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The purpose of this paper is to carry out a tolerance analysis with geometric tolerances by means of the Jacobian model. Tolerance analysis is an important task to design and to manufacture high-precision mechanical assemblies; it has received considerable attention by the literature. The Jacobian model is one of the methods proposed by the literature for tolerance analysis. The Jacobian model cannot deal with geometric tolerances for mechanical assemblies. The geometric tolerances may not be neglected for assemblies, as they significantly influence their functional requirements.

This paper presents how it is possible to deal with geometric tolerances when a tolerance analysis is carried out by means of a Jacobian model for a 2D and 3D assemblies for which the geometric tolerances applied to the components involve only translational deviations. The three proposed approaches modify the expression of the stack-up function to overcome the shortage of Jacobian model that the geometric error cannot be processed.

The proposed approach has been applied to a case study. The results of the case study show how, when a statistical approach is implemented, the Jacobian model with the three developed methods gives results very similar to those due to other models of the literature, such as vector loop and variational.

In particular, the proposed approach may be applied only when the applied geometrical tolerances involve translational variations in 3D assemblies.

Tolerance analysis is a valid tool to foresee geometric interferences among the components of an assembly before getting the physical assembly. It involves a decrease of the manufacturing costs.

The original contribution of the paper is due to three methods to make a Jacobian model able to consider form and geometric deviations.

The purpose of this paper is to carry out an assembly tolerance analysis by means of a combined Jacobian model and skin model shape. The former is based on small displacements modeling of points using 6 × 6 transformation matrices of open kinematic chains in robotics. The latter easily models toleranced features with all kinds of geometric deviations.

This paper presents the procedure of performing tolerance analysis by means of the Jacobian model and skin model shape for assemblies. The point cloud-based discrete representative is able to model the actual toleranced surfaces instead of the ideal or associated ones in an assembly, which brings the simulation tools closer to reality.

The proposed method has the advantage of skin model shape which is suitable for geometric tolerances management along the product life cycle and contact analysis of kinematic small variations, as well as, with the Jacobian, enabling transformation of locally expressed parts deviations to globally expressed functional requirements. The result of the case study shows the accuracy of the method.

The proposed approach has not been developed fully; other functional features such as the pyramid are still ongoing challenges.

It is an effective method for supporting design, manufacturing and inspection by providing a quantitative analysis of the effects of multi-tolerances on the final functional key characteristics and for predicting the quality level.

The paper is original in taking advantages of both Jacobian model and skin model shape to consider all geometric tolerances in assembly.

The purpose of this paper is to propose a novel mathematical model to present the three-dimensional tolerance of a discrete surface and to carry out an approach to analyze the tolerance of an assembly with a discrete surface structure. A discrete surface is a special structure of a large surface base with several discrete elements mounted on it, one, which is widely used in complex electromechanical products.

The geometric features of discrete surfaces are separated and characterized by small displacement torsors according to the spatial relationship of discrete elements. The torsor cluster model is established to characterize the integral feature variation of a discrete surface by integrating the torsor model. The influence and accumulation of the assembly tolerance of a discrete surface are determined by statistical tolerance analysis based on the unified Jacobian-Torsor method.

The effectiveness and superiority of the proposed model in comprehensive tolerance characterization of discrete surfaces are successfully demonstrated by a case study of a phased array antenna. The tolerance is evidently and intuitively computed and expressed based on the torsor cluster model.

The tolerance analysis method proposed requires much time and high computing performance for the calculation of the statistical simulation.

The torsor cluster model achieves the three-dimensional tolerance representation of the discrete surface. The tolerance analysis method based on this model predicts the accumulation of the tolerance of components before their physical assembly.

This paper proposes the torsor cluster as a novel mathematical model to interpret the tolerance of a discrete surface.

Assembly errors of aeroengine rotor must be controlled to improve the aeroengine efficiency. However, current method cannot truly reflect assembly errors of the rotor in working state owing to difficulties in error analysis. Therefore, the purpose of this study is to establish an optimization method for aeroengine rotor stacking assembly.

The assembly structure of aeroengine rotor is featured. Rotor eccentricity is optimized based on Jacobian–Torsor model. Then, an optimization method for assembly work is proposed. The assembly process of the high-pressure compressor rotor and the high-pressure turbine rotor as the rotor core assembly is mainly considered.

An aeroengine rotor is assembled to verify the method. The results show that the predicted eccentricity differed from the measured eccentricity by 6.1%, with a comprehensive error of 8.1%. Thus, the optimization method has certain significance for rotor assembly error analysis and assembly process optimization.

In view of the error analysis in the stacking assembly of aeroengine rotor, an innovative optimization method is proposed. The method provides a novel approach for the aeroengine rotor assembly optimization and is applicable for the assembly of high-pressure compressor rotor and high-pressure turbine rotor as the rotor core assembly.

The conventional statistical method of three-dimensional tolerance analysis requires numerous pseudo-random numbers and consumes enormous computations to increase the calculation accuracy, such as the Monte Carlo simulation. The purpose of this paper is to propose a novel method to overcome the problems.

With the combination of the quasi-Monte Carlo method and the unified Jacobian-torsor model, this paper proposes a three-dimensional tolerance analysis method based on edge sampling. By setting reasonable evaluation criteria, the sequence numbers representing relatively smaller deviations are excluded and the remaining numbers are selected and kept which represent deviations approximate to and still comply with the tolerance requirements.

The case study illustrates the effectiveness and superiority of the proposed method in that it can reduce the sample size, diminish the computations, predict wider tolerance ranges and improve the accuracy of three-dimensional tolerance of precision assembly simultaneously.

The proposed method may be applied only when the dimensional and geometric tolerances are interpreted in the three-dimensional tolerance representation model.

The proposed tolerance analysis method can evaluate the impact of manufacturing errors on the product structure quantitatively and provide a theoretical basis for structural design, process planning and manufacture inspection.

The paper is original in proposing edge sampling as a sampling strategy to generating deviation numbers in tolerance analysis.

To improve the trajectory tracking accuracy of 6R decoupled manipulator in singularity region, this paper aims to propose a singularity avoidance algorithm named “singularity separation plus improved Gaussian distribution damped reciprocal”.

The manipulator is divided into forearm and wrist, and the corresponding singularity factors are separated based on kinematics calculation. Singularity avoidance is achieved by replacing the common reciprocal with the improved Gaussian distribution damped reciprocal.

Compared with common damped reciprocal algorithm and classical Gaussian distribution algorithm, the continuity of the proposed algorithm is improved and the tracking error is minimized. The simulation and experiment results prove effectiveness and practicability of the proposed algorithm.

This study has an important significance to improve the efficiency and operation accuracy of 6R decoupled manipulator.

The assembly simulation in tolerance analysis is one of the most important steps for the tolerance design of mechanical products. However, most assembly simulation methods are based on the rigid body assumption, and those assembly simulation methods considering deformation have a poor efficiency. This paper aims to propose a novel efficient and precise tolerance analysis method based on stable contact to improve the efficiency and reliability of assembly deformation simulation.

The proposed method comprehensively considers the initial rigid assembly state, the assembly deformation and the stability examination of assembly simulation to improve the reliability of tolerance analysis results. The assembly deformation of mating surfaces was first calculated based on the boundary element method with optimal initial assembly state, then the stability of assembly simulation results was assessed by the density-based spatial clustering of applications with noise algorithm to improve the reliability of tolerance analysis. Finally, combining the small displacement torsor theory, the tolerance scheme was statistically analyzed based on sufficient samples.

A case study of a guide rail model demonstrated the efficiency and effectiveness of the proposed method.

The present study only considered the form error when generating the skin model shape, and the waviness and the roughness of the matching surface were not considered.

To the best of the authors’ knowledge, the proposed method is original in the assembly simulation considering stable contact, which can effectively ensure the reliability of the assembly simulation while taking into account the computational efficiency.

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.

Aims to present a new approach for formulating state‐space equations of an electromechanical actuator using magnetic flux linkages as state variables.

The model is based on employment of discrete databases and their interpolation. The algorithm of determination of databases defining the flux/current characteristics of an actuator is described. Graphical interpretation of variable transformation is presented. A simplified, two‐axis model of reluctance motor is used to illustrate the application of the proposed modelling technique. Comparison with the classical model of the motor is used to verify the validity of the method. Analysis is focused on determination of saturation phenomenon influence on formulation methodology and on correctness of obtained results.

A very good agreement is observed between reference dq model and the proposed model. The main problem of the presented method is the existence of undefined entries in databases. Sufficiently dense databases can be used to overcome the problem.

The model is limited to actuators in which eddy currents and hysteresis phenomenon can be neglected. Future research will be concentrated on evaluation of different interpolation strategies of databases used in the model for realistic saturation conditions.

The model can be used as a library block for testing various control strategies for actuators without standard simplifying assumptions (e.g. sinusoidal winding distribution). It can be implemented in any simulational software (e.g. SIMULINK) as its block diagram is simple and no numerical differentiation is necessary in derivation of the model data.

Presents an extension of state‐space model of an actuator based on database discretised description of variables to two or more state variables.

Determinative locating and riveting distortions are highly coupled at assembly locale. Recent methods only take every tested or assumed locating errors at the mating surface into the process planning for the assemblies in a simple form. However, the growth of part number makes it nearly infeasible to take every locating error at every mating surface into the dimensional precision calculation. This paper aims to provide a solid riveting process planning for the reduction of practical locating-related distortions.

Large-scale metrology firstly measures the determinative coordinates for the locating-deviated key points. Iterative finite element (FE) analyses then calculate the riveting-related key point distortions from every rivet upsetting directions (UDs) and assembly sequence. These key points on the actual assembly contour and relative FE nodes yield two virtual planes. Virtual plane manipulation adds the riveting distortions into the locating-deviated coordinates. Finally, optimal algorithm integrates the iterative FE analyses with virtual plane manipulation.

Case studies validate that the virtual plane manipulation coincides with the test well, and the proposed method has good compensation of practical locating distortion.

The optimized rivet UDs may be set in a chaotic distribution, which may complicate the abundant riveting operations and the assembly appearance. Therefore, the use of automatic riveting systems can overcome the operational complexity, and the industrial design of rivet UD distribution will improve the assembly appearance.

The optimized UDs and assembly sequence are for assembly workers or automatic riveting systems.

The proposed method is the first to reduce the determinative locating distortion by a novel and efficient solid riveting process planning in detail, and the solid riveting process designed is conservative and accurate for practice.