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Inverse Kinematics Analysis of General 6R Serial Robot Mechanism Based on Groebner Base

WANG Yan, HANG Lu-bin, YANG Ting-li

《机械工程前沿（英文）》 2006年 第1卷 第1期   页码 115-124 doi: 10.1007/s11465-005-0022-7

摘要：

This study presents a solution for the inverse kinematics problem in serial 6R manipulator. Using only seven equations composed of Duffy s four kinematical equations containing three angles and three corresponding angles identical equations instead of the traditional 14 equations, the authors reduced the inverse kinematics problem in the general 6R manipulator to a univariate polynomial with a minimum degree based on the Groebner Base method. From that, they concluded that the maximum number of the solutions is 16, generally. Also, the mathematics mechanization method can be extended to solve other mechanism problems involving nonlinear equations symbolically.

关键词： identical     manipulator     univariate polynomial     mechanism     traditional    

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Analysis of the kinematic characteristics of a high-speed parallel robot with Schönflies motion: Mobility, kinematics, and singularity

Fugui XIE,Xin-Jun LIU

《机械工程前沿（英文）》 2016年 第11卷 第2期   页码 135-143 doi: 10.1007/s11465-016-0389-7

摘要：

This study introduces a high-speed parallel robot with Schönflies motion. This robot exhibits a promising prospect in realizing high-speed pick-and-place manipulation for packaging production lines. The robot has four identical limbs and a single platform. Its compact structure and single-platform concept provides this robot with good dynamic response potential. A line graph method based on Grassmann line geometry is used to investigate the mobility characteristics of the proposed robot. A generalized Blanding rule is also introduced into this procedure to realize mutual conversion between the line graphs for motions and constraints. Subsequently, the inverse kinematics is derived, and the singularity issue of the robot is investigated using both qualitative and quantitative approaches. Input and output transmission singularity indices are defined based on the reciprocal product in screw theory and the virtual coefficient by considering motion/force transmission performance. Thereafter, the singular loci of the proposed robot with specific geometric parameters are derived. The mobility analysis, inverse kinematics modeling, and singularity analysis conducted in this study are helpful in developing the robot.

关键词： parallel robot     mobility     inverse kinematics     singularity     transmission performance    

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Inverse kinematics analysis and numerical control experiment for PRS-XY style hybrid machining tool

JIA Dongyong, ZHANG Jianmin, SUN Hongchang, NIU Zhigang

《机械工程前沿（英文）》 2007年 第2卷 第2期   页码 235-238 doi: 10.1007/s11465-007-0041-7

摘要： This paper analyzed the inverse kinematics for the new Parallel rotate slider- axes (PRS-) style hybrid machining tool and educed the five axes linkage inverse kinematics transform formula on the basis of the coordinates of the and virtual axes. The program for the PRS-XY style hybrid machining tool in accordance with the program manner for the common numerical control (NC) machine tool was made. The results of the experiments prove that the inverse kinematics transform formula is correct.

关键词： numerical     accordance     transform formula     virtual     slider-    

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Motion capability analysis of a quadruped robot as a parallel manipulator

Jingjun YU,Dengfeng LU,Zhongxiang ZHANG,Xu PEI

《机械工程前沿（英文）》 2014年 第9卷 第4期   页码 295-307 doi: 10.1007/s11465-014-0317-7

摘要：

This paper presents the forward and inverse displacement analysis of a quadruped robot MANA as a parallel manipulator in quadruple stance phase, which is used to obtain the workspace and control the motion of the body. The robot MANA designed on the basis of the structure of quadruped mammal is able to not only walk and turn in the uneven terrain, but also accomplish various manipulating tasks as a parallel manipulator in quadruple stance phase. The latter will be the focus of this paper, however. For this purpose, the leg kinematics is primarily analyzed, which lays the foundation on the gait planning in terms of locomotion and body kinematics analysis as a parallel manipulator. When all four feet of the robot contact on the ground, by assuming there is no slipping at the feet, each contacting point is treated as a passive spherical joint and the kinematic model of parallel manipulator is established. The method for choosing six non-redundant actuated joints for the parallel manipulator from all twelve optional joints is elaborated. The inverse and forward displacement analysis of the parallel manipulator is carried out using the method of coordinate transformation. Finally, based on the inverse and forward kinematic model, two issues on obtaining the reachable workspace of parallel manipulator and planning the motion of the body are implemented and verified by ADAMS simulation.

关键词： quadruped robot     actuated joints selection     kinematics analysis     motion planning     parallel manipulator    

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Research on transmission principle and kinematics analysis for involute spherical gear

PAN Cun-yun, WEN Xi-sen, YANG Kun-yu, XU Xiao-jun, LIU Min, YAO Qi-shui

《机械工程前沿（英文）》 2006年 第1卷 第2期   页码 183-193 doi: 10.1007/s11465-006-0010-6

摘要： A new kind of transmission-type spherical gear called ring involute spherical gear mechanism is introduced. Compared to the famous TRALLFA spherical gear, this new spherical gear has an involute tooth profile, and a ring tooth that is distributed continuously on the surface of the sphere. This allows the gear to overcome two disadvantages of the TRALLFA spherical gear: the drive principle error and the manufacturing difficulty. The new transmission and the formation principle of the tooth s surface of the new spherical gear mechanism are first introduced, then another mechanism, called disk rack, is introduced, which is derived from the spherical gear mechanism when one of the spherical gear s tooth number reaches infinity. To make the research more convenient, every part of the new spherical gear mechanism is named. In the following sections, some problems are discussed, such as the assembly form, the construction characteristics, the correct meshing condition, the continuum transmission condition and so on. Furthermore, the paper deduces the surface formula of the conjugate teeth profiles, which proves that the conjugate teeth profiles is also one of the ringed involute spherical gear. In order to analyze the relationship between two coordinate systems, which is attached respectively to the diving spherical gear and the driven spherical gear, the orientation cosine matrix method is utilized. By series rotational transformation, the kinematics model and inverse kinematics model are deduced. Using the method for calculating the transmission ratio of planet gear train, the relationship of the two oscillating angle between output axis and the bracket is established. Based on the research, the kinematics graphic simulation of spherical gear mechanism and disk rack are made respectively. The results prove correctness of the kinematics model.

关键词： rotational transformation     orientation     Furthermore     conjugate     number    

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Ahybrid biogeography-based optimization method for the inverse kinematics problem of an 8-DOF redundant

Zi-wu REN,Zhen-hua WANG,Li-ning SUN

《信息与电子工程前沿（英文）》 2015年 第16卷 第7期   页码 607-616 doi: 10.1631/FITEE.14a0335

摘要： The redundant humanoid manipulator has characteristics of multiple degrees of freedom and complex joint structure, and it is not easy to obtain its inverse kinematics solution. The inverse kinematics problem of a humanoid manipulator can be formulated as an equivalent minimization problem, and thus it can be solved using some numerical optimization methods. Biogeography-based optimization (BBO) is a new biogeography inspired optimization algorithm, and it can be adopted to solve the inverse kinematics problem of a humanoid manipulator. The standard BBO algorithm that uses traditional migration and mutation operators suffers from slow convergence and prematurity. A hybrid biogeography-based optimization (HBBO) algorithm, which is based on BBO and differential evolution (DE), is presented. In this hybrid algorithm, new habitats in the ecosystem are produced through a hybrid migration operator, that is, the BBO migration strategy and DE/best/1/bin differential strategy, to alleviate slow convergence at the later evolution stage of the algorithm. In addition, a Gaussian mutation operator is adopted to enhance the exploration ability and improve the diversity of the population. Based on these, an 8-DOF (degree of freedom) redundant humanoid manipulator is employed as an example. The end-effector error (position and orientation) and the ‘away limitation level’ value of the 8-DOF humanoid manipulator constitute the fitness function of HBBO. The proposed HBBO algorithm has been used to solve the inverse kinematics problem of the 8-DOF redundant humanoid manipulator. Numerical simulation results demonstrate the effectiveness of this method.

关键词： Inverse kinematics problem     8-DOF humanoid manipulator     Biogeography-based optimization (BBO)     Differential evolution (DE)    

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Singularity and workspace analysis of three isoconstrained parallel manipulators with schoenflies motion

Po-Chih LEE, Jyh-Jone LEE

《机械工程前沿（英文）》 2012年 第7卷 第2期   页码 163-187 doi: 10.1007/s11465-012-0324-5

摘要：

This paper presents the analysis of three parallel manipulators with Schoenflies-motion. Each parallel manipulator possesses two limbs in structure and the end-effector has three DOFs (degree of freedom) in the translational motion and one DOF in rotational motion about a given direction axis with respect to the world coordinate system. The three isoconstrained parallel manipulators have the structures denoted as CuuUwHw-//-CvvUwHw, CuRuuUhw-//-CvRvvUhwand CuPuUhw-//- CvPvUhw. The kinematic equations are first introduced for each manipulator. Then, Jacobian matrix, singularity, workspace, and performance index for each mechanism are subsequently derived and analysed for the first time. The results can be helpful for the engineers to evaluate such kind of parallel robots for possible application in industry where pick-and-place motion is required.

关键词： parallel manipulator     schoenflies motion     kinematics     singularity     workspace     performance index    

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A comprehensive analysis of a 3-P (Pa) S spatial parallel manipulator

Yuzhe LIU,Liping WANG,Jun WU,Jinsong WANG

《机械工程前沿（英文）》 2015年 第10卷 第1期   页码 7-19 doi: 10.1007/s11465-015-0324-3

摘要：

In this paper, a novel 3-degree of freedom (3-DOF) spatial parallel kinematic machine (PKM) is analyzed. The manipulator owns three main motions (two rotations and one translation) and three concomitant motions (one rotation and two translations). At first, the structure of this spatial PKM is simplified according to the characteristic of each limb. Secondly, the kinematics model of this spatial PKM is set up. In addition, the relationship between the main motions and concomitant motions is studied. The workspaces respectively based on the outputs and inputs are derived and analyzed. Furthermore, the velocity model is put forward. Two indexes based on the velocity model are employed to investigate the performance of this spatial PKM. At last, the output error model can be obtained and simulated. The comprehensive kinematics analysis in this paper is greatly useful for the future applications of this spatial PKM.

关键词： parallel mechanism     concomitant motions     kinematics     workspaces     error model    

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Drive system design and error analysis of the 6 degrees of freedom segment erector of shield tunneling

Hu SHI, Guofang GONG, Huayong YANG

《机械工程前沿（英文）》 2011年 第6卷 第3期   页码 369-376 doi: 10.1007/s11465-011-0223-1

摘要：

Focusing on a segment erector of a shield-tunneling machine developed with 6 degrees of freedom (DOF) and controlled by electro-hydraulic proportional systems, the kinematics of the segment erection process is presented. The perturbation method in the error analysis is introduced to establish the position and attitude error model, considering a number of factors such as the hydraulic drive, control accuracy, and tolerance in manufacturing and assembly. Dynamic simulations are carried out to obtain the controlling precision of electrohydraulic drive systems. Formulas for calculating the position and attitude error of the grip hand of the segment erector are derived. The calculation results verify the practicality and effectiveness of the error analysis, providing a foundation for practical designing, manufacturing, and assembling of the segment of the erecting mechanism.

关键词： shield tunneling machine     segment erector     kinematics     position and attitude precision    

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Kinematic, workspace and singularity analysis of a new parallel robot used in minimally invasive surgery

Alin STOICA, Doina PISLA, Szilaghyi ANDRAS, Bogdan GHERMAN, Bela-Zoltan GYURKA, Nicolae PLITEA

《机械工程前沿（英文）》 2013年 第8卷 第1期   页码 70-79 doi: 10.1007/s11465-013-0365-4

摘要：

In the last ten years, due to development in robotic assisted surgery, the minimally invasive surgery has greatly changed. Until now, the vast majority of robots used in surgery, have serial structures. Due to the orientation parallel module, the structure is able to reduce the pressure exerted on the entrance point in the patient’s abdominal wall. The parallel robot can also handle both a laparoscope as well an active instrument for different surgical procedures. The advantage of this parallel structure is that the geometric model has been obtained through an analytical approach. The kinematic modelling of a new parallel architecture, the inverse and direct geometric model and the inverse and direct kinematic models for velocities and accelerations are being determined. The paper will demonstrate that with this parallel structure, one can obtain the necessary workspace required for a minimally invasive operation. The robot workspace was generated using the inverse geometric model. An in-depth study of different types of singularity is performed, allowing the development of safe control algorithms of the experimental model. Some kinematic simulation results and the experimental model of the robot are presented in the paper.

关键词： parallel robot     minimally invasive surgery     kinematics     simulation    

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General closed-form inverse kinematics for arbitrary three-joint subproblems based on the product of

《机械工程前沿（英文）》 2022年 第17卷 第2期 doi: 10.1007/s11465-022-0681-7

摘要： The inverse kinematics problems of robots are usually decomposed into several Paden–Kahan subproblems based on the product of exponential model. However, the simple combination of subproblems cannot solve all the inverse kinematics problems, and there is no common approach to solve arbitrary three-joint subproblems in an arbitrary postural relationship. The novel algebraic geometric (NAG) methods that obtain the general closed-form inverse kinematics for all types of three-joint subproblems are presented in this paper. The geometric and algebraic constraints are used as the conditions precedent to solve the inverse kinematics of three-joint subproblems. The NAG methods can be applied in the inverse kinematics of three-joint subproblems in an arbitrary postural relationship. The inverse kinematics simulations of all three-joint subproblems are implemented, and simulation results indicating that the inverse solutions are consistent with the given joint angles validate the general closed-form inverse kinematics. Huaque III minimally invasive surgical robot is used as the experimental platform for the simulation, and a master–slave tracking experiment is conducted to verify the NAG methods. The simulation result shows the inverse solutions and six sets given joint angles are consistent. Additionally, the mean and maximum of the master–slave tracking experiment for the closed-form solution are 0.1486 and 0.4777 mm, respectively, while the mean and maximum of the master–slave tracking experiment for the compensation method are 0.3188 and 0.6394 mm, respectively. The experiments results demonstrate that the closed-form solution is superior to the compensation method. The results verify the proposed general closed-form inverse kinematics based on the NAG methods.

关键词： inverse kinematics     Paden–Kahan subproblems     three-joint subproblems     product of exponential     closed-form solution    

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Fast forward kinematics algorithm for real-time and high-precision control of the 3-RPS parallel mechanism

Yue WANG, Jingjun YU, Xu PEI

《机械工程前沿（英文）》 2018年 第13卷 第3期   页码 368-375 doi: 10.1007/s11465-018-0519-5

摘要：

A new forward kinematics algorithm for the mechanism of 3-RPS (R: Revolute; P: Prismatic; S: Spherical) parallel manipulators is proposed in this study. This algorithm is primarily based on the special geometric conditions of the 3-RPS parallel mechanism, and it eliminates the errors produced by parasitic motions to improve and ensure accuracy. Specifically, the errors can be less than 10-6 . In this method, only the group of solutions that is consistent with the actual situation of the platform is obtained rapidly. This algorithm substantially improves calculation efficiency because the selected initial values are reasonable, and all the formulas in the calculation are analytical. This novel forward kinematics algorithm is well suited for real-time and high-precision control of the 3-RPS parallel mechanism.

关键词： 3-RPS parallel mechanism     forward kinematics     numerical algorithm     parasitic motion    

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Generation of closed-form inverse kinematics for reconfigurable robots

ZHAO Jie, WANG Weizhong, GAO Yongsheng, CAI Hegao

《机械工程前沿（英文）》 2008年 第3卷 第1期   页码 91-96 doi: 10.1007/s11465-008-0013-6

摘要： For reconfigurable robots, the automatic generation of inverse kinematics is a key problem, because such robots may assume various configurations. In this paper, the screw and product-of-exponentials (POE) formula are used to model the kinematics of reconfigurable robots. The POE formula can be converted to canonical subproblems through decomposition and adjoint transformation. Three classes and 28 types of subproblems containing geometric or algebraic solutions are identified and solved, which can be reused in different configurations. A generalized, decomposable, and reusable approach for close-form inverse kinematics of reconfigurable robots is developed based on POE and subproblems. The effectiveness of this method is shown in an example.

关键词： different     effectiveness     generation     reconfigurable     algebraic    

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一种改进BP算法在机械手逆运动学中的应用

吴爱国,郝润生

《中国工程科学》 2005年 第7卷 第7期   页码 34-38

摘要：

通过对传统BP算法的分析，提出了一种改进激励函数的学习方法，并且在神经网络的每一层采用不同的学习速率，以提高训练速度；采用所提出的改进BP算法，训练多层前向神经网络，建立机械手逆运动学模型，仿真结果表明了该算法的有效性；与传统BP算法相比，大大提高了机械手逆运动学的精度。

关键词： 神经网络     BP算法     激励函数     机械手     逆运动学    

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Oscillation frequency of simplified arterial tubes

Hui AN, Fan HE, Lingxia XING, Xiaoyang LI

《机械工程前沿（英文）》 2009年 第4卷 第3期   页码 300-304 doi: 10.1007/s11465-009-0038-5

摘要： To construct the spatial kinetic equation of an arterial tube and obtain its radial natural frequency, a linear-elastic and small deformation condition is assumed. The theoretical analysis is first presented and the finite element method is then used to numerically simulate the spatial kinematics. The results show that the first-order frequency is 15.8 Hz and the obtained exact analytical solutions agree well with numerical solutions, which proves that the theoretical analysis and numerical simulation are both correct.

关键词： spatial kinematics     natural frequency     finite element method    

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标题 作者 时间 类型 操作

Inverse Kinematics Analysis of General 6R Serial Robot Mechanism Based on Groebner Base

WANG Yan, HANG Lu-bin, YANG Ting-li

期刊论文

Analysis of the kinematic characteristics of a high-speed parallel robot with Schönflies motion: Mobility, kinematics, and singularity

Fugui XIE,Xin-Jun LIU

期刊论文

Inverse kinematics analysis and numerical control experiment for PRS-XY style hybrid machining tool

JIA Dongyong, ZHANG Jianmin, SUN Hongchang, NIU Zhigang

期刊论文

Motion capability analysis of a quadruped robot as a parallel manipulator

Jingjun YU,Dengfeng LU,Zhongxiang ZHANG,Xu PEI

期刊论文

Research on transmission principle and kinematics analysis for involute spherical gear

PAN Cun-yun, WEN Xi-sen, YANG Kun-yu, XU Xiao-jun, LIU Min, YAO Qi-shui

期刊论文

Ahybrid biogeography-based optimization method for the inverse kinematics problem of an 8-DOF redundant

Zi-wu REN,Zhen-hua WANG,Li-ning SUN

期刊论文

Singularity and workspace analysis of three isoconstrained parallel manipulators with schoenflies motion

Po-Chih LEE, Jyh-Jone LEE

期刊论文

A comprehensive analysis of a 3-P (Pa) S spatial parallel manipulator

Yuzhe LIU,Liping WANG,Jun WU,Jinsong WANG

期刊论文

Drive system design and error analysis of the 6 degrees of freedom segment erector of shield tunneling

Hu SHI, Guofang GONG, Huayong YANG

期刊论文

Kinematic, workspace and singularity analysis of a new parallel robot used in minimally invasive surgery

Alin STOICA, Doina PISLA, Szilaghyi ANDRAS, Bogdan GHERMAN, Bela-Zoltan GYURKA, Nicolae PLITEA

期刊论文

General closed-form inverse kinematics for arbitrary three-joint subproblems based on the product of

期刊论文

Fast forward kinematics algorithm for real-time and high-precision control of the 3-RPS parallel mechanism

Yue WANG, Jingjun YU, Xu PEI

期刊论文

Generation of closed-form inverse kinematics for reconfigurable robots

ZHAO Jie, WANG Weizhong, GAO Yongsheng, CAI Hegao

期刊论文

一种改进BP算法在机械手逆运动学中的应用

吴爱国,郝润生

期刊论文

Oscillation frequency of simplified arterial tubes

Hui AN, Fan HE, Lingxia XING, Xiaoyang LI

期刊论文