scholarly journals Research on Influence of Joint Clearance on Precision of 3-TPT Parallel Robot

2019 ◽  
Vol 10 (1) ◽  
pp. 287-298
Author(s):  
Chunxia Zhu ◽  
Zhiyu Zhao
Keyword(s):  
Matrix Method ◽  
Parallel Mechanism ◽  
Parallel Robot ◽  
Error Model ◽  
Independent Method ◽  
Position Error ◽  
Joint Clearance ◽  
Ideal State ◽  
Moving Platform ◽  
The Ideal

Abstract. The error model of the working accuracy of parallel mechanism was established in this paper. The D-H matrix method and error independent method were used to analyze the clearance error of mechanism joint based on the inverse position kinematics solution. The theoretical model describing the position error of the moving platform position error affected by its joint clearance was developed when the moving platform was parallel to fixed platform in the ideal state; the clearance error model of 3-TPT Parallel mechanism was established based on D-H matrix method and error independent method while the joint clearance error source was given. The effect of joint clearance error on the working accuracy of 3-TPT parallel mechanism was analyzed by Monte Carlo method. The effect of posture error due to revolution of the moving platform about coordinate axis on the error of parallel mechanism was simulated and analyzed based on D-H matrix method in the non-ideal state.

Error Comparison and Analysis of Parallel and Constraint Mechanism for 3-TPS Hybrid Machine Tool

2011 ◽  
Vol 127 ◽  
pp. 277-282
Author(s):  
Peng Fei Dang ◽  
Li Jin Fang
Keyword(s):  
Machine Tool ◽  
Parallel Mechanism ◽  
Parallel Robot ◽  
Error Model ◽  
Position Error ◽  
Robot Kinematics ◽  
Motion Error ◽  
Movable Plate ◽  
Hybrid Machine Tool ◽  
Hybrid Machine

This paper establishes position error model based on parallel robot kinematics theory, and analyses position error of the 3-TPS hybrid machine tool. Firstly, to calculate position error of the movable plate caused by the parallel mechanism links, through error model of the parallel mechanism which is established through inverse kinematics of the hybrid machine tool. Then, according to the error model of constraint mechanism established by transformation matrix method, the position error has been simulated and calculated. Finally, this paper compares the effects of both mechanisms. The analysis indicates the link error of constraint mechanism has more influence on movable plate posture than parallel mechanism, and provides help with motion error compensation and kinematic calibration.

Dynamic Response and Nonlinear Characteristics of Spatial Parallel Mechanism With Spherical Clearance Joint

2019 ◽  
Vol 14 (4) ◽  
Author(s):  
Chen Xiulong ◽  
Li Yuewen ◽  
Jia Yonghao
Keyword(s):  
Dynamic Response ◽  
Contact Force ◽  
Dynamic Equation ◽  
Parallel Mechanism ◽  
Joint Clearance ◽  
Spherical Joint ◽  
Nonlinear Characteristics ◽  
Clearance Joint ◽  
Spatial Parallel Mechanism ◽  
Moving Platform

Spherical joint is a type of common kinematic pair in spatial parallel mechanism. The existence of spherical joint clearance has many adverse effects on the mechanism. A method of forecasting the dynamic behaviors of spatial parallel mechanism with spherical clearance joint is proposed. The 4-UPS-UPU spatial parallel mechanism with spherical clearance is taken as the research object, the dynamic response, and nonlinear characteristics of the mechanism are studied. The kinematic model and the contact force model of the spherical clearance are established. The dynamic equation of the spatial parallel mechanism with spherical joint clearance is derived by Newton–Euler method. The above-mentioned dynamic equation is solved by using the ODE113 function that is based on a variable order numerical differential algorithm in matlab. The dynamic responses of moving platform with different clearance values are analyzed. The contact force and the center trajectory of the sphere at the spherical joint are obtained. In addition, the phase trajectory, Poincare map, and bifurcation diagram are analyzed, and the nonlinear characteristics of the spherical clearance joint and the moving platform are obtained. By comparing the results, such as the acceleration of moving platform and the contact force, with virtual prototype simulation, the correctness of the dynamic equation of the spatial parallel mechanism with spherical clearance joint and the analysis results are verified. The researches show that the change of clearance value has a great influence on the motion state of spherical clearance joint, and chaos phenomena appears in the clearance joint with the increase in the clearance value. And the impact phenomenon appears between the spherical joint elements, which makes the mechanism generated vibration.

Displacement Analysis of the 4SPS-2CCS Mechanism Based on Hyper-Chaotic Newton-Downhill Method

2011 ◽  
Vol 230-232 ◽  
pp. 733-737
Author(s):  
You Xin Luo ◽  
Xiao Yi Che ◽  
Bin Zeng
Keyword(s):  
Mathematical Model ◽  
Real Number ◽  
Matrix Method ◽  
Parallel Mechanism ◽  
Parallel Robot ◽  
Number Range ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Henon Mapping ◽  
Solutions Of Equations

The forward displacement analysis of parallel mechanism is attributed to find the solutions of complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of Newton-downhill method, we can find all the solutions of equations quickly. Based on utilizing hyper-chaotic Hénon mapping to obtain initial points, a new method of finding all real number solutions of the nonlinear questions is proposed. Using cosine matrix method, the author established the mathematical model of forward displacement for the generalized 4SPS-2CCS parallel robot mechanism and a numerical example is given. Compared to the quaternion method building mathematical model, the result shows cosine matrix method building mathematical model and hyper-chaotic Newton-downhill method finding solution is brief and high calculation efficiency as the calculation is done in real number range. The proposed method has universality which can be used in forward displacement of other parallel mechanism.

Block Adjacency Matrix Method for Analyzing the Configuration Transformations of Metamorphic Parallel Mechanisms

2014 ◽  
Author(s):  
Duanling Li ◽  
Chunxia Li ◽  
Zhonghai Zhang ◽  
Xianwen Kong
Keyword(s):  
Adjacency Matrix ◽  
Matrix Method ◽  
Parallel Mechanism ◽  
New Method ◽  
Parallel Mechanisms ◽  
Adjacency Matrices ◽  
Moving Platform ◽  
Internal Configuration ◽  
Spherical Motion ◽  
Metamorphic Mechanisms

Metamorphic transformation is a fundamental and key issue in the design and analysis of metamorphic mechanisms. It is tedious to represent and calculate the metamorphic transformations of metamorphic parallel mechanisms using the existing adjacency matrix method. To simplify the configuration transformation analysis, we propose a new method based on block adjacency matrix to analyze the configuration transformations of metamorphic parallel mechanisms. A block adjacency matrix is composed of three types of elements, including limb matrices that are adjacency matrices each representing a limb of a metamorphic parallel mechanism, row matrices each representing how a limb is connected to the moving platform, and column matrices each representing how a limb is connected to the base. Manipulations of the block adjacency matrix for analyzing the metamorphic transformations are presented systematically. If only the internal configuration of a limb changes, the configuration transformations can be obtained by simply calculating the corresponding limb matrix. A 3-URRRR metamorphic parallel mechanism, which has five configurations including a 1-DOF translation configuration and a 3-DOF spherical motion configuration, is taken as an example to illustrate the effectiveness of the proposed approach to the metamorphic transformation analysis of metamorphic parallel mechanism.

The Accuracy Analysis of Parallel Mechanism Assembly Robot

2013 ◽  
Vol 423-426 ◽  
pp. 2769-2775 ◽  
Author(s):  
Xin Rong Liu
Keyword(s):  
Parallel Mechanism ◽  
Joint Angle ◽  
Parallel Robot ◽  
Accuracy Analysis ◽  
Analysis Model ◽  
Error Sources ◽  
Positioning Accuracy ◽  
Moving Platform ◽  
Position And Orientation ◽  
High Repeatability

Parallel robot has the advantages of high rigidity,high bearing capacity and high repeatability of positioning accuracy,and make it more and more widely used in the field of industrial applications.In this paper,the 3-RRR parallel mechanism assembly robot was used as the research object;introduced the sources of error in the parallel mechanism operation platform's position and orientation,furthermore,analyzed the factors of the error sources;then built up that parallel robot's error analysis model,solved the error model with the differential equation,and analyzed the error of parallel robot's structural in rod length,joint angle,the moving platform and the base platform's radius of circle,then simulated with MATLAB.Research shows that All structure errors in parallel mechanism increased by the X axis monotone increasing.

Displacement Analysis of the 3SPS-3CCS Mechanism Based on Hyper-Chaotic Newton-Downhill Method

2011 ◽  
Vol 467-469 ◽  
pp. 401-406 ◽  
Author(s):  
You Xin Luo ◽  
Xiao Yi Che ◽  
Bin Zeng
Keyword(s):  
Mathematical Model ◽  
Real Number ◽  
Matrix Method ◽  
Parallel Mechanism ◽  
Parallel Robot ◽  
Number Range ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Chaotic Sequences ◽  
Chaos System

The forward displacement analysis of parallel mechanism is attributed to find the solutions of complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of Newton-downhill method, we can find all the solutions of equations quickly. Making use of existing chaos system and discovering new chaos system to generate chaotic sequences with good properties is the key to the Newton-downhill method based on Chaos sequences. Based on utilizing hyper-chaotic Hénon mapping to obtain initial points, a new method of finding all real number solutions of the nonlinear questions is proposed. Using cosine matrix method, the author established the mathematical model of forward displacement for the generalized 3SPS-3CCS parallel robot mechanism and a numerical example is given. Compared to the quaternion method building mathematical model, the result shows cosine matrix method building mathematical model and hyper-chaotic Newton-downhill method finding solution is brief and high calculation efficiency as the calculation is done in real number range. The proposed method has universality which can be used in forward displacement of other parallel mechanism.

Effects of Spherical Clearance Joint on Dynamics of Redundant Driving Spatial Parallel Mechanism

Robotica ◽  
2020 ◽  
pp. 1-17
Author(s):  
Xiulong Chen ◽  
Jingyao Guo
Keyword(s):  
Dynamic Characteristics ◽  
Parallel Mechanism ◽  
Dynamic Responses ◽  
Joint Clearance ◽  
Parallel Mechanisms ◽  
Spherical Joint ◽  
Ideal Situation ◽  
Spatial Parallel Mechanism ◽  
Redundant Drive ◽  
The Ideal

SUMMARY This paper proposes a dynamic modeling method of redundant drive spatial parallel mechanism, dynamics of 4-UPS-RPU redundant driving spatial parallel mechanism considering spherical joint clearance are analyzed. The dynamic equation of spherical joint clearance with Lagrange multiplier is built. The influences of single clearance and multiple clearances on dynamic responses of redundant drive spatial parallel mechanisms are analyzed under different clearance values. The results show that the dynamic characteristics of the mechanism with single clearance are basically consistent with the ideal situation, and the dynamic characteristics of the mechanism with multi-clearance are significantly different from the ideal situation.

The Republic

2019 ◽  
pp. 205-229
Author(s):  
Dominic Scott
Keyword(s):  
Political Theory ◽  
Left Behind ◽  
Ideal State ◽  
The Republic ◽  
Individual Justice ◽  
The Individual ◽  
Political Right ◽  
First Time ◽  
The Ideal

This chapter presents a reading of Plato’s Republic. The Republic is among Plato’s most complex works. From its title, the first-time reader will expect a dialogue about political theory, yet the work starts from the perspective of the individual, coming to focus on the question of how, if at all, justice contributes to an agent’s happiness. Only after this question has been fully set out does the work evolve into an investigation of politics—of the ideal state and of the institutions that sustain it, especially those having to do with education. But the interest in individual justice and happiness is never left behind. Rather, the work weaves in and out of the two perspectives, individual and political, right through to its conclusion. All this may leave one wondering about the unity of the work. The chapter shows that, despite the enormous range of topics discussed, the Republic fits together as a coherent whole.

scholarly journals Research of Calibration Method for Industrial Robot Based on Error Model of Position

2021 ◽  
Vol 11 (3) ◽  
pp. 1287
Author(s):  
Tianyan Chen ◽  
Jinsong Lin ◽  
Deyu Wu ◽  
Haibin Wu
Keyword(s):  
Coordinate System ◽  
Industrial Robot ◽  
Calibration Method ◽  
Error Model ◽  
Position Error ◽  
Industrial Robots ◽  
Positioning Error ◽  
Robot Position ◽  
General Measurement ◽  
Parameter Error

Based on the current situation of high precision and comparatively low APA (absolute positioning accuracy) in industrial robots, a calibration method to enhance the APA of industrial robots is proposed. In view of the "hidden" characteristics of the RBCS (robot base coordinate system) and the FCS (flange coordinate system) in the measurement process, a comparatively general measurement and calibration method of the RBCS and the FCS is proposed, and the source of the robot terminal position error is classified into three aspects: positioning error of industrial RBCS, kinematics parameter error of manipulator, and positioning error of industrial robot end FCS. The robot position error model is established, and the relation equation of the robot end position error and the industrial robot model parameter error is deduced. By solving the equation, the parameter error identification and the supplementary results are obtained, and the method of compensating the error by using the robot joint angle is realized. The Leica laser tracker is used to verify the calibration method on ABB IRB120 industrial robot. The experimental results show that the calibration method can effectively enhance the APA of the robot.

KINEMATICS AND WORKSPACE ANALYSIS OF A 3 DEGREE OF FREEDOM PARALLEL MECHANISM WITH PARALLELOGRAM LINKAGE

2017 ◽  
Vol 41 (5) ◽  
pp. 922-935
Author(s):  
HongJun San ◽  
JunSong Lei ◽  
JiuPeng Chen ◽  
ZhengMing Xiao ◽  
JunJie Zhao
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Analytical Method ◽  
Theoretical Basis ◽  
Parallel Mechanism ◽  
Graphical Method ◽  
Degree Of Freedom ◽  
Workspace Analysis ◽  
Fixed Base ◽  
Moving Platform

In this paper, a 3-DOF translational parallel mechanism with parallelogram linkage was studied. According to the space vector relation between the moving platform and the fixed base, the direct and inverse position solutions of this mechanism was deduced through analytical method. In addition, the error of the algorithm was analyzed, and the algorithm had turned out to be effective and to have the satisfactory computational precision. On the above basis, the workspace of this mechanism was found through graphical method, which was compared with that of finding through Monte Carlo method, and there was the feasibility for analyzing the workspace of the mechanism by graphical method. The characteristic of the mechanism was analyzed by comparing the results of two analysis methods, which provided a theoretical basis for the application of the mechanism.

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