Level Detection Equipment for Measuring the Influence of Different Leveling Accuracies on Linear Error

This study developed a level detection equipment which is used in computer numerical control (CNC) machine tool to determine the impact of leveling accuracy on rectilinear motion accuracy. When the CNC precision machine tool has accuracy deterioration under external load or internal stress, mainly caused error is leveling error, this research and development equipment can immediate to analyze and measurement. The allowable error of leveling accuracy can be obtained after experimental validation. The kinematic error relatively increases with leveling error. When the leveling accuracy is within the allowable error, the kinematic error relatively decreases. The main kinematic error items measured in this study include EXX, EBY, EAX, and EYY. The level detection equipment is developed in this study, and the fuzzy regression analysis is used for modeling. The model that has high accuracy in the test of the X -axis is R 2 = 0.9764 and P = 0.0506 , and Y -axis is R 2 = 0.9756 and P = 0.0524 . In terms of filtering, Kalman filtering is used for signal processing, the measured values and X -axis and Y -axis after filtering are improved by 94.1% and 86.2%, respectively, the repeatability of this system is about A grade capability of precision (Cp), resolution is ±0.0001°, and the stability is at least B grade capability of accuracy (Ca). This equipment has the advantages of low cost, high precision, and 2-axis measurement. This machine tool which has the straightness increases with X and Y axes’ leveling accuracy errors, when the X / Y leveling accuracy is within ±0.01 mm/m, and there is the best straightness and conforms to the ISO230 standard (Lee et al., 2020).

A Comprehensive Numerical Study on the Number of Identifiable Kinematic Parameters of Parallel Mechanisms

Kinematic error model plays an important role in improving the positioning accuracy of robot manipulators by kinematic calibration. The identifiability of kinematic parameters in the error model directly affects the positioning accuracy of the mechanism. And the number of identifiable kinematic parameters determines how many parameters can be accurately identified by kinematic calibration, which is one of the theoretical basis of kinematic error modeling. For serial mechanisms, a consensus has been reached that the maximum number of identifiable kinematic parameters is 4R + 2P + 6, where R and P represent the numbers of revolute and prismatic joints, respectively. Due to complex topologies of parallel mechanisms, there is still no agreement on the formula of the maximum number of identifiable parameters. In this paper, a comprehensive numerical study on the number of identifiable kinematic parameters of parallel mechanisms is conducted. The number of identifiable parameters of 3802 kinds of limbs with different types or actuation arrangements are analyzed. It can be concluded that the maximum number of identifiable kinematic parameters is Σ i = 1 n 4Ri + 2Pi + 6 − Ci − 2(PP)i/3(PPP1)i/(2Ri + 2Pi)(PPP)i, where Ci represents the number of joints whose motion cannot be measured and n denotes the number of limbs in a parallel mechanism; (PP)i, (PPP1)i, and (PPP)i represent two consecutive unmeasurable P joints, three consecutive P joints in which two of them cannot be measured, and three unmeasurable P joints, respectively.

Experimental Analysis on the Effectiveness of Kinematic Error Compensation Methods for Serial Industrial Robots

Based on the established serial 6-DOF robot calibration experiment platform, this paper aims to analyze and compare the effects of four error compensation methods, which are pseudotarget iteration-based error compensation method with three different forms and the Newton–Raphson-based error compensation method. Firstly, the pose error model of the serial robot is established based on the M-DH model in this paper. The calibration results show that the accuracy of the Staubli TX60 robot has been greatly improved. The average comprehensive position accuracy is increased by 88.7%, and the average comprehensive attitude accuracy is increased by 56.6%. Secondly, the principles of the four error compensation methods are discussed, and the effectiveness of the four error compensation methods are compared through experiments. The results show that the four error compensation methods can achieve error compensation well. The compensation accuracy is consistent with the identification accuracy of the kinematic model. The pseudotarget iteration with differential form has the best performance by the comprehensive consideration of accuracy and computational efficiency. Error compensation determines whether the accuracy of the identified model can be achieved. This paper presents a systematic experimental validation research on the effectiveness of four error compensation methods, which provides a reliable reference for the kinematic error compensation of industrial robots.

Comparing approaches for multi-axis kinematic positioning in machine tools

Maintaining minimal levels of geometric error in the finished workpiece is of increasing importance in the modern production environment; there is considerable research on the identification, verification and calibration of machine tool kinematic error, and the development of Postprocessor implementations to generate NC-code optimised for machining accuracy. The choice of multi-axis positioning function at the controller, however, is an often-overlooked potential source of kinematic error which can be responsible for costly mistakes in the production environment. This paper presents an investigation into how mis-management of the positional error parameters that define the rotary-axes’ pivot point can lead to unintended variations in multi-axis positioning. Four approaches for kinematic positioning on a Fanuc-based controller are considered, which reference two separate parameter locations to define the pivot point – managing the kinematics within the Postprocessor itself, full five-axis positioning with a fixture offset, full five-axis with rotation tool centre point control and 3+2-axis with a tilted workplane. Error vectors across four sets of rotary-axis indexations are simulated based on the theoretical kinematic model, to highlight the expected differences in geometric error attributable to mismatched pivot point parameters. Finally, the simulation results are verified experimentally, demonstrating the importance of maintaining a consistent approach in both programming and operation environments.

Mathematical Model of Dynamic-Kinematic Error of a Harmonic Drive

Reducing the kinematic error when designing a high-precision drive with a harmonic gear train (HGT) is an urgent task. Currently, a large number of studies have been conducted to determine this parameter, but the effect of the wave generator rotation frequency on the kinematic error of the HGT has been considered insufficiently. A mathematical model is proposed for determining the frequency response of the HGT dynamic-kinematic error, taking into account the elastic interaction of its elements and the error of the cam mounting. The results of the calculated determination of the frequency response of a HGT with a cam wave generator are presented. The presence of several resonant frequencies that occur due to periodic changes in the relative position of the HGT elements and the vector of the cam mounting error is defined. It is proved that the two main resonant frequencies are caused by the rotation of the vector of the cam mounting error relative to the large axis of the wave generator and the balls of the flexible bearing.

A Novel Error Equivalence Model on the Kinematic Error of the Linear Axis of High-End Machine Tool

The kinematic errors of the linear axis play a key role in machining precision of high-end CNC (Computer Numerical Control) machine tool. The quantification of error relationship is still an urgent problem to be solved in the assembly process of the linear axis, especially considering the effect of the elastic deformation of rollers. A systematic error equivalence model of slider is proposed to improve the prediction accuracy for kinematic errors of the linear axis which contains the base, the linear guide rail and carriage. Firstly, the geometric errors of assembly surface of linear guide rail are represented by small displacement torsor. According to the theory of different motion of robots, the error equivalence model of a single slider is established, namely the geometric error of assembly surface of linear guide rail and the pose error of slider is equivalent to the elastic deformation of roller. Based on the principle of vector summation, the kinematic error of a single slider is mapped to the carriage and the kinematic error of the linear axis is obtained. Besides, experiments validation of kinematic error model of the linear axis is carried out. It is indicated that the proposed model is accurate and feasible. The proposed model can provide an accurate guidance for the manufacturing and operation performance of the linear axis in quantification, and a more effective reference for the engineers at the design and assembly stage.