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In typical model-based calibration, linearization errors are derived inevitably, and non-negligible negative impact will be induced on the identification results if the rotational kinematic errors are not small enough or the lengths of links are too long, which is common in the industrial cases. Thus, an accurate two-step kinematic calibration method minimizing the linearization errors is presented for a six-DoF serial robot to improve the calibration accuracy.

The negative impact of linearization on identification accuracy is minimized by removing the responsible linearized kinematic errors from the complete kinematic error model. Accordingly, the identification results of the dimension-reduced new model are accurate but not complete, so the complete kinematic error model, which achieves high identification accuracy of the rest of the error parameters, is combined with this new model to create a two-step calibration procedure capable of highly accurate identification of all the kinematic errors.

The proportions of linearization errors in measured pose errors are quantified and found to be non-negligible with the increase of rotational kinematic errors. Thus, negative impacts of linearization errors are analyzed quantitatively in different cases, providing the basis for allowed kinematic errors in the new model. Much more accurate results were obtained by using the new two-step calibration method, according to a comparison with the typical methods.

This new method achieves high accuracy with no compromise on completeness, is easy to operate and is consistent with the typical method because the second step with the new model is conveniently combined without changing the sensors or measurement instrument setup.

The purpose of this paper is to propose an error model for serial robot kinematic calibration based on dual quaternions.

The dual quaternions are the combination of dual-number theory and quaternion algebra, which means that they can represent spatial transformation. The dual quaternions can represent the screw displacement in a compact and efficient way, so that they are used for the kinematic analysis of serial robot. The error model proposed in this paper is derived from the forward kinematic equations via using dual quaternion algebra. The full pose measurements are considered to apply the error model to the serial robot by using Leica Geosystems Absolute Tracker (AT960) and tracker machine control (T-MAC) probe.

Two kinematic-parameter identification algorithms are derived from the proposed error model based on dual quaternions, and they can be used for serial robot calibration. The error model uses Denavit–Hartenberg (DH) notation in the kinematic analysis, so that it gives the intuitive geometrical meaning of the kinematic parameters. The absolute tracker system can measure the position and orientation of the end-effector (EE) simultaneously via using T-MAC.

The error model formulated by dual quaternion algebra contains all the basic geometrical parameters of serial robot during the kinematic calibration process. The vector of dual quaternion error can be used as an indicator to represent the trend of error change of robot’s EE between the nominal value and the actual value. The accuracy of the EE is improved after nearly 20 measurements in the experiment conduct on robot SDA5F. The simulation and experiment verify the effectiveness of the error model and the calibration algorithms.

This paper aims to propose a calibration model for kinematic parameters identification of serial robot to improve its positioning accuracy, which only requires position measurement of the end-effector.

The proposed model is established based on local frame representation of the product of exponentials (local POE) formula, which integrates all kinematic errors into the twist coordinates errors; then they are identified with the tool frame’ position deviations simultaneously by an iterative least squares algorithm.

To verify the effectiveness of the proposed method, extensive simulations and calibration experiments have been conducted on a 4DOF SCARA robot and a 5DOF drilling machine, respectively. The results indicate that the proposed model outperforms the existing model in convergence, accuracy, robustness and efficiency; fewer measurements are needed to gain an acceptable identification result.

This calibration method has been applied to a variable-radius circumferential drilling machine. The machine’s positioning accuracy can be significantly improved from 11.153 initially to 0.301 mm, which is well in the tolerance (±0.5 mm) for fastener hole drilling in aircraft assembly.

An accurate and efficient kinematic calibration model has been proposed, which satisfies the completeness, continuity and minimality requirements. Due to generality, this model can be widely used for serial robot kinematic calibration with any combination of revolute and prismatic joints.

This paper aims to propose a united kinematic calibration method for a dual-machine system in automatic drilling and riveting. The method takes both absolute and relative pose accuracy into account, which will largely influence the machining accuracy of the dual-machine system and assembly quality.

A comprehensive kinematic model of the dual-machine system is established by the superposition of sub-models with pose constraints, which involves base frame parameters, kinematic parameters and tool frame parameters. Based on the kinematic model and the actual pose error data measured by a laser tracker, the parameters of coordinated machines are identified by the Levenberg–Marquardt method as a multi-objective nonlinear optimization problem. The identified parameters of the coordinated machines will be used in the control system.

A new calibration method for the dual-machine system is developed, including a comprehensive kinematic model and an efficient parameter identification method. The experiment results show that with the proposed method, the pose accuracy of the dual-machine system was remarkably improved, especially the relative position and orientation errors.

This method has been used in an aircraft assembly project. The calibrated dual-machine system shows a good performance on system coordination and machining accuracy.

This paper proposes a new method with high accuracy and efficiency for the dual-machine system calibration. The research can be extended to multi-machine and multi-robot fields to improve the system precision.

This paper aims to address the issue of model discontinuity typically encountered in traditional Denavit-Hartenberg (DH) models. To achieve this, we propose the use of a local Product of Exponentials (POE) approach. Additionally, a modified calibration model is presented which takes into account both kinematic errors and high-order joint-dependent kinematic errors. Both kinematic errors and high-order joint-dependent kinematic errors are analyzed to modify the model.

Robot positioning accuracy is critically important in high-speed and heavy-load manufacturing applications. One essential problem encountered in calibration of series robot is that the traditional methods only consider fitting kinematic errors, while ignoring joint-dependent kinematic errors.

Laguerre polynomials are chosen to fitting kinematic errors and high-order joint-dependent kinematic errors which can avoid the Runge phenomenon of curve fitting to a great extent. Levenberg–Marquard algorithm, which is insensitive to overparameterization and can effectively deal with redundant parameters, is used to quickly calibrate the modified model. Experiments on an EFFORT ER50 robot are implemented to validate the efficiency of the proposed method; compared with the Chebyshev polynomial calibration methods, the positioning accuracy is improved from 0.2301 to 0.2224 mm.

The results demonstrate the substantial improvement in the absolute positioning accuracy achieved by the proposed calibration methods on an industrial serial robot.

A three-dimensional (3D) printing error simulation approach is proposed to analyze the influence of tilted vertical beams on the 3D printing accuracy. The purpose of this study is to analyze the influence of such errors on printing accuracy and printing quality for delta-robot 3D printer.

First, the kinematic model of a delta-robot 3D printer with an ideal geometric structure is proposed by using vector analysis. Then, the normal kinematic model of a nonideal delta-robot 3D robot with tilted vertical beams is derived based on the above ideal kinematic model. Finally, a 3D printing error simulation approach is proposed to analyze the influence of tilted vertical beams on the 3D printing accuracy.

The results show that tilted vertical beams can indeed cause 3D printing errors and further influence the 3D printing quality of the final products and that the 3D printing errors of tilted vertical beams are related to the rotation angles of the tilted vertical beams. The larger the rotation angles of the tilted vertical beams are, the greater the geometric deformations of the printed structures.

Three vertical beams and six horizontal beams constitute the supporting parts of the frame of a delta-robot 3D printer. In this paper, the orientations of tilted vertical beams are shown to have a significant influence on 3D printing accuracy. However, the effect of tilted vertical beams on 3D printing accuracy is difficult to capture by instruments. To reveal the 3D printing error mechanisms under the condition of tilted vertical beams, the error generation mechanism and the quantitative influence of tilted vertical beams on 3D printing accuracy are studied by simulating the parallel motion mechanism of a delta-robot 3D printer with tilted vertical beams.

Presents the kinematic calibration of an H4 parallel prototype robot using a vision‐based measuring device. Calibration is performed according to the inverse kinematic model method, using first the design model then a model developed for calibration purpose. To do so, the end‐effector pose (i.e. position and orientation) has to be measured with the utmost accuracy. Thus, first the practical accuracy of the low‐cost vision‐based measuring system is evaluated to have a precision in the order of magnitude of 10μ_it;m and 10^−3° for a 1,024×768 pixel CCD camera. Second, the prototype is calibrated using the easy‐to‐install vision system, yielding a final positioning accuracy of the end‐effector reduced from more than 1cm down to less than 0.5mm. Also provides a discussion on the use of such a method on commercial systems.

Calibrating kinematic parameters is one of the efficient ways to improve the robot's positioning accuracy. A method based on the product-of-exponential (POE) formula to calibrate the kinematic parameters of serial industrial robots is proposed. The paper aims to discuss these issues.

The forward kinematics is established, and the general positioning error model is deduced in an explicit expression. A simplified model of robot's positioning error is established as both the error of reference configuration and the error of rigid displacement of the base coordinating system with respect to the measuring coordinating system are equivalently transferred to the zero position errors of the robot's joints. A practical calibration model is forwarded only requiring 3D measuring based on least-squares algorithm. The calibration system and strategy for calibrating kinematic parameters are designed.

By the two geometrical constrains between the twist coordinates, each joint twist only has four independent coordinates. Due to the equivalent error model, the zero position error of each joint can cover the error of reference configuration and rigid displacement of the robot base coordinating system with respect to the measuring coordinating system. The appropriate number of independent kinematic parameters of each joint to be calibrated is five.

It is proved by a group of calibration experiments that the calibration method is well conditioned and can be used to promote the level of absolute error of end effector of industrial robot to 2.2 mm.

The purpose of this paper is to clarify the effect of material hardening model and lump-pass method on the thermal-elastic-plastic (TEP) finite element (FE) simulation of residual stress induced by multi-pass welding of materials with cyclic plasticity.

Nickel-base alloy and stainless steel, which are used in J-type weld for manufacturing the nuclear reactor pressure head, can easily harden during multi-pass welding. The J-weld welding experiment is carried out and the temperature cycle and residual stress are measured to validate the TEP simulation. Thermal-mechanical sequence coupling method is employed to get the welding residual stress. The lumped-pass model and pass-by-pass FE model are built and two materials hardening models, kinematic hardening model and mixed hardening model, are adopted during the simulations. The effects of material hardening models and lumped-pass method on the residual stress in J-weld are distinguished.

Based on the kinematic hardening model, the stresses simulated with the lumped-pass FE model are almost consistent with those obtained by the pass-by-pass FE model; while with the mixed hardening material model, the lumped-pass method has great effect on the simulated stress.

A computation with mixed isotropic-kinematic material seems not to be the appropriate solution when using the lumped-pass method to save the computation time.

In the simulation of multi-pass welding residual stress involved in materials with cyclic plasticity, the material hardening model should be carefully considered. The kinematic hardening model with lump-pass FE model can be used to get better simulation results with less computation time. The results give a direction for welding residual stress simulation for the large structure such as the reactor pressure vessel.

The purpose of this paper is to present a distance accuracy-based industrial robot kinematic calibration model. Nowadays, the repeatability of the industrial robot is high, while the absolute positioning accuracy and distance accuracy are low. Many factors affect the absolute positioning accuracy and distance accuracy, and the calibration method of the industrial robot is an important factor. When the traditional calibration methods are applied on the industrial robot, the accumulative error will be involved according to the transformation between the measurement coordinate and the robot base coordinate.

In this manuscript, a distance accuracy-based industrial robot kinematic calibration model is proposed. First, a simplified kinematic model of the robot by using the modified Denavit–Hartenberg (MDH) method is introduced, then the proposed distance error-based calibration model is presented; the experiment is set up in the next section.

The experimental results show that the proposed calibration model based on MDH and distance error can improve the distance accuracy and absolute position accuracy dramatically.

The proposed calibration model based on MDH and distance error can improve the distance accuracy and absolute position accuracy dramatically.