This paper proposes a laser tracker based kinematic calibration of a 3-degree-of-freedom (DoF) rotational parallel manipulator that would be applied in tracking and positioning fields. The process is implemented in this paper by four steps: 1) formulation of the geometric error model of this manipulator by means of screw theory considering all possible geometric source errors, which is followed by the verification of this error model employing SolidWorksź software. 2) sensitivity analysis of all geometric source errors based upon Monte Carlo method and remove some errors that have little influence on the pose accuracy of the moving platform in order to decrease the difficulty and complexity of the kinematic calibration. 3) error parameter identification and kinematic calibration experiment using laser tracker. 4) error compensation by amending controller model. Kinematic calibration experiment results of this 3-DoF rotational parallel manipulator show that three angular deviations are improved from 1.97°, 0.24° and 1.75° to 0.53°, 0.10° and 0.19° respectively within the prescribed workspace. Geometric error modeling based on screw theory is presented.The geometric error model is verified based upon the software method.Calibration includes sensitivity analysis, measurement plan and error identification.Software simulation and experiment are given to verify kinematic calibration flow.

Kinematic calibration of a 3-DoF rotational parallel manipulator using laser tracker

This paper proposes a product of exponential (POE) model to integrate the geometric errors of multi-axis machine tools. Firstly, three twists are established to represent the six basic error components of each axis in an original way according to the geometric definition of the errors and twists. The three twists represent the basic errors in x, y, and z directions, respectively. One error POE model is established to integrate the three twists. This error POE formula is homogeneous and can express the geometric meaning of the basic errors, which is precise enough to improve the accuracy of the geometric error model. Secondly, squareness errors are taken into account using POE method to make the POE model of geometric errors more systematic. Two methods are proposed to obtain the POE models of squareness errors according to their geometric properties: The first method bases on the geometric definition of errors to obtain the twists directly; the other method uses the adjoint matrix through coordinate system transformation. Moreover, the topological structure of the machine tools is introduced into the POE method to make the POE model more reasonable and accurate. It can organize the obtained 14 twists and eight POE models of the three-axis machine tools. According to the order of these POE models multiplications, the integrated POE model of geometric errors is established. Finally, the experiments have been conducted on an MV-5A three-axis vertical machining center to verify the model. The results show that the integrated POE model is effective and precise enough. The error field of machine tool is obtained according to the error model, which is significant for the error prediction and compensation.

Product of exponential model for geometric error integration of multi-axis machine tools

Anomaly detection of time series is an important topic that has been widely studied in many application areas. A number of computational methods were developed for this task in the past few years. However, the existing approaches still have many drawbacks when they were applied to specific questions. In this paper, we proposed a meta-feature-based anomaly detection approach (MFAD) to identify the abnormal states of a univariate or multivariate time series based on local dynamics. Differing from the traditional strategies of “sliding window” in anomaly detection, our method first defined six meta-features to statistically describe the local dynamics of a 1-D sequence with arbitrary length. Second, multivariate time series was converted to a new 1-D sequence, so that each of its segmented subsequence was represented as one sample with six meta-features. Finally, the anomaly detection of univariate/multivariate time series was implemented by identifying the outliers from the samples in a 6-D transformed space. In order to validate the effectiveness of MFAD, we applied our method on various univariate and multivariate time series datasets, including six well-known standard datasets (e.g. ECG and Air Quality) and eight real-world datasets in shield tunneling construction. The simulation results show that the proposed method MFAD not only identifies the local abnormal states in the original time series but also drastically reduces the computational complexity. In summary, the proposed method effectively identified the abnormal states of dynamical parameters in various application fields.

Detecting Anomalies in Time Series Data via a Meta-Feature Based Approach

This paper proposes the precision enhancement of five-axis machine tools using product-of-exponential (POE) formulas through geometric error modeling and compensation. Firstly, two issues of geometric error Denavit–Hartenberg (D-H) models for five-axis machine tools are discussed for further improvement: models of squareness errors and position of rotary axes. Three D-H models of squareness errors and three expressions of position of rotary axes are represented and analyzed. Secondly, POE formulas are established to solve the two problems and to realize the modeling and compensation. The rotation twists and rotation POE formulas of rotary axes are established with the help of the clear geometric meaning of twists to describe their positions and motions. Then, corresponding POE formulas of squareness errors are established by analyzing their geometric definition. All motion POE formulas, rotation POE formulas, and error POE formulas are multiplied in certain order to obtain the final geometric error POE formula of five-axis machine tools. In addition, Jacobian of twists is calculated easily and reasonably with the twists of each axis for the geometric error compensation. Thirdly, experiments are conducted on one SmartCNC500 five-axis machine tool in order to verify the effectiveness of error POE formula and corresponding compensation.

Product-of-exponential formulas for precision enhancement of five-axis machine tools via geometric error modeling and compensation

Cutterhead torque is an important operational parameter that reflects the obstruction degree of geological environment to shield tunneling machine. Accurate multi-step prediction for cutterhead torque is of crucial significance for ensuring efficient and safe propulsion of shield tunneling machine. In this study, a novel hybrid multi-step prediction model combining variational mode decomposition (VMD), empirical wavelet transform (EWT) and long short-term memory (LSTM) network is proposed for shield tunneling machine cutterhead torque. To begin with, the VMD is employed to decompose the original cutterhead torque subsequences into some subsequences and residual sequence, and the residual sequence is further decomposed by the EWT. The combination of VMD and EWT significantly reduces the complexity of the original cutterhead torque sequence. On this basis, the LSTM neural network is employed to predict each subsequence in multiple time steps, and finally add the prediction results of each subsequence to realize the multi-step cutterhead torque prediction. To demonstrate performance of the presented VMD-EWT-LSTM-based approach, comparisons with recent prediction algorithms in six datasets is conducted. The results testify that accuracy of the VMD-EWT-LSTM-based prediction approach is better than other methods. In six datasets, from 1st step prediction to 5th step prediction, the average accuracy of presented prediction approach reaches 97.7%, 97.2%, 96.9%, 96.7% and 96.3%, respectively. Hence, the VMD-EWT-LSTM-based approach can accurately predict cutterhead torque of shield tunneling machine in multiple time steps.

A VMD-EWT-LSTM-based multi-step prediction approach for shield tunneling machine cutterhead torque

Geometric Error Modeling of Machine Tools Based on Screw Theory

https://www.tpbin.com/Uploads/Subjects/12e3e456-b160-4757-9cd8-629d1ab8e4b7.pdf

Force transmission characteristics for the non-equidistant arrangement thrust systems of shield tunneling machines

Research on characteristics of deformation in thrust system for EPB shield machines

Stiffness is one of the most important criteria in machine tool design. The stiffness of a gantry machine tool based on a 3-DOF planar parallel mechanism was analyzed by considering the deformation of the parallel links and the joints. The differential error model was used to develop the machine tool stiffness matrix. The solution gave contour plots of the position stiffness and the rotation stiffness. The simulation shows that the joint stiffness has an important effect on the machine tool stiffness; therefore, high stiffness joints should be used in parallel or hybrid machine tools. The results also show that the position stiffness is symmetric along the Y direction and the rotation stiffness is asymmetric in the machine tool working space.

Stiffness analysis of gantry hybrid machine tools

Tracking errors affect the motion accuracy of parallel mechanisms. This paper describes a method to reduce tracking errors of parallel mechanisms using a planar parallel mechanism with two degrees of freedom as an example. The mechanism dynamics are deduced from the kinematics using the Lagrange multiplier approach. The robust trajectory tracking control strategy accounts for model errors and external disturbances using linear feedback theory for the non-linear system, which ensures system stability and limits the effects of disturbances. Simulations show that the trajectory tracking control significantly reduces tracking errors with faster error convergence speed. The control method can be applied to various kinds of parallel mechanisms.

Tang Xiaoqiang

Papers

Geometric Error Modeling of Machine Tools Based on Screw Theory

Force transmission characteristics for the non-equidistant arrangement thrust systems of shield tunneling machines

Research on characteristics of deformation in thrust system for EPB shield machines

Stiffness analysis of gantry hybrid machine tools

Robust trajectory tracking control of a planar parallel mechanism