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The existing studies on profile error analysis and machining accuracy measurement do not consider the impact of the theoretical errors on the machine tool accuracy measurement. Therefore, this study proposes an estimation method of the surface profile error based on the normal section plane, using the theoretical flank milled surface for comparison. This effectively improves the accuracy of profile error estimation. The theoretical flank milled surface is the surface machined by flank milling under ideal conditions. Hence, compared to the traditional analysis method based on the designed three-dimensional model of S-shaped test pieces, the calculated profile error of this method does not include theoretical errors, thereby eliminating the impact of theoretical errors on machine tool accuracy measurement and evaluation. First, an improved method for continuous parameterized dual spline interpolation was proposed. It simplifies the solution of the singular problem of the coefficient matrix of the spline basis function and obtains a continuous ideal machining tool axis trajectory surface with complete geometric characteristics. Next, a method for constructing the theoretical flank milled surface machined with a cylindrical milling tool using equidistant mapping characteristics was proposed; then, the differential transformation relationship at the cutting contact point of the curved surface under the influence of tool path errors was established. Furthermore, the normal section plane method based on the differentiation of the cutting contact point was proposed. The problem of solving the distance from a point to a surface is converted to the problem of solving the distance from a point to a curve in the normal section plane. This improves the accuracy of profile error estimation. The effectiveness of the method was verified by comparing the analysis results of the profile errors of a typical cylindrical surface with the point to surface and the point to curve methods.

This paper proposes a novel approach to calculating the dynamic error distribution reflected on an S-shaped test piece. First, a numerical model of an S-shaped test piece is established, and the distribution characteristics for the twist angle and curvature are analysed. Second, a delay continuous method (DCM), which can transform the discrete input into a delayed step input, is presented to express the single-axis dynamic error affected by the input quantitatively in the form of a mathematical expression. Based on the sinusoidal input, the feasibility of the DCM is verified by comparing the experimental results of a Simulink simulation model and a mathematical expression derived by the DCM. Third, according to a new three-point tangential (NTPT) positioning algorithm and the DCM, this article makes the first attempt to investigate the quantitative calculation method of the influence of the dynamic performance of a servo feed system for five-axis numerical control (NC) machine tools on the dynamic error distribution for S-shaped test pieces after processing. Parameter p, representing the dynamic characteristic of the servo feed system, is varied to compare the difference of the dynamic error distribution law on S-shaped test pieces. The calculation results show that the parameter p can be adjusted to reduce the dynamic error of the final machined test pieces. It is important to improve the dynamic performance of servo feed systems for five-axis NC machine tools and enhance the machining quality of test pieces. In addition, compared with the calculation results of the dynamic error distribution for an NAS979 test piece, the S-shaped test piece can reflect the dynamic performance of the servo feed system for five-axis NC machine tools more accurately and effectively. Finally, the effectiveness of the proposed calculation method is verified through processing experiments on a five-axis NC machine tool.

In five-axis flank milling operations, the intersecting surfaces of different cutting edges create roughness on the milled surfaces that cannot be ignored in situations with strict requirements, especially in aeronautical manufacturing. To focus on motion problems in milling operations, this paper presents a new model that utilizes elliptical paths as cutting edge trajectories on 3D surface topography machined by peripheral milling. First, the cutter parallel axis offset and location angle are considered, which change the location of the ellipse center and intersection point of the cutting edges. Then, through the proposed model, the predicted surface topography is obtained, and the factors that affect the development tendency of roughness are analyzed. Next, the effects of the cutter location position (CLP) geometric parameters, cutter parallel axis offset and curvature on the roughness are evaluated by a numerical simulation. Finally, machining tests are carried out to validate the model predictions, and the results show that the surface topography predictions correspond well with the experimental results.

The detection method for direct machining the standard test pieces, which is commonly employed to exhibit the machining precision of five-axis machine tools, can truly reflect the dynamic accuracy of five-axis machine tools in the actual machining process. Existing theories on explaining the phenomenon that the ability of S-shaped test pieces to detect dynamic accuracy for five-axis machine tools are stronger than those of NAS979 test pieces mostly used the qualitative research methods, and they cannot be quantitatively used to reveal the mathematical relationship between machine tools and test pieces. Therefore, this article makes the first attempt to investigate the quantitative evaluation method for the validity of dynamic accuracy test pieces. The dynamic error function of the servo feed system in the frequency domain was derived first by establishing the mechanical system model and control system model. The method of dipole cancellation was used to acquire a simplified transfer function for the dynamic error affected by the input. Based on the zero-order hold property of the discrete input signals, the expression of dynamic error affected by input in the time domain, which intuitively shows the mathematical relationship among the machine tool performances, the test piece characteristics and the dynamic error of the servo feed system, was obtained. Then, the novel evaluation methods of the linear combinatorial value and the combinatorial linear combinatorial value were proposed. A series of comparative analyses between an S-shaped test piece and an NAS979 test piece were carried out based on the proposed new evaluation methods. A machining experiment conducted on a five-axis machine tool is used to verify the evaluation results.

Purpose This paper aims to present a new trajectory optimization approach targeting spray painting applications that satisfies the paint thickness requirements of complex-free surfaces. Design/methodology/approach In this paper, a new trajectory generation approach is developed to optimize the transitional segments at the junction of adjacent patches for straight line, convex arc and concave arc combinations based on different angles between normal vectors of patches. In addition, the paint parameters including the paint gun velocity, spray height and the distance between adjacent trajectories have been determined in the generation approach. Then a thickness distribution model is established to simulate the effectiveness of trajectory planning. Findings The developed approach was applied to a complex-free surface of various curvatures, and the analysis results of the trajectory optimization show that adopting different transitional segment according to the angle between normal vectors can obtain the optimal trajectory. Based on the simulation and experimental validation results, the proposed approach is effective at improving paint thickness uniformity, and the obtained results are consistent with the simulation results, meaning that the simulation model can be used to predict the actual paint performance. Originality/value This paper discusses a new trajectory generation approach to decrease the thickness error values to satisfy spray paint requirements. According to the successfully performed simulation and experimental results, the approach is useful and practical in overcoming the challenge of improving the paint thickness quality on complex-free surface.

The accuracy of high speed five-axis machine tool is mainly determined by the contour accuracy of machine tools. The contour accuracy evaluation and improvement of 5-axis machine tools have always been concerned. In order to simplify the calculation of five-axis contour error considering the synchronization between tool tip position and tool orientation, a novel five-axis contour evaluation index TCCE(Two-point Cutter location Contour Error) is proposed in this paper, which is based on the tool axis trajectory surface. The calculating method of the proposed index by NC servo encoder input from 5-axis machine tools is introduced. Finally, the experiment is performed to evaluate the trajectory accuracy and servo matching performance of the machine tool with the proposed contour error evaluation index and the calculating method.

Supplemental material, sj-pdf-2-pic-10.1177_0954406220962150 for A novel approach to calculating the dynamic error reflected on an S-shaped test piece by Weiwei He, Liping Wang and Liwen Guan in Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

Supplemental material, sj-pdf-1-pic-10.1177_0954406220962150 for A novel approach to calculating the dynamic error reflected on an S-shaped test piece by Weiwei He, Liping Wang and Liwen Guan in Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

Supplemental material, sj-pdf-3-pic-10.1177_0954406220962150 for A novel approach to calculating the dynamic error reflected on an S-shaped test piece by Weiwei He, Liping Wang and Liwen Guan in Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

Cutting coefficient identification plays a critical role in the calculation of cutting forces in the milling process. However, it is difficult to predict the cutting coefficients in the arc part of general end mills because of the various geometrical conditions along the cutting edge. This paper first introduces an improved identification model of specific cutting coefficients for the arc part of ball-end and bull-nose cutters. Then, the analytical expressions for the semi-empirical mechanistic identification of the cubic polynomial shear coefficients and constant edge coefficients are derived. In these expressions, elevation, axial immersion angle and local radius polynomial functions are used to describe the variation in the shear coefficients along the tool axis. Finally, the proposed identification model is applied to obtain the cutting coefficients for three end mills: a D12r6 ball-end cutter, a D12r3 bull-nose cutter, and a D16r3 bull-nose cutter. The matched validation cutting tests, which are slot millings with large cutting depths, are performed to compare the predictive ability of different polynomial functions. The results show that the local radius polynomial function covers all the geometric parameters and thus is more suitable for predicting the cutting coefficients of general end mills. Considering the differences in tool geometry, it is necessary to select the appropriate polynomial variable for predicting cutting coefficients outside the identified range of cutting depth.

With the closed-loop structure, parallel manipulators possess some inherent advantages, such as high stiffness, enhanced dynamics, and compact structure. As a result, parallel manipulators gradually gain wide application. In the great variety of parallel manipulators, a kind of high-speed parallel robot, the limb of which is composed of active pendulum and passive parallelogram, gets popular and has realized industrial application firstly. Dynamic performance is the core of the high-speed parallel manipulator, which is usually illustrated through dynamic performance analysis with the aid of the index. Thus, developing reasonable dynamic performance indices is of great theoretical and practical significance for the high-speed parallel manipulator. In this paper, the Coefficient of Variation of joint-space Inertia (CVI) index is proposed to illustrate the acceleration consistency of each limb of the parallel manipulator. By taking the X4 high-speed pick-and-place parallel manipulator as object, the dynamic model and joint-space inertia matrix is established, and the dynamic performance analysis is carried out with the proposed CVI index and the existing Joint-Reflected Inertia (JRI) index. Simulation results illustrate changes of the dynamic performance of the X4 parallel manipulator, and reveal that the JRI index is well complemented with the CVI index. Finally, the workspace with good dynamic performance is discussed. This paper provides a new approach for dynamic analysis and optimal design of high-speed parallel manipulator. Limb Jacobian matrices of the X4 manipulator are given.Dynamic model and inertia matrix of the X4 manipulator are deduced.The CVI index is proposed to evaluate the dynamic performance.Dynamic performance of the X4 mahipulator is analyzed with indices.The workspace with good dynamic performance is disscussed.

S-shaped test piece aims to assess the performance of five-axis numerical control (NC) machine tools. When the draft international standard (DIS) was introduced at the 79th ISO/TC39SC2 meeting, it was agreed that this test piece would be included. The S-shaped test piece, however, has undeveloped surfaces, which contribute to theoretical error. Because the test piece is used to assess the performance of machine tools and to conduct error tracing, theoretical error should not be included in the detection results obtained by the coordinate measuring machine (CMM). Therefore, the S-shaped test piece, excluding the influences of theoretical error, is crucial to research. This paper calculates the theoretical error of the S-shaped test piece when processed with the single-point offset (SPO) position method and proposes pre-compensation (PRC) and post-compensation (POC) methods to eliminate the influences of theoretical error. We conducted a theoretical analysis to compare three methods, the two compensation methods and the one uncompensated method, and verified the results through actual experiments. Research from principle and practice demonstrates that both the PRC and POC methods compensated for theoretical error up to 0.01 mm and that PRC is more accurate when considering the difference of approximately ±0.0015 mm.

Accuracy detection for five-axis numerical control (NC) machine tools that can truly reflect their practical machining precision is of crucial importance. Standard test pieces are commonly employed for this purpose. However, poor accuracy detection performance is obtained when the test pieces used here are applied to five-axis NC machine tools. This paper introduces a new S-shaped test piece that is exclusively designed for the precision detection of five-axis NC machine tools. The S-shaped test piece integrates numerous characteristics associated with aviation parts and has been widely adopted by machine tool makers. This article presents a numerical model of the latest S-shaped test piece and shows that its side surfaces represent typical undevelopable ruled surfaces. The curvature changes along the ruled lines inevitably produce a theoretical error. Thus, machining methods seek to reduce the theoretical error as much as possible. Based on basic summaries of five existing positioning algorithms, a novel algorithm is proposed to position the tool head using three points, wherein two are tangential to the top and bottom boundary curves, respectively, and the third is tangential to the midpoint of the ruled line. The proposed positioning algorithm together with five existing positioning algorithms is applied to the S-shaped test piece, and a numerical error performance analysis is conducted. The results indicate that the machined surface reduces the theoretical error by at least 96% compared to all the existing numerical positioning algorithms except for Redonnet’s algorithm. Compared with Redonnet’s algorithm, the accuracy of the proposed algorithm is equivalent, although the proposed algorithm reduces the calculation time by 62.7%, and is not sensitive to the initial values. Hence, the computational process demonstrates that the proposed method is efficient, robust, and universal. Finally, simulation results were confirmed through an actual machining experiment.

This paper studies the effect of structure parameters on the dynamic characteristics of a planar PRRRP parallel manipulator. The stiffness model is derived by considering the effect of joint. Based on the stiffness matrix, the vibration equation of this parallel manipulator is investigated to study the dynamic characteristics. The natural frequency is computed, and the effect of Y and Z coordinate on the natural frequency is discussed. Moreover, the sensitivity model of the dynamic characteristic to critical structure parameters is proposed. The thickness of column and leg, the radial stiffness of bearing, and the lumped mass on the end-effector are determined based on the natural frequency and sensitivity index. The results are useful to the structure design of parallel manipulators.

This paper presents a novel step kinematic calibration method for a 3 degree-of-freedom (DOF) planar parallel kinematic machine tool, based on the minimal linear combinations (MLCs) of error parameters. The method using mapping of linear combinations of parameters in error transfer multi-parameters coupling system changes the modeling, identification and error compensation of geometric parameters in the general kinematic calibration into those of linear combinations of parameters. By using the four theorems of the MLCs, the sets of the MLCs that are respectively related to the relative precision and absolute precision are determined. All simple and feasible measurement methods in practice are given, and identification analysis of the set of the MLCs for each measurement is carried out. According to the identification analysis results, a step calibration including step measurement, step identification and step error compensation is determined by taking into account both measurement costs and observability. The experiment shows that the proposed method has the following merits: (1) the parameter errors that cannot influence precision are completely avoided; (2) it reflects the mapping of linear combinations of parameters more accurately and enhances the precision of identification; and (3) the method is robust, efficient and effective, so that the errors in position and orientation are kept at the same order of the measurement noise. Due to these merits, the present method is attractive for the 3-DOF planar parallel kinematic machine tool and can be also applied to other parallel kinematic machine tools with weakly nonlinear kinematics.

SUMMARYThis paper addresses the dynamic dexterity of a planar 2-degree of freedom (DOF) parallel manipulator with virtual constraint. Without simplification, the dynamic formulation is derived by using the virtual work principle. The condition number of the inertia matrix of the dynamic equation is presented as a criterion to evaluate the dynamic dexterity of a manipulator. In order to obtain the best isotropic configuration of the dynamic dexterity in the whole workspace, two global performance indices, which consider the mean value and standard deviation of the condition number of the inertia matrix, respectively, are proposed as the objective function. For a given set of geometrical and inertial parameters, the dynamic dexterity of the parallel manipulator is more isotropic in the center than at the boundaries of the workspace.

This paper addresses optimal kinematic design of a PRRRP (P-prismatic joint, R-revolute joint) parallel manipulator that is horizontally actuated by linear actuators. Kinematically, the symmetrical PRRRP parallel manipulator has only one geometric parameter, i.e., the link length of each of the two legs. Here, we propose a design approach utilizing a performance chart and local performance specification. The key problem in the design of the manipulator is the determination of not the link length but the workspace that the manipulator can reach satisfying the design specification. Such a kind of workspace when the link length unit is defined as the basic good-condition workspace (GCW). For the manipulator studied here, the link length is actually the ratio of the desired task workspace to the basic GCW. This paper gives an effective method to obtain the basic GCW with respect to indices in closed forms. One of the advantages of the method is that the basic GCW is achieved by taking into account both the global and local indices. DOI: 10.1115/1.2712224

Ra = 3.2, and it can be improved to better that Ra = 1.6 by polishing. The dimensional accuracy relative to size is about ±0.1 mm for dimensions less than 200 mm.

The optimization method for the structure of a 6-DOF parallel robot mechanism is presented for minimizing the driving velocity. Firstly, the velocity model is given according to the kinematics theory of rigid body, which effectively avoids the fussy derivation process. The velocity target function is obtained by inequality transformation. Finally the optimization is performed by GA with global search capability. Comparison result verified the optimization method.

Dynamic manipulability is a very important issue that should be considered for problems of parallel manipulator design. In order to study the dynamic optimization of a 2-DOF planar parallel manipulator, which is used in a heavy duty hybrid machine, genetic algorithm (GA) is used in the dynamic manipulability optimization. Based on the kinematic analysis, the dynamic equation of the 2-DOF parallel manipulator is derived using the virtual work principle method. Furthermore, global dynamic manipulability (GDM) is introduced to measure the dynamic performance of the manipulator. Then the dynamic optimization based GA method is analyzed. From the numerical simulation, it is proved that the dynamic optimization considering GDM proposed in this paper can ameliorate the dynamic performance of the parallel manipulator well.

The force cueing algorithm is a primary source of flight simulation fidelity for dynamic seat. This paper presents a new optimal force cueing algorithm which incorporates a mathematical model of human body pressure system and otolith system. Linear perceptual models of the pilot in both dynamic seat and aircraft are built, then the cueing algorithm is derived by optimizing the mean-square error between the models. A comparison of the force cues produced by a dynamic seat is presented, using this cueing algorithm and earlier conventional algorithms: classical filter and adaptive filter. It is shown that the new algorithm performs more rapidly respond within the limitations of the dynamic seat, also a significant improvement of force cue fidelity are implemented in this algorithm compared to other two algorithms.

Taking a 3-TPT parallel machine tool as example, two different methods resolving the workspace problem of parallel machine tool are discussed. One is common analytical method that is to solve the available workspace by solving kinematical inverse equation of parallel machine tool. Due to analytical method is complex and hard to get exact workspace, the other new one by using virtual prototype technique to resolve the workspace problem is put forward. It is simple and clear in thought process as a shortcut and available to use in wide range, i.e., only a model of virtual prototype of parallel machine tool is needed to develop with some constraint conditions given, the workspace can be found out directly without complex derivation process. The two methods mentioned above are compared with each other, and the results indicate that the method by virtual prototype technique is more visual and practical and simpler.

A method based on screw theory is proposed to perform mobility analysis of a 3-UPU manipulator with three translational degrees. The method includes four steps: (1) representation of motions of joints in each serial kinematic chain in a 3-UPU manipulator with screws (twist system); (2) generation of wrenches reciprocal to all twists in each serial chain; (3) put wrenches of all three! serial kinematic chains together in a reference frame; (4) analyse all wrenches of all serial chains independently and get the independent constraint motions of end effector. If the number of the allowed independent motions is more than the number of anticipant degrees of freedom, the parallel manipulator has uncontrollable degrees of freedom and is in singular configuration. Three types of singularity are given and posture calculating method for each type of singularity is proposed.

The combined framework and measurement design, a key part of the integrated analysis and design platform of PKMs. Accomplishes the PKM design from simple kinematic model to real machine tool. In this work, the combined structure and measurement design of PKM was studied, and the design method was presented, which includes establishing modular components library, substituting and parameterizing. Base on this work, the relative perfect design system of PKM was acquired.

Kinematics analysis and dimensional synthesis are two important problems of a parallel manipulator. Dimensional synthesis is optimization of the kinematic parameters according to desired workspace or other design requirements. In this paper, the dimensional synthesis of a 3-DOF parallel manipulator, which mimics DELTA robots, is studied considering maximum inscribed workspace and reciprocal of the condition number on the workspace section based on the concept. The kinematic model of the 3-DOF parallel manipulator is given at first. The golden section search is used to search the workspace of the manipulator and mesh the boundary. Then the algorithm for calculating the inscribed workspace and dimensional synthesis considering the inscribed workspace are presented. Thirdly, the distribution of dexterity index on the workspace section and dimensional synthesis considering the reciprocal of condition number is studied. The two dimensional synthesis results are compared at the end of the paper. While the synthesis methodology of the manipulator is studied. It is helpful to improve design efficiency of the 3-DOF parallel manipulator. The quickly design for the manipulator can be performed through the proposed methods of dimensional synthesis.