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A Comparative Study on Kinematic Calibration for a 3-DOF parallel manipulator Using the Complete-Minimal,Inverse-Kinematic and Geometric-Constraint Error Models

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Chinese Journal of Mechanical Engineering 2023年第5期36卷 206-230页

作者： Haiyu Wu Lingyu Kong Qinchuan Li Hao Wang Genliang Chen State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong UniversityShanghai 200240China Intelligent Robot Research Center Zhejiang LabHangzhou 311100China School of Mechanical Engineering Zhejiang Sci-Tech UniversityHangzhou 310018China

Kinematic calibration is a reliable way to improve the accuracy of parallel manipulators, while the error model dramatically afects the accuracy, reliability, and stability of identifcation results. In this paper, a comparison study on kinematic calibration for a 3-DOF parallel manipulator with three error models is presented to investigate the relative merits of diferent error modeling methods. The study takes into consideration the inverse-kinematic error model, which ignores all passive joint errors, the geometric-constraint error model, which is derived by special geometric constraints of the studied RPR-equivalent parallel manipulator, and the complete-minimal error model, which meets the complete, minimal, and continuous criteria. This comparison focuses on aspects such as modeling complexity, identifcation accuracy, the impact of noise uncertainty, and parameter identifability. To facilitate a more intuitive comparison, simulations are conducted to draw conclusions in certain aspects, including accuracy, the infuence of the S joint, identifcation with noises, and sensitivity indices. The simulations indicate that the complete-minimal error model exhibits the lowest residual values, and all error models demonstrate stability considering noises. Hereafter, an experiment is conducted on a prototype using a laser tracker, providing further insights into the diferences among the three error models. The results show that the residual errors of this machine tool are signifcantly improved according to the identifed parameters, and the complete-minimal error model can approach the measurements by nearly 90% compared to the inverse-kinematic error model. The fndings pertaining to the model process, complexity, and limitations are also instructive for other parallel manipulators.

关键词： Kinematic calibration parallel manipulator Error modeling Product of exponential(POE)

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A modified similitude analysis method for the electro-mechanical performances of a parallel manipulator to solve the control period mismatch problem

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Science China(Technological Sciences) 2022年第3期65卷 541-552页

作者： WU Jun SONG YuYao LIU ZiLin LI GuoFa State Key Laboratory of Tribology and Institute of Manufacturing Engineering Department of Mechanical EngineeringTsinghua UniversityBeijing 100084China Beijing Key Lab of Precision/Ultra-precision Manufacturing Equipment and Control Beijing 100084China Key Laboratory of CNC Equipment Reliability Ministry of EducationJilin UniversityChangchun 130022China

Due to the discrete feature and performance limitation of the numerical controller,the control period sometimes cannot meet the constraints of the scaled model in similitude analysis,which brings the control period mismatch *** traditional similitude analysis methods are not able to solve this problem since the controller is treated as continuous system in these *** paper proposes a modified similitude analysis method to solve the control period mismatch problem,and the electro-mechanical performances of a 2-DOF parallel manipulator is *** on the model of dynamic and control system,most of the similitude laws are derived by taking the controller as continuous *** the transfer function of the controller in discrete form is established,and the similitude law related to control period is derived to figure out the cause of mismatch *** modified method,named long period equivalent,is proposed to solve the mismatch problem by using the least square method and superposition ***,the scaled model of the parallel manipulator is determined based on the modified similitude analysis method.

关键词： similitude analysis control period mismatch parallel manipulator electro-mechanical performance discrete system

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Workspace and Accuracy Analysis on a Novel 6‑UCU Bone‑attached parallel manipulator

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Chinese Journal of Mechanical Engineering 2022年第3期35卷 148-160页

作者： Kaijie Dong Duanling Li Xingyu Xue Chang Xu Haowei Wang Xianming Gao School of Automation Beijing University of Posts and TelecommunicationsBeijing 100876China th Research Institute of China Electronics Technology Group Corporation Hefei 340100China Beijing Institute of Spacecraft System Engineering China Academy of Space TechnologyBeijing 100094China College of Mechanical and Electrical Engineering Shaanxi University of Science and TechnologyXi’an 712000China

With the increasingly more extensive application of the medical surgical robot in the clinic,higher requirements have been put forward for medical *** bone-attached robot,a popular orthopedic robot in recent years,has a tendency of miniaturization and ***,a bone-attached parallel manipulator(PM)based on 6-UCU(universalcylindrical-universal)configuration is proposed,which is characterized by small volume,compact structure,high precision and six-dimensional force *** optimize the structure and make it more compact,the workspace of the 6-UCU PM is analyzed based on the analysis of three kinds of constraint,and workspace model is established through spherical coordinate search *** study also analyzes the influence of structural parameters on workspace,which may contribute to improving the efficiency of design and ensuring small-sized robots possess relatively large ***,to improve the motion accuracy,an error modeling method is developed based on the structure of 6-UCU *** to this established error model,the output pose error curves are drawn using MATLAB software when the structure parameters change,and the influence of the structure and pose parameters change on the output pose error of PMs is *** proposed research provides the instruction to design and analysis of small PMs such as bone-attached robots.

关键词： Medical robot Bone-attached robot parallel manipulator Workspace analysis Accuracy analysis

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Inertia Match of a 3-RRR Reconfigurable Planar parallel manipulator

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Chinese Journal of Mechanical Engineering 2009年第6期22卷 791-799页

作者： SHAO Zhufeng TANG Xiaoqiang CHEN Xu WANG Liping Department of Precision Instruments and Mechanology Tsinghua University Beijing 100084 China

Inertia match of the parallel manipulator means the ratio of the inertial load of the parallel manipulator converted to each actuator shaft and the moment of inertia of the actuator is kept within a reasonable range. Currently there are many studies on parallel manipulators, but few mention inertia parameters and inertia match of parallel manipulators. This paper focuses on the inertia characteristics of the 3-RRR reconfigurable planar parallel manipulator. On the basis of the inverse dynamic formulations deduced with the principle of virtual work, the inertia matrix of the 3-RRR planar parallel manipulator in the actuator space is obtained in algebraic form. Then, by unifying the dimension and averaging diagonal elements of the inertia matrix, the equivalent inertia of the parallel manipulator, which is the inertial load of the parallel manipulator converted to each actuator shaft, is determined. By transforming the inertia problem of the 3-RRR parallel manipulator into that of the serial multi-bar manipulator, the practicality of the equivalent inertia deduced by inverse dynamics is demonstrated. According to the physical meaning of the inertia equation, the manipulator is divided in to three parts. Further analysis is carried out on the contribution of each part to the equivalent inertia and their distributions in the required workspace, revealing that the passive links cannot ignored in calculating the equivalent inertia of the parallel manipulator. Finally, the inertia match for the 3-RRR reconfigurable parallel manipulator under three configurations is accomplished, and reducers are selected. The equivalent inertia calculation and the inertial match results illustrate that the inertia math is a necessary step to the design of the parallel manipulator, and inertia parameters dramatically affect dynamic performances of parallel manipulators. Besides, the equivalent inertia and inertial match principles, proposed in the paper, can be widely applied in the dynamic

关键词： inertia match equivalent inertia inverse dynamics parallel manipulator

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Traversing the singularity hypersurface by applying the input disturbances to 6-SPS parallel manipulator

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2008年第11期9卷 1539-1551页

作者： Yu-tong LI Yu-xin WANG Shuang-xia PAN Rui-qin GUO College of Mechanical Engineering and Energy Zhejiang University Hangzhou 310027 China Department of Mechanical Engineering Tongji University Shanghai 200092 China

The singular points of a 6-SPS Stewart platform are distributed on the multi-dimensional singularity hypersurface in the task-space, which divides the workspace of the manipulator into several singularity-free regions. Because of the motion un- certainty at singular points, while the manipulator traverses this kind of hypersurface from one singularity-free region to another, its motion cannot be predetermined. In this paper, a detailed approach for the manipulator to traverse the singularity hypersurface with its non-persistent configuration is presented. First, the singular point transfer disturbance and the pose disturbance, which make the perturbed singular point transfer horizontally and vertically, respectively, are constructed. Through applying these disturbances into the input parameters within the maximum loss control domain, the perturbed persistent configuration is transformed into its corresponding non-persistent one. Under the action of the disturbances, the manipulator can traverse the singularity hypersurface from one singularity-flee region to another with a desired configuration.

关键词： parallel manipulator Singularity hypersurface Singularity-free moving region

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Kinetostatics Analysis of a Novel 6-DOF parallel manipulator with Three Planar Limbs and Equipped with Three Fingers

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Chinese Journal of Mechanical Engineering 2014年第5期27卷 919-927页

作者： LU Yi LI Xuepeng College of Mechanical Engineering Yanshan University Key Laboratory of parallel Robot and Mechatronic System of Hebei Province Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of National Education

It is significant to develop a robot hand with high rigidity by a 6-DOF parallel manipulator（PM）.However,the existing6-DOF PMs include spherical joint which has less capability of pulling force bearing,less rotation range and lower precision under alternately heavy loads.A novel 6-DOF PM with three planar limbs and equipped with three fingers is proposed and its kinematics and statics are analyzed systematically.A 3-dimension simulation mechanism of the proposed manipulator is constructed and its structure characteristics is *** kinematics formulae for solving the displacement,velocity,acceleration of the platform,the active legs and the fingers are *** statics formulae are derived for solving the active forces of PM and the finger *** analytic example is given for solving the kinematics and statics of proposed manipulator and the analytic solved results are verified by the simulation *** is proved from the error analysis of analytic solutions and simulation solutions that the derived analytic formulae are correct and provide the theoretical and technical foundations for its manufacturing,control and application.

关键词： parallel manipulator planar limbs finger kinematics statics

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Three-degree-of-freedom parallel manipulator to Track the Sun for Concentrated Solar Power Systems

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Chinese Journal of Mechanical Engineering 2015年第4期28卷 793-800页

作者： ASHITH SHYAM R B GHOSAL A Robotics and Design Lab Indian Institute of Science

In concentrated solar power（CSP） generating stations, incident solar energy is reflected from a large number of mirrors or heliostats to a faraway receiver. In typical CSP installations, the mirror needs to be moved about two axes independently using two actuators in series with the mirror effectively mounted at a single point. A three degree-of-freedom parallel manipulator, namely the 3-RPS parallel manipulator, is proposed to track the sun. The proposed 3-RPS parallel manipulator supports the load of the mirror, structure and wind loading at three points resulting in less deflection, and thus a much larger mirror can be moved with the required tracking accuracy and without increasing the weight of the support structure. The kinematics equations to determine motion of the actuated prismatic joints in the 3-RPS parallel manipulator such that the sun＇s rays are reflected on to a stationary receiver are developed. Using finite element analysis, it is shown that for same sized mirror, wind loading and maximum deflection requirement, the weight of the support structure is between 15% and 60% less with the 3-RPS parallel manipulator when compared to azimuth-elevation or the target-aligned configurations.

关键词： 3-RPS parallel manipulator Heliostat Solar tracking

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PARAMETRIC IDENTIFICATION OF parallel manipulator WITH REDUNDANCY DRIVEN BY PNEUMATIC MUSCLES

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Chinese Journal of Mechanical Engineering 2008年第1期21卷 66-71页

作者： ZHU Xiaocong TAO Guoliang CAO Jian State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

A new parameter estimation algorithm is proposed for parametric identification of a parallel manipulator driven by pneumatic muscles with redundancy. Due to the special physical properties of the parallel manipulator studied, the regression model for parametric identification is characterized by multieollinearity, which will result in unreliable and inaccurate parameter estimations with large eovarianee if the conventional parameter estimation algorithm based on single error minimizing criterion is used. To improve the quality of parameter estimation and achieve high precise posture trajectory tracking control of the parallel manipulator, a new parameter estimation algorithm based on composite error minimizing criterion is developed in need of theoretical contractive forces of pneumatic muscles. The experimental results indicate that the proposed algorithm integrated with adaptive robust control could provide reliable parametric identification and greatly enhance the control accuracy in the trajectory tracking control of the parallel manipulator, and that the variation of known theoretical contractive forces of pneumatic muscles has slight influence on the control performance.

关键词： Pneumatic muscle parallel manipulator Redundancy Parameter estimation

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Singularity Analysis of a 3-RPS parallel manipulator Using Geometric Algebra

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Chinese Journal of Mechanical Engineering 2015年第6期28卷 1204-1212页

作者： LI Qinchuan XIANG Ji'nan CHAI Xinxue WU Chuanyu Mechatronic Institute Zhejiang Sci-Tech University

Singular configurations must be avoided in path planning and control of a parallel manipulator. However, most studies rarely focus on an overall singularity loci distribution of lower-mobility parallel mechanisms. Geometric algebra is employed in analysis of singularity of a 3-RPS parallel manipulator. Twist and wrench in screw theory are represented in geometric algebra. Linear dependency of twists and wrenches are described by outer product in geometric algebra. Reciprocity between twists and constraint wrenches are reflected by duality. To compute the positions of the three spherical joints of the 3-RPS parallel manipulator, Tilt-and-Torsion angles are used to describe the orientation of the moving platform. The outer product of twists and constraint wrenches is used as an index for closeness to singularity（ICS） of the 3-RPS parallel manipulator. An overall and thorough perspective of the singularity loci distribution of the 3-RPS parallel manipulator is disclosed, which is helpful to design, trajectory planning and control of this kind of parallel manipulator.

关键词： singularity parallel manipulator geometric algebra

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An inertial parameter identification method of eliminating system damping effect for a six-degree-of-freedom parallel manipulator

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Chinese Journal of Aeronautics 2015年第2期28卷 582-592页

作者： Tian Tixian Jiang Hongzhou Tong Zhizhong He Jingfeng Huang Qitao School of Mechatronics Engineering Harbin Institute of Technology

A new simple and effective inertial parameter identification method based on sinusoidal vibrations of a six-degree-of-freedom parallel manipulator is proposed. Compared with previously known identification algorithms, the advantages of the new approach are there is no need to design the excitation trajectory to consider the condition number of the observation matrix and the inertial matrix can be accurately defined regardless of the effect of viscous friction. In addition, the use of a sinusoidal exciting trajectory allows calculation of the velocities and accelerations from the measured position response. Simulations show that the new approach has acceptable tolerance of dry friction when using a simple coupling parameter modified formula. The experimental application to the hydraulically driven Stewart platform demonstrates the capability and efficiency of the proposed identification method.

关键词： Hydraulically Identification Inertial parameter parallel manipulator Sinusoidal vibration

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