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The linear robot path is tangential and curvature discontinuity, which will lead to vibration and unnecessary hesitation during execution. Local corner transition method and local spline interpolation method are used in state-of-art industrial robot controller to reduce vibration, while local corner transition method cannot interpolate target points and local spline interpolation method cannot constrain chord errors. This research proposes a robot path local interpolation method that eliminates deficiencies of each method. The smoothing method satisfies all of the following requirements: G1 continuity, target point interpolation and chord tolerance confined, shape-preserving (free of self-intersection), and unified parameterization. The generated smooth path consists of linear path and circular arc path with G1 continuity. A geometric iterative method cooperating with local corner transition method is used to generate local interpolation path. Simulations and actual experiments verify the generated smooth path is G1 continuous, tolerance constrained, shape-preserving, and have high computational efficiency.

In five-axis machining, drastic change of tool axis has negative effects on machining efficiency and quality. Our published work proposed a unified mathematical framework to generate smooth tool-axis field and implemented in 1D domain (Yan et al., J Manuf Syst 48:30–37, 2018). In this paper, we extend the mathematical framework to 2D domain and the framework is an integral functional problem converting diverse machining requirements, such as gouge and collision free, smoothness, into mathematical expressions. A tool-axis vector field (TAVF) defined on the freeform surface is calculated by optimizing the integral functional problem. The surface is discrete into triangular mesh, and the discrete TAVF calculation problem is solved by a numeric 2D finite element method (FEM). Subsequently, the proposed algorithm is implemented to generate field-generated tool path (FGTP). The tool path has been used in machining hub of blade disk (blisk). The blisk is a complex workpiece that impellers should be gouge avoided. Machining experiments indicate that tool path generated by the proposed algorithm can avoid collision and improve smoothness on the whole surface. The freeform surface machining quality is highly improved compared with that machined by region-partitioned tool path (RPTP).

Piecewise linear segments (presented by a sequence of G01 G-Codes) are the widely adopted tool path format for five-axis computer numerical control (CNC) machining. Nevertheless, the G01 tool path has only G0 continuity, which may lead to feedrate and acceleration fluctuation, and produce machinery vibration and unexpected slowdowns during the process. Thus, tool path smoothing method such as B-spline fitting is developed to increase the continuity of the tool paths. This work proposes a six-dimensional B-spline fitting method with arc-length parameterization and quality evaluation/refinement for five-axis tool paths. First, establish the relationship of cutter contact (CC) error, and cutter location (CL) error and tool-axis error to ensure that the CC error of five-axis B-spline tool path can be accurately computed. Second, six-dimensional B-spline tool paths generated by three-axis B-spline fitting method in six-dimensional space are parameterized with arc-length, satisfying the stability condition of tool axis. Third, the chord errors of the fitted six-dimensional B-spline tool paths are computed using the Hausdorff distance. The chord error computation, smoothness assessment, and refinement algorithm are performed together to ensure the fitting quality. The simulation result demonstrates that the proposed six-dimensional fitting method is effective and suitable for five-axis blade machining, and the evaluation/refinement algorithm can ensure that the five-axis B-spline tool paths are shape-preserving strictly and satisfy the chord error constraint. The experimental results show that the proposed six-dimensional fitting method improves the machining quality and is suitable for industrial applications.

As a special processing method, engraving in bangles often needs engineers’ much handwork and have low production efficiency before. In recent years, 5-axis machining technology is introduced to im...

Kinematic calibration of industrial robots is an effective method of improving robot accuracy, and thus robot performance, especially when working with offline programming. The state-of-art industrial applications are lacking an easy-to-operate, reliable, and economic solution, hence forbidding frequent on-site calibration. This study presents a robot kinematic calibration method to improve the accuracy of six-axis industrial robots, using multiple location constraints. The robot parameters are calibrated by controlling a robot to reach the same location in different poses. Two standard devices and a non-contact equipment, non-bar device, are used for measurement. The proposed calibration process applies three identification methods and two compensation methods that can be mixed and matched, allowing flexible combinations of solutions to fit various industrial conditions. The proposed measurement/calibration system is economic, easy-to-operate, reliable, and suitable for express user-site industrial robot kinematic calibration, avoiding extensive production interruption. Actual experiments are carried out to verify the effects of joint zero calibration. These experiments demonstrate the proposed method’s ability to improve the accuracy of robots, and thus improve the robot work quality using offline programming.

5-axis hybrid additive-subtractive manufacturing is a new and promising technology for many industrial applications. Because of its complexity, the machining simulation is very important to verify the effectiveness of tool path. However, most simulation methods are proposed for subtractive manufacturing and additive manufacturing separately. This paper presents a novel geometric simulation technique for the 5-axis hybrid additive-subtractive manufacturing, which is based on Laser Engineered Net Shaping (LENS) and milling. In the proposed method, 5-axis additive swept volume elements are represented with Tri-dexel models and then converted into triangular meshes for visualization. Workpiece after additive manufacturing can be then used as a workblank for subtractive manufacturing simulation. Finally, a geometric simulation module is developed based on SIEMENS NX software to demonstrate the feasibility of the proposed simulation method.

In multi-axis machining, sudden change of tool-axis orientation has adverse effects on the machining quality and efficiency. In this paper, we proposed a mathematical framework to generate smooth tool-axis variation even on part surfaces lacking G2 and/or G1 continuities. An integral functional is formulated as the object function to represent the measurement of the rate of tool-axis change. The functional is covariant so that the result is independent of surface parameterization and applicable to non-Euclidean geometry. The minimization of the integral functional ensures minimal fluctuation of tool-axis. Other machining requirements, such as gouging-free, preferred (or greedy) direction, are incorporated into this optimization problem as constraints. The unified optimization problem is solved by a Finite Element Method (FEM) numerical method. The proposed algorithm is implemented in the planar sections of blade rough machining to produce tool path with smooth tool-axis variation. Machining results indicate that the presented algorithm can improve machining quality/efficiency and avoid gouging.

While machining width is an important factor of the machining time of freeform surface finishing operations, in reality the kinematic capability of the machine tool is usually the bottleneck of achieving higher feed speed and optimal machining time. The purpose of this paper is to conveniently (and approximately) determine the optimal cut direction considering the speed kinematic capability of the machine tool, without having to compute the actual tool path. We propose a mathematical instrument, called Machine Kinematic Metric (MKM), to easily evaluate infinitesimal machining time on a freeform surface based on machine kinematic consideration. It's a tensor field similar to the metric tensor in differential geometry. MKM is integrated over the part surface to approximate the cut-direction-dependent total machining time, and used to determine the optimal cut direction that minimizes the machining time. To validate the accuracy of the prediction using MKM, we apply the method and compute the machini...

In order to improve the quality of the tool path, different machining requirements have to be considered in the tool path generation process. The traditional tool path generation methods only consider one or a few requirements and ignore the others due to the lack of comprehensive mathematic framework. Tool path generated in this way normally is not fully optimized since different requirements could compete or even conflict with each other. Targeting at this issue, this paper presents a unified mathematic framework based on field theory to generate tool path for both planar and freeform surface, where the three most important factors in NC machining, i.e., the smoothness, evenness, and machining efficiency of tool path can be considered. In the proposed framework, a field-based cost functional and a gradient-field-based inequality constraint functional is established, so as to convert the multi-objective tool path computation into a functional minimization problem with inequality constraints. Then, a finite element method (FEM)-based numerical method is proposed to solve the multi-variable nonlinear optimization problem. After that, two smooth tool path generation methods are proposed with taking the step-over as constraint. To further improve the machining efficiency, this paper also provides a hybrid method that combines zigzag and spiral pattern tool path. Experiments on blade machining and simulation show that the proposed method can produce smooth tool paths, while the machining efficiency can be improved at the same time. In addition to the above advantages, the proposed mathematical framework is extensible by incorporating different machining requirements into it, making it possible to generate tool path when multi-objective is considered.

Previous optimization-driven tool-path planning methods provide an effective approach to machining error control in five-axis flank milling of ruled surfaces. However, the finished part typically exhibits poor surface roughness. This paper proposes a new planning method for overcoming this problem. The proposed method generates a spline-curve-constrained tool path that produces minimized geometrical deviations on the machined surface, maintains satisfactory surface quality, and reduces the dimensionality in the solution space. A particle swarm optimization scheme was developed to determine the coefficients of the curve equations defining the constrained tool motion. A machining experiment was conducted and the measurement results validated the proposed method.

Heavy-duty forging manipulators are essential handling equipments for integrated open-die forging plants. This article presents a forging manipulator with serial–parallel hybrid mechanism and develops its closed-form kinematic solutions (inverse and direct) based on the detailed geometric description of the mechanism. The kinematic Jacobian matrix is also derived analytically. Case studies for kinematical simulation, workspace, and kinetostatic analysis are conducted throughout the developing process. The closed-form kinematic solution provides the foundation of simulation and control design, and the results of case studies demonstrate the special features of the proposed mechanism in load capacity and compliant manipulation ability for heavy tasks in automatic open-die forging processes.

A virtual plant, built in a computer by using computer graphic (CG) and Virtual Reality (VR), can model the precise and whole structure of an integrated manufacturing system and simulate its physical and logical behavior in operation. This paper aims to reveal the advanced modeling and VR realization methods in developing a virtual forging plant for automatic and programmed open-die forging processes. Two sub-models, component model and process model, compose the overall modeling architecture of a virtual integrated open-die forging plant. The coordinated motion simulation of the integrated system is realized through a kinematic modeling method. A compound stiffness modeling method is then developed to simulate the mechanical behavior in operation. The process simulation of the virtual plant is conducted on the basis of the above two modeling methods. A practical application example of virtual plant for integrated open-die forging process is presented towards the end.Copyright © 2009 by ASME