Geometric Error Modeling Method Research Articles

Sensitivity Analysis and Accuracy Synthesis of a Deployable Antenna Considering Clearances and Link Tolerances

Abstract Antenna panels of a satellite are usually deployed and supported by a deployable mechanism. The accuracy of the deployable mechanism is important because it directly affects the performance of the satellite. This article focuses on the accuracy analysis of a deployable antenna considering the coupled effects of joint clearances and link tolerances, and based on which, two accuracy synthesis methods are further discussed. A novel geometric error modeling method is proposed to estimate the error space of the outer panel of the antenna. The advantages of the proposed method are that it can handle the overconstrained constraints efficiently and decouple the positioning error and orientation error. Moreover, the error space is visualized using a sampling method. Based on the proposed error modeling method, the maximum orientation and positioning errors are computed, and following which, sensitives of the antenna accuracy to tolerances considering various sizes of clearances are analyzed. Finally, two optimization methods for accuracy synthesis are discussed, and instructive conclusions are drawn.

A general approach for geometric error modeling of over-constrained hybrid robot

The geometric error model is critical to improve the absolute accuracy of an over-constrained hybrid robot, with the structure combining serial and parallel robots. Due to common constraints or redundant constraints in over-constrained mechanism, the motion of passive joints is always over-determined, which would destroy the rationality of previous error model. In this article, a geometric error modeling method of over-constrained hybrid robot based on the product of exponential formula is proposed. For any over-constrained robot, the existence and expression of constraint equations among geometric errors are deduced, thus above over-determined problem is solved. In addition, redundant errors are eliminated to ensure the minimality of error model. Due to constraint equations, the maximal number of identifiable errors is less than previous results, 4r+2p+6, where r and p denote the number of equivalent revolute and prismatic joints. Due to the standard modeling process, the method can be applied in any over-constrained hybrid robot. The method is validated by kinematic calibration of a 5-DOF 2UPU/SP-RR hybrid robot, and the results show that pose errors of this robot decrease by about 90%.

Geometric error modeling of the contact probe in a three-dimensional screw thread measuring machine

In this study, the influence of the geometric error of a contact probe on the accuracy of thread measurement was investigated to improve the measurement accuracy of three-dimensional (3D) screw thread measuring machines. The structure and measurement principle of the 3D thread measuring machine were studied, and the geometric error sources of the contact probe were analyzed. The principles of space coordinate transformation and the geometric theorem were used to establish a geometric model of the error sources. The experimental platform and the standard ball measurement of the three-coordinate machine were configured to verify the geometric error model. The results revealed that the measurement error was significantly reduced after compensation by the model. The proposed geometric error modeling method provides a clear theoretical basis for the accurate compensation of contact probe deviations and further improves the measurement accuracy of 3D thread measuring machines.

Design and analysis of full-scale scanning system for curved glass based on motion and 3D features.

In recent years, mobile phones with glass curved screens have become more and more widely used. The irregular shape of the curved screen and the light transmittance characteristic of the glass have brought great challenges to its automatic defect detection. Aiming at the defect detection of the glass cover of the curved screen, this paper designs a full-scale scanning system by combining motion and three-dimensional (3D) features. First, a scanning system is constructed, and a geometric error modeling method is proposed to improve the accuracy of the scanning system; second, based on the point cloud of the 3D glass cover obtained by the scanning system, a point cloud registration method is presented by integrating the motion and 3D features; finally, the laser tracker is further used to calibrate the scanning system to analyze the mechanical error. Experimental results show that the introduction of straightness error and perpendicularity error can effectively solve the mismatch and fault problems of point cloud registration, and improve the accuracy of the scanning system. In addition, the registration method proposed in this paper can effectively reconstruct the complete point cloud of 3D glass cover for detection. The reconstruction accuracy of the plane part can reach 0.031 mm, and that of the curved part can reach 0.091 mm.

Assembly Error Modeling and Calculating Method of Precision Mechanical System

Nowadays, there is no effective quantitative analysis method to describe the influence of design tolerance on the machining error of parts and the assembly accuracy of mechanical system at the design stage, which makes it difficult to analyze, predict and control the assembly accuracy in the actual assembly process, Aiming at this problem, a method for representation and modeling of geometric errors of parts is proposed. Furthermore, based on the above-mentioned geometric error modeling method of parts, a research method of geometric error transfer analysis and modeling for precision mechanical system oriented to actual assembly process is proposed.

High precision and fast solution method for linearized assembly contact point of geometric error surface

The geometric error modeling method for assembly[1] proposes a feasible basis for the assembly process considering manufacturing error. However, contacting two mounting surfaces with geometric error and finding their actual contact points are two main difficulties in the study of real three-dimensional parts assembly methods. A high-precision and fast solution method for linearized assembly contact points considering geometric errors is proposed by calculating the point cloud spatial pose of the actual contact surface. This method is suitable for spatial pose calculation in high precision plane assembly of rigid parts, which enables fast, accurate and quantitative solution of the positional relationship of components during assembly and measurement, and improves the accuracy and efficiency of spatial pose prediction and control.

A Geometric Error Modeling Method and Trajectory Optimization Applied in Laser Welding System

In this paper, a geometric error modeling method is carried out on six-axis motion platform (SMP) in laser welding system (LWS), and an optimized algorithm is proposed for the alignment in LWS based on the error model. First, the topological structure of the given SMP is analyzed, and related homogeneous transformation matrices which are used for standing the orientation of SMP are established. By these matrices, the geometric error model is developed mathematically. Then, the error model is used for predicting the alignment deviations. A corresponding series of experiments for calculating the optical power loss in alignment are employed, and the comparison between simulation and experiments results indicate the validation of the error model. Furthermore, an optimized algorithm is applied to search the optimum aligning trajectory. Compared to conventional method, this algorithm has a broader range in searching extreme value, which can reduce the computational volume and improve the efficiency. It is also beneficial for improving the success rate of escaping from the local minimum spot and finding the optimum alignment spot. The error model is helpful to analyze the error propagation process and improve the alignment efficiency in LWS, which can be applied to other similar multi-axis precise system.

Geometric error analysis of an over-constrained parallel tracking mechanism using the screw theory

This paper deals with geometric error modeling and sensitivity analysis of an over-constrained parallel tracking mechanism. The main contribution is the consideration of over-constrained features that are usually ignored in previous research. The reciprocal property between a motion and a force is applied to tackle this problem in the framework of the screw theory. First of all, a nominal kinematic model of the parallel tracking mechanism is formulated. On this basis, the actual twist of the moving platform is computed through the superposition of the joint twist and geometric errors. The actuation and constrained wrenches of each limb are applied to exclude the joint displacement. After eliminating repeated errors brought by the multiplication of wrenches, a geometric error model of the parallel tracking mechanism is built. Furthermore, two sensitivity indices are defined to select essential geometric errors for future kinematic calibration. Finally, the geometric error model with minimum geometric errors is verified by simulation with SolidWorks software. Two typical poses of the parallel tracking mechanism are selected, and the differences between simulation and calculation results are very small. The results confirm the correctness and accuracy of the geometric error modeling method for over-constrained parallel mechanisms.