small bearing capacity of the conventional active compliant docking system. This method can also be used for the docking of other large components.

Material variation is inevitable in volume production, especially the sheet metal thickness variation, which influences part stiffness characteristic. The purpose of this paper is to present a new variation model of compliant sheet metal assembly with consideration of material variation influence.

The theory of computational solid mechanics is used to obtain the relationship between part stiffness matrix and material characteristic. The method of influence coefficients is adopted to deduce the assembly variation model.

Material variation‐induced influence coefficients to assembly variation are obtained, and a variation model of compliant sheet metal assembly with sources of material variations, part geometric variations and fixture variations is presented. Analysis shows that material variation has an important influence to assembly variations.

A quantitative relationship between assembly variations and material thickness variations is firstly given and a new variation model of compliant sheet metal assembly is presented to help designers to more exactly predict the assembly variation and diagnose variation sources.

Assembly variation analysis generally demands probability distributions of variation sources. However, due to small production volume in aircraft manufacturing, especially prototype manufacturing, the probability distributions are hard to obtain, and only the small-sample data of variation sources can be consulted. Thus, this paper aims to propose a variation analysis method driven by small-sample data for compliant aero-structure assembly.

First, a hybrid assembly variation model, integrating rigid effects with flexibility, is constructed based on the homogeneous transformation and elasticity mechanics. Then, the bootstrap approach is introduced to estimate a variation source based on small-sample data. The influences of bootstrap parameters on the estimation accuracy are analyzed to select suitable parameters for acceptable estimation performance. Finally, the process of assembly variation analysis driven by small-sample data is demonstrated.

A variation analysis method driven by small-sample data, considering both rigid effects and flexibility, is proposed for aero-structure assembly. The method provides a good complement to traditional variation analysis methods based on probability distributions of variation sources.

With the proposed method, even if probability distribution information of variation sources cannot be obtained, accurate estimation of the assembly variation could be achieved. The method is well suited for aircraft assembly, especially in the stage of prototype manufacturing.

A variation analysis method driven by small-sample data is proposed for aero-structure assembly, which can be extended to deal with other similar applications.

A new deviation propagation model considering the form defects in compliant assembly process is proposed. The purpose of this paper is to analyze the deviation propagation by using the basic deviation fields. In particular, each basic deviation field is defined with a generalized compliance matrix of part.

First, the form defects of parts may be decomposed into a linear combination of basic deviation fields, which are constructed by the eigen-decomposition of the structure stiffness of parts with ideal dimensions. Each basic deviation field is defined with a generalized compliance of part. Moreover, by analyzing the relationship between the basic deviation fields before and after assembling process, a new sensitive matrix is obtained in which each value expresses the correlation of a basic deviation field between the parts and the assembly.

This model may solve the deviation propagation problems of compliant assembly with considering form defects. Here, one case is used to illustrate the deviation propagation in the assembly process. The results indicate that the proposed method has higher accuracy than the method of influence coefficient when the entire deviation fields of parts are considered. Moreover, the numerical results with the proposed method basically agree with the experimental measurements.

Owing to the hypothesis of linear superposition of basic deviation fields, the research in this paper is limited to the parts with linear elastic deformation. However, the entire form defects of parts are considered rather than the deviations of the local feature points. It may be extended to analyze the three-dimensional deviations of complex thin-walled parts.

A deviation propagation model considering parts form defects is developed to achieve more accurate predictions of assembly deviation by using the basic deviation fields.

The structure stiffness is greatly affected by the fixture constraints during assembly due to the flexibility of large-scale thin-walled structures. The compliant deformation of structures is usually not consistent for the non-uniform stiffness in various clamping schemes. The purpose of this paper is to investigate the correlation between the assembly quality and the clamping schemes of structures with various initial deviations and geometrical parameters, which is based on the proposed irregular quadrilateral plate element via absolute nodal coordinate formulation (ANCF).

Two typical clamping schemes are specified for the large-scale thin-walled structures. Two typical deviation modes are defined in both free and clamping states in the corresponding clamping schemes. The new irregular quadrilateral plate element via ANCF is validated to analyze the compliant deformation of assembled structures. The quasi-static force equilibrium equations are extended considering the factors of clamping constraints and geometric deviations.

The initial deviations and geometrical parameters strongly affect the assembly deviations of structures in two clamping schemes. The variation tendencies of assembly deviations are demonstrated in details with the circumferential clamping position and axial clamping position in two clamping schemes, providing guidance to optimize the fixture configuration. The assembly quality of structures with deviations can be improved by configuration synthesis of the clamping schemes.

Typical over-constraint clamping schemes and deviation modes in clamping states are defined for large-scale thin-walled structures. The plate element via ANCF is extended to analyze the assembly deviations of thin-walled structures in various clamping schemes. Based on the proposed theoretical model, the effects of clamping schemes and initial deviations on the deformation and assembly deviation propagation of structures are investigated.

This study aims to present a model and analysis of automotive body outer cover panels (OCPs) assembly systems to predict assembly variation. In the automotive industry, the OCPs assembly process directly influences the quality of the automobile body appearance. However, suitable models to describe variation propagation of OCPs assembly systems remain unknown.

An adaptive state space model for OCPs assembly systems is introduced to accurately express variation propagation, including variation accumulation and transition, where two compliant deviations make impacts on key product characteristics (KPCs) of OCP, and the impacts are accumulated from welding process to threaded connection process. Another new source of variation from threaded connection is included in this model. To quantify the influence of variation from threaded connection on variation propagation, the threaded connection sensitivity matrix is introduced to build up a linear relationship between deviation from threaded connection and output deviation in KPCs. This matrix is solved by homogeneous coordinate transformation. The final deviation of KPCs will be transferred to ensure gaps and flushes between two OCPs, and the transition matrix is considered as a unit matrix to build up the transition relationship between different states.

A practical case on the left side body structure is described, where simulation result of variation propagation reveals the basic rule of variation propagation and the significant effect of variation from threaded connection on variation propagation of OCPs assembly system.

The model can be used to predict assembly variation or potential dimension problems at a preliminary assembly phase. The calculated results of assembly variation guide designers or technicians on tolerance allocation, fixture layout design and process planning.

The purpose of this paper is to propose a hybrid algorithm of the heuristic algorithm and the orthogonal design to optimize schemes of welding points (WPs). Assembly variation plays an important role in product manufacture. Different schemes of WPs can influence the sensitivity matrices between part and assembly variations.

The paper proposes a hybrid algorithm to optimize schemes of WPs among components. The hybrid algorithm is composed of the heuristic algorithm and the orthogonal design. The heuristic algorithm is used to optimize the initial scheme; moreover, the last result is generated according to the orthogonal table. Although the algorithm cannot assure generating the optimal scheme, it can acquire the satisfying result by using few times of finite element analysis.

Finally, a rear bracket lamp assembly is illustrated to optimize the schemes of WPs between two components. Results show that the algorithm is efficient to generate the optimized WPs scheme for sheet metal assemblies.

A hybrid algorithm is proposed to optimize schemes of WPs among components, which is composed of the heuristic algorithm and the orthogonal design.