Phương pháp phân tích ưu hóa mô hình động học robot song song

博士留学生学位论文
并联机器人运动学模型优化解析方法研究

作 者 姓 名 TRANG THANH TRUNG (庄成忠 )
学 科 专 业

机械制造及其自动化

指 导 教 师

李伟光 教授

所 在 学 院

机械与汽车工程学院

论文提交日期

20 17 年 11 月


Optimization Analysis Method of Parallel Manipulator
Kinematic Model

A Dissertation Submitted for the Degree of Doctor

Candidate：Trang Thanh Trung
Supervisor：Prof. Li Weiguang

South China University of Technology
Guangzhou, China

2


分类号：TP242

学校代号：10561

学 号：201312800054

华南理工大学博士学位论文

并联机器人运动学模型优化解析方法研究

作者姓名：TRANG THÀNH TRUNG(庄成忠)

指导教师姓名、职称：李伟光教授/博士生导师

申请学位级别：工学博士

学科专业名称：机械制造及其自动化

研究方向：精密制造装备与现代控制技术
论文提交日期：2017 年 11 月 11 日

论文答辩日期：2018 年 03 月 12 日

学位授予单位：华南理工大学

学位授予日期：

年 月

日

答辩委员会成员：
主席： 张永俊教授

.

委员：

赵学智教授

黄平教授

姚锡凡教授

李伟光教授

.





摘 要
本文的主要目的是建立一个新的算法，以简化所有类型的并联机器人的运动学问
题的解决，而不限制自由度的数量。该算法适用于各种并联机器人结构，具有精度高、
可靠性好、执行时间短、比现有方法更易于使用的特点。五连杆并联机器人的数值模

拟和实验结果表明，该方法可用于解决各种并联机器人的运动学问题，对于结构复杂
和自由度多的并联机器人，该方法也具有计算时间短、精度高、可靠性高、结果收敛
快等优点。此外，本文还扩展了该方法在机器人公差设计领域的应用。通过两个仿真
实验验证了该方法的可行性；计算和仿真结果也说明了所提出的公差分配方法的准确
性和效率。
首先，在研究手臂机器人优化问题的基础上，本论文提供了新的接入方法以寻找
运动学参数，即将传统并联机器人运动学问题转换成有约束的非线性最优化问题，其
目标函数是 Rosenbrock-Banana 函数。经过很多试验，在非线性优化问题中 RosenbrockBanana 函数最合适是广义简约算法。从运动学控制试验中直接寻找，将缩短编程开发
时间。
其次，本文提出一种新的方式分类并联机器人，非棱柱并联机器人与棱柱并联机
器人，包括 3 种：非棱柱并联机器人（类型 1），棱柱并联机器人分成两种：主动棱柱
关节连接到固定平台的并联机器人（类型 2）和第二棱柱关节连接到固定平台的并联机
器人（类型 3）。本文描述所有并联机器人结构的模式化和将并联机器人运动学问题数
学模型转换成求解最优化问题的方式。对于类型 1 并联机器人，将初始数学模型转化为
最优问题时，目标函数为二次函数，因此直接应用广义简约求解运动学问题，而类型 2
和类型 3 的初始数学模型机器人是四次幂函数，与所提出的方法不相容。因此，本文提
出用同等代替结构将两类并联机器人（2 型和 3 型）的目标函数形式从四次幂函数降为
二次函数来解决这一问题，通过这种变换之后符合提出的方法。
第三，Excel 微软应用程序支持数学解析，并通过求解机器人的运动学问题，给出
了各类机器人的典型并联机器人解决方案。在两个不同的空间（关节空间和工作空间）
之间的唯一解决方案的保证已经充分论证。可靠性和精密度试验结果表明，所提出的
方法是非常可靠和准确的。通过与其它算法相比较，求解最优运动问题的顺序二次规
划和遗传算法，提出的方法的精度更高（约从二个到四个数量级），并且具有较短的执
行时间。

I


第四，逆运动学的结果作为实时控制机器人轨迹的信息，通过 Adams 仿真以及五
连杆并联机器人的实验表明，该方法能够实际应用于并联机器人控制。

最后，除了用于并行机器人运动学求解外，本论文提出的方法还可以应用于一个
新领域中—机器人制造设计，即确定成品工序容差以保证末端执行器的估计正确度和
精度。该技术不仅能应用在并行机器人而且还可以应用给手臂机器人。通过两个实例
验证了上述方法的可行性和计算结果, 该方法能准确、有效设计公差构件。

关键词：并联机器人；运动学问题；优化问题；同等代替结构；广义简约梯度法；制
造设计误差。

II


Abstract
The primary objective of this dissertation is to build a new algorithm that simplifies the
resolution of the kinematic problems for all types of parallel robots without limiting the number
of degrees of freedom. This algorithm applies to various parallel robotic structures in a general
order with high accuracy and reliability, shorter execution time, easier to use than current
methods. To this end, the numerical simulation and experiment results of parallel Scara robots
prove that the proposed method can be applied to solve kinematic problems for a variety of
parallel robots regardless of its structures and degree of freedom with several advantages such
as shorter computation time, high precision, high reliability and rapid convergence of results.
In addition, this dissertation also extends the application of the proposed method in the field of
robot tolerance design. Two examples are used to verify the feasibility of the proposed method;
the accuracy and efficiency of the proposed method for generating tolerance allocations are also
illustrated by calculations and simulation results.
Firstly, based on optimal problem applied on the robot arm the dissertation proposes a new
approach to find kinematic parameters by transforming the kinematic problem of the traditional
parallel robot into a nonlinear optimization with the objective function Rosenbrock-Banana.
Through many tests, the best algorithm for the Rosenbrock-Banana function in the optimal
problem is the General Reduced Gradient (GRG) method. Direct recovery of the kinematic
control resulting from the optimal problem will reduce the preparation time of the

programmable data.
Secondly, classification of a parallel robot based on texture with or without prismatic joints,
the dissertation has been grouped into three types of parallel robots: the non-prismatic parallel
robot (type 1) and the prismatic parallel robots including the parallel robot with the active
prismatic joints connected to its base (type 2), the parallel robot with the second prismatic joints
from its base (type 3). The dissertation presented modeling for all types of parallel robot
structures and how to convert the mathematical model of the kinematic problem of the parallel
robot to the optimal form. The situations that may arise when applying the proposed method on
the three types of parallel robots are fully argued. With type 1 of parallel robot, the initial
mathematical models when transforming into optimal problem, the object function is the
quadratic function, so directly apply the GRG to solve the kinematic problem but the initial
mathematical models of type 2 and type 3 robots are the quaternary function, which is
incompatible with the proposed method. Thus, the dissertation proposes to solve this problem
by using the equivalent substitution configuration to downgrade the object function form of the

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two types of robots (type 2 and type 3) from quaternary function to quadratic function, which
is compatible with the proposed method.
Thirdly, the Microsoft-Excel solver application supports mathematical resolution, to
illustrate the example, by solving the kinematic problem of the robot for some typical parallel
robots for each type of robot are presented in detail. The assurance of a unique solution between
two different spaces (joint space and work space) has been fully argued. The results of the
reliability and precision tests showed that the proposed method was very reliable and accurate.
By comparing with other algorithms to solve an optimal problem, which are Sequential
Quadratic Programming and the Genetic Algorithm to solve the optimal kinematic problem, the
proposed method has exceeded the accuracy (approximately from 102 to 104 times) and has
shorter execution time.
Fourthly, the results of the inverse kinematic problem are used as information to control

the trajectory of the robot in real time, presented in detail and illustrated by the Adams
simulation software as well as experiments in the Scara parallel robot. Experimental results
demonstrated the capability, accuracy and feasibility of the proposed method when applied to
robot control in practice.
Finally, in addition to solving the kinematic problem of the parallel robot, the dissertation
also developed a new application of the method proposed in the field of the manufacture of
robots in order to design the tolerances of the components (links and joints) to ensure the given
accuracy of the end effector and vice versa. This technique applies not only to parallel robots
but also to the robot arm. Two examples are used to verify the feasibility of the above method
and the calculated result that the method can produce tolerance allocations accurately and
efficiently.
Key words: Parallel robot; kinematics problem; optimization problem; equivalent structure;
General Reduced Gradient method; tolerance design

IV


目 录
摘 要 ........................................................................................................................................... I
Abstract .................................................................................................................................... III
目 录 ......................................................................................................................................... V
Contents ................................................................................................................................. VIII
图目录 ...................................................................................................................................... XI
表目录 .....................................................................................................................................XV
第一章 绪论 ............................................................................................................................... 1
1.1 机器人信息的初始化方法 ........................................................................................... 1
1.2 机器人运动学、模型与解决方法 ............................................................................... 2
1.2.1 机器人运动学 ..................................................................................................... 2
1.2.2 建模的方法 ......................................................................................................... 3
1.2.3 解决模型的方法 ................................................................................................. 7

1.2.4 并联机器人运动学问题求解方法综述 ............................................................. 9
1.3 研究方向 ..................................................................................................................... 13
1.4 研究对象和研究方法 ................................................................................................. 14
1.5 本论文的内容 ............................................................................................................. 14
第二章 各类机器人运动学问题优化的数学模型 ................................................................. 17
2.1 引言 ............................................................................................................................. 17
2.2 机器人运动学优化形式 ............................................................................................. 17
2.2.1 机器人运动学的最优数学模型 ....................................................................... 17
2.2.2 手臂机器人优化问题的基础 ........................................................................... 19
2.2.3 最优运动问题 ................................................................................................... 23
2.2.4 算法图 ............................................................................................................... 23
2.2.5 均匀的精密结构 ............................................................................................... 25
2.2.6 差分计算对准确性的影响 ............................................................................... 27
2.3 并联机器人的关联向量方程类型 ............................................................................. 30

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2.3.1 手臂机器人和并联机器人相关矢量方程的建立方法差异 ........................... 30
2.3.2 非棱柱并联机器人（类型 1） ........................................................................ 31
2.3.3 棱柱并联机器人 ............................................................................................... 36
2.3.4 手臂机器人与并联机器人数学模型的异同点 ............................................... 40
2.4 本章小结 ..................................................................................................................... 42
第三章 并联机器人运动学问题的广义简化梯度算法研究 ................................................. 43
3.1 引言 ............................................................................................................................. 43
3.2 广义简化梯度算法 ..................................................................................................... 43
3.3 Microsoft-Excel 求解器优化应用介绍...................................................................... 47
3.4 使用广义简化梯度算法解决并行机器人的运动问题 ............................................. 50
3.4.1 并联机器人（类型 1） .................................................................................... 50
3.4.2 同等代替结构和变量公式 ............................................................................... 59

3.4.3 第一棱柱关节连接到固定平台的并联机器人（类型 2） ............................ 63
3.4.4 第二棱柱关节连接到固定平台的并联机器人（类型 3） ............................ 85
3.4.5 两种不同空间之间的独特的解决方案的保证 ............................................. 104
3.4.6 测试新方法的可靠性 .................................................................................... 105
3.4.7 测试新方法的精度和准确度与其他方法的比较 ......................................... 108
3.5 本章小结 ................................................................................................................... 117
第四章 仿真与实验研究 ....................................................................................................... 118
4.1 引言 ........................................................................................................................... 118
4.2 实验的内容 ............................................................................................................... 118
4.3 背景设计实验 ........................................................................................................... 118
4.3.1 五连杆并联机器人 ......................................................................................... 118
4.3.2 建立运动学特性的关节的五连杆并联机器人 ............................................. 127
4.4 测试模拟和数值结果的准确性 ............................................................................... 145
4.4.1 以图形方式检查数学的结果 ......................................................................... 146
4.4.2 测试结果与数学模拟软件 ............................................................................. 149
4.5 实验研究 ................................................................................................................... 153
4.5.1 实验设置 ......................................................................................................... 153

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4.5.2 机电-电子-软件基本参数 .............................................................................. 155
4.5.3 设计控制系统软件 ......................................................................................... 160
4.5.4 经验和讨论结果 ............................................................................................ 168
4.6 本章小结 ................................................................................................................... 176
第五章 使用广义简约梯度算法确定机器人运动关节的公差参数 ................................... 178
5.1 引言 ........................................................................................................................... 178
5.2 公差设计文献综述 ................................................................................................... 178
5.3 公差最优问题的形成 ............................................................................................... 182
5.4 公差优化问题的求解方法 ....................................................................................... 183

5.5 关节运动公差的确定 ............................................................................................... 183
5.6 通过使用逆运动学确定连杆尺寸和关节自由径向运动的公差 ........................... 186
5.7 数值模拟实例 ........................................................................................................... 188
5.7.1 手臂机器人 ..................................................................................................... 188
5.7.2 并联机器人 ..................................................................................................... 190
5.8 检查提出的方法的准确性 ....................................................................................... 193
5.9 本章小结 ................................................................................................................... 194
第六章 结论和展望 ............................................................................................................... 195
6.1 结论 ........................................................................................................................... 195
6.2 主要创新点 ............................................................................................................... 197
6.3 展望 ........................................................................................................................... 197
参考文献 ................................................................................................................................ 199
附录 I...................................................................................................................................... 211
攻读博士学位期间取得的研究成果 .................................................................................... 224
致 谢...................................................................................................................................... 225

VII


Contents
摘 要 ...........................................................................................................................................I
Abstract .................................................................................................................................. III
目 录 ......................................................................................................................................... V
Contents................................................................................................................................VIII
List of figures .......................................................................................................................... XI
List of tables .......................................................................................................................... XV
Chapter 1 Introduction ............................................................................................................ 1
1.1 Methods for information initialization of robot ................................................................ 1
1.2 Robot kinematics, models and methods ........................................................................... 2
1.2.1 Robot kinematics ........................................................................................................ 2

1.2.2 Modelling phase ......................................................................................................... 3
1.2.3 Model survey phase .................................................................................................... 7
1.2.4 An overview of methods for solving kinematic problems of parallel robot............... 9
1.3 Research orientation ....................................................................................................... 13
1.4 Subjects and research methods ....................................................................................... 14
1.5 Contents of the present thesis ......................................................................................... 14
Chapter 2 Mathematical Bases for Changing from the Robot Kinematic Problem to the
Optimization Problem............................................................................................................ 17
2.1 Introduction..................................................................................................................... 17
2.2 Robot kinematic under the optimization form ................................................................ 17
2.2.1 The optimal mathematical model of robotic kinematic............................................ 17
2.2.2 Bases for optimization problems on the robot arm .................................................. 19
2.2.3 The optimal movement problem .............................................................................. 22
2.2.4 Algorithm diagram ................................................................................................... 23
2.2.5 The uniform precision structure ............................................................................... 25
2.2.6 The effect of the difference calculation on the accuracy of the problem ................. 27
2.3 Types of associated vector equations for parallel robots ................................................ 30
2.3.1 Difference in the way to build the associated vector equations for robot arms and
parallel robots .................................................................................................................... 30
2.3.2 The non-prismatic parallel robot (Type 1) ............................................................... 31
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2.3.3 The prismatic parallel robots .................................................................................... 36
2.3.4 Identify similarities in the mathematical model of parallel robots and robot arms.. 40
2.4 Chapter conclusion ......................................................................................................... 42
Chapter 3 Application of Generalized Reduced Gradient Algorithm to Solve the
Kinematic Problem of Parallel Robots ................................................................................. 43
3.1 Introduction..................................................................................................................... 43
3.2 Generalized Reduced Gradient algorithm ...................................................................... 43

3.3 Introduction of optimization application of solver in Microsoft-Excel .......................... 47
3.4 Resolution of the Kinematic Problems of Parallel Robots using Generalized Reduced
Gradient algorithm ................................................................................................................ 50
3.4.1 Parallel robot of type 1 ............................................................................................. 50
3.4.2 Equivalent substitution configuration and the formulation of variables change ...... 59
3.4.3 Parallel robot of type 2 ............................................................................................. 64
3.4.4 Parallel robot of type 3 ............................................................................................. 86
3.4.5 The assurance of unique solution between two different spaces ............................ 105
3.4.6 Testing the reliability of the novel method ............................................................. 107
3.4.7 Testing the precision of the novel method and compare accuracy with other methods
......................................................................................................................................... 110
3.5 Chapter’s conclusion .................................................................................................... 119
Chapter 4 Simulation and Experimental Study ................................................................ 120
4.1 Introduction................................................................................................................... 120
4.2 Content of experiment .................................................................................................. 120
4.3 Based on experimental design ...................................................................................... 120
4.3.1 Parallel Scara robot ................................................................................................ 120
4.3.2 Settings of kinematic characteristics of joints for Parallel Scara robot .................. 129
4.4 Testing simulation and accuracy of numerical results .................................................. 147
4.4.1 Inspection of results by graphics ............................................................................ 148
4.4.2 Inspection of results by simulation software .......................................................... 151
4.5 Experimental study ....................................................................................................... 155
4.5.1 Experimental setup ................................................................................................. 155
4.5.2 Basic parameters of mechanical-electrical-electronic components........................ 157
4.5.3 Design of control system software ......................................................................... 162
4.5.4 Results of experiments and discussion ................................................................... 170
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4.6 Chapter conclusions ...................................................................................................... 178

Chapter 5 Application Generalized Reduced Gradient Algorithm to Determine
Tolerance Design of Robot Parameters .............................................................................. 180
5.1 Introduction................................................................................................................... 180
5.2 Literature review of tolerance design ........................................................................... 180
5.3 The formation of the optimal problem .......................................................................... 184
5.4 Solution method for the optimization problem ............................................................. 185
5.5 Determination of the tolerance of joint angle movement ............................................. 185
5.6 Determination of the deviation of link dimensions and joint free radial movement by
using inverse kinematic ...................................................................................................... 187
5.7 The example of numerical simulation .......................................................................... 189
5.7.1 Robot arm ............................................................................................................... 189
5.7.2 Parallel Robot ......................................................................................................... 192
5.8 Checking the accuracy of the proposed method ........................................................... 195
5.9 Chapter conclusion ....................................................................................................... 196
Chapter 6 Conclusions and Future Works ......................................................................... 197
6.1 Conclusions................................................................................................................... 197
6.2 The main points of innovation ...................................................................................... 199
6.3 Future works ................................................................................................................. 199
References ............................................................................................................................. 201
Appendix I............................................................................................................................. 211
Achievement of research ...................................................................................................... 226
Acknowledgments................................................................................................................. 227

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List of figures
Figure 1-1 Diagram of closed loop on robot arrm and parallel robot ....................................... 3
Figure 1-2 Closed loop vector ................................................................................................... 4
Figure 1-3 Parallel structured Robot ......................................................................................... 5

Figure 1-4 Kinematics circuit of one limb of parallel robot ..................................................... 6
Figure 1-5 Control Diagram in joint space................................................................................ 8
Figure 1-6 Control Diagram in work space ............................................................................... 9
Figure 1-7 The subject of the overall research program ......................................................... 16
Figure 2-1 Algorithm diagram for solving the inverse robot kinematic problem ................... 24
Figure 2-2 The general closed loop scheme for any limb ....................................................... 30
Figure 2-3 Planar parallel robot 3RRR ................................................................................... 32
Figure 2-4 Parallel Delta robots (a) and the vector expansion loop for ith limb (b) ............... 33
Figure 2-5 The detailed generalized coordinates for the point C ............................................ 34
Figure 2-6 Setting up moving reference frames ...................................................................... 34
Figure 2-7 The detailed generalized model of the ith limb of the SRS parallel robot ............ 36
Figure 2-8 TPM parallel robot (a) and the generalized model of a one limb vector (b) ......... 37
Figure 2-9 Parallel planar 3RPR Robot................................................................................... 38
Figure 2-10 The detailed generalized model of the ith limb of a 3-RPS parallel robot .......... 39
Figure 2-11 The detailed generalized model of the ith limb of a 6-SPS parallel robot........... 40
Figure 2-12 Differences and similarities between the mathematical models of Robot Arm and
Parallel robot...................................................................................................................... 42
Figure 3-1 Solver parameter dialog box .................................................................................. 47
Figure 3-2 Add- Ins of additional setting of Solver ................................................................ 48
Figure 3-3 3RRR planar parallel robot and the moving trajectory across twelve points belong
to an ellipse ........................................................................................................................ 51
Figure 3-4 Set the objective function and constraints for IKP of 3RRR robot ....................... 54
Figure 3-5 Set the objectives function and constraints for FKP of 3RRR robot ..................... 57
Figure 3-6 The displacement graph of controlled joint variables i (with i=1,2,3) of 3RRR
parallel robot ...................................................................................................................... 59
Figure 3-7 TPM robot with prismatic active joint and the substitution configuration for a limb
of PRRR robot by using two revolute joints to replace one prismatic joint ...................... 60
Figure 3-8 (a) Stewart Gough robot with SPS configuration

XI

(b) The equivalent substitution configuration ........................................................... 61
Figure 3-9 The geometric relation between the original variable  li  and the new one  2i  as
the actuator type is changed............................................................................................... 62
Figure 3-10 Equivalent substitution configuration for some parallel robot structures contains
prismatic joints .................................................................................................................. 64
Figure 3-11 The moving trajectory of the PRRR robot is needed to control .......................... 64
Figure 3-12 The detailed substitution configuration for a limb of the PRRR robot ............... 66
Figure 3-13 Settings of objective function and constraints of IKP robot PRRR .................... 74
Figure 3-14 Settings of objective functions and constraints of FKP in robot PRRR .............. 80
Figure 3-15 The converted displacement graph of 3 equivalent joint variables between the
substitution configuration and the original structure of the PRRR robot .......................... 85
Figure 3-16 The moving trajectory of Stewart Gough robot needed to control ...................... 86
Figure 3-17 Substitution configuration for one limb of Stewart Gough robot........................ 87
Figure 3-18 Settings of objectives function and constraints of IKP Stewart Gough robot ..... 92
Figure 3-19 Settings of objective functions and constraints of FKP Stewart Gough robot .... 99
Figure 3-20 The converted displacement graph of 6 equivalent joint variables between the
substitution configuration and the original structure of Stewart Gough robot ................ 105
Figure 3-21 The multidirectional relation between joint space and workspace in parallel
kinematic robots .............................................................................................................. 106
Figure 3-22 The close relationship of kinematic database of the linking equation ............... 107
Figure 4-1 The parallel scara robot with two translation degrees of freedom and detailed
development of right limb ............................................................................................... 121
Figure 4-2 Equivalent kinematic diagram and detail development of the right limb of Scara
parallel robot .................................................................................................................... 122
Figure 4-3 Experimental trajectory need to controlled ......................................................... 123
Figure 4-4 Settings of the objective function and constraints of IKP parallel scara robot .... 125
Figure 4-5 Settings of the objective function and constraints of FKP parallel scara robot ... 127
Figure 4-6 The graph of displacement of variable 1 ........................................................... 139

Figure 4-7 The displacement graph of variable 1 .............................................................. 140
Figure 4-8 The graph of acceleration of variable 1 ............................................................ 140
Figure 4-9 The displacement graph of variable  2 ............................................................. 146
Figure 4-10 The graph of the velocity of variable  2 ........................................................... 147

XII


Figure 4-11 The graph of acceleration of variable  2 .......................................................... 147
Figure 4-12 The kinematic problem of parallel scara robot measured by graphics .............. 148
Figure 4-13 The kinematic structure of parallel scara robot in Adams software .................. 152
Figure 4-14 The displacement graph of variable 1 and  2 in the Adams software ........... 152
Figure 4-15 Diagram of experimental robotic structure........................................................ 155
Figure 4-16 PCMM measurements in the form of robot .................................................. ….153
Figure 4-17 Drawing of asembly of experimental robotic structure .................................... 156
Figure 4-18 Servo motor used in the experiment .................................................................. 158
Figure 4-19 Servo amplifier MR-E-10A E ............................................................................ 158
Figure 4-20 Speed reduce gearbox used in the experiment .................................................. 159
Figure 4-21 Rolling bearings................................................................................................. 159
Figure 4-22 Omron encoder .................................................................................................. 160
Figure 4-23 Electronic caliper ............................................................................................... 160
Figure 4-24 Interface of database collection in the laboratory.............................................. 161
Figure 4-25 Rigid couplings .................................................................................................. 161
Figure 4-26 Arduini Uno R3 microcontrollers and technical parameters .............................. 162
Figure 4-27 Diagram of systematic control algorithm .......................................................... 164
Figure 4-28 Interface of the system controlling parallel scara robot .................................... 164
Figure 4-29 General Embedded System used in the control system ..................................... 166
Figure 4-30 Serial communication events ............................................................................. 167
Figure 4-31 Motion control method ...................................................................................... 167
Figure 4-32 The method of moving coordinates of end-effector .......................................... 168

Figure 4-33 Diagram of systematic hardware principles ...................................................... 169
Figure 4-34 The diagram of installation of robot in practical experiment ............................ 170
Figure 4-35 Errors of controlled trajectory between experimental and simulation .............. 176
Figure 4-36 Error of parameter of controlled angles 1 &  2 between experimental and
simulation ........................................................................................................................ 177
Figure 4-37 Error of secondary parameters 1 & 2 between experimental and simulation . 177
Figure 4-38 Error of translational joint L1 & L2 in the orginal configuration between
experimental and simulation ............................................................................................ 177
Figure 5-1 The movement with the smallest step of moving platform between two points in
space ................................................................................................................................ 186

XIII


Figure 5-2 Several types of clearance to be controlled in joints ........................................... 186
Figure 5-3 The transmission deviation of restricted angle caused by mechanic clearance
defined by (5-10) ............................................................................................................. 187
Figure 5-4 Tolerance choice of built-up links ....................................................................... 189
Figure 5-5 The use of calculated tolerance results ................................................................ 189
Figure 5-6 The equivalent kinematic diagram of robot Fanuc S900W ................................. 190
Figure 5-7 Six allowable moving points of the end-effector in the limited deviation range of
a sphere ............................................................................................................................ 190
Figure 5-8 The 3-RRR planar parallel robot ......................................................................... 193
Figure 5-9 The errors of control trajectory............................................................................ 196

XIV


List of tables
Table 1-1 Advantages, disadvantages and limitations of some methods solving parallel

kinematic problem ............................................................................................................. 11
Table 2-1 Value of function y in the break points ................................................................... 27
Table 3-1 Solver’s terms in the program interface .................................................................. 49
Table 3-2 Meaning of options in the item Option of Solver ................................................... 49
Table 3-3 Coordinates of twelve key points of the trajectory and the variation of the angle φ in
each key point .................................................................................................................... 51
Table 3-4 Interface of declaration of the kinematic problems of 3RRR parallel robots .......... 53
Table 3-5 IKP result of 3RRR parallel robot ........................................................................... 55
Table 3.6 The error of the objective functions, running time (seconds) and the iterations of each
key point in IKP of 3RRR parallel robot ........................................................................... 55
Table 3-7 FKP results of 3RRR parallel robot ........................................................................ 57
Table 3-8 The error of the objective functions, running time (seconds) and iterations of each
set of control parameter in FKP of 3RRR parallel robot ................................................... 57
Table 3-9 The error control of 3RRR parallel robot ................................................................ 58
Table 3-10 Coordinates of 24 key points in the trajectory that needs to controlled ................ 64
Table 3-11 Interface of declaration of IKP of parallel robot PRRR ........................................ 88
Table 3-12 Results of IKP of parallel robot PRRR, the 1st limb (rad)..................................... 74
Table 3-13 Results of IKP of parallel robot PRRR, the 2nd limb (rad) .................................... 75
Table 3-14 Results of IKP of parallel robot PRRR, the 3rd limb (rad) .................................... 76
Table 3-15 IKP results of parallel robot PRRR in conversion into control variable L in the
original configure, error of objective functions, time (second) and iterations of each key
point ................................................................................................................................... 77
Table 3-16 Interface of declaration of FKP of parallel robot PRRR ....................................... 79
Table 3-17-3-18 Results of FKP in parallel robot PRRR ........................................................ 81
Table 3-19 Results of FKP in parallel robot PRRR, error of objective function, time (second)
and iterations key point...................................................................................................... 83
Table 3-20 The control error of parallel robot PRRR.............................................................. 84
Table 3-21 Coordinates of twenty-four key point under trajectory that need to be controlled of
6SPS robot ......................................................................................................................... 86
Table 3-22 Interface of declaration of IKP with Stewart Gough parallel robot ...................... 91

Table 3-23 IKP results of Stewart Gough parallel robot, value of angles 1i ......................... 93
XV


Table 3-24 IKP results of Stewart Gough parallel robot, value of angles  2i ........................ 94
Table 3-25 IKP results of Stewart Gough parallel robot, value of angles  3i ....................... 95
Table 3-26 IKP results of Stewart Gough parallel robot, when exchange into control variable L
in the original configuration. The error of objective function, time (seconds) and iterations
in each key point. ............................................................................................................... 95
Table 3-27 The interface of declaration of FKP with Stewart Gough parallel robot .............. 96
Table 3-28 FKP results of Stewart Gough parallel robot, value of angles 1i ........................ 99
Table 3-29 FKP results of Stewart Gough parallel robot, value of angles  2i ...................... 100
Table 3-30 FKP results of Stewart Gough parallel robot, value of angles  3i ..................... 101
Table 3-31 FKP results of Stewart Gough parallel robot, value of control coordinates in each
key point .......................................................................................................................... 101
Table 3-32 FKP results of Stewart Gough parallel robot, control value Li , error of object
function, time (second) and iterations in the key point ................................................... 102
Table 3-33 The error control of control for Stewart Gough parallel robot ............................ 103
Table 3-34 The results of the objective function at 12 controlled trajectory points of 3RRR
planar parallel robot in Matlab ........................................................................................ 107
Table 3-35 The results of the objective function at 24 controlled trajectory points of TPM robot
in Matlab .......................................................................................................................... 108
Table 3-36 The results of the objective function at 24 controlled trajectory points of Stewart
Gough robot in Matlab .................................................................................................... 109
Table 3-37 The results of the objective function and solver time for each keypoint for 3RRR
robot in FKP .................................................................................................................... 112
Table 3-38 The results of the objective function and solver time for each keypoint for 3RRR
robot in IKP ..................................................................................................................... 113
Table 3-39 The results of the objective function and solver time for each keypoint for 3PRRR
robot in FKP .................................................................................................................... 113

Table 3-40 The results of the objective function and solver time for each keypoint for 3PRRR
robot in IKP ..................................................................................................................... 114
Table 3-41 The results of the objective function and solver time for each keypoint for Stewart
Gough robot 6SPS in FKP ............................................................................................... 115
Table 3-42 The results of the objective function and solver time for each keypoint for Stewart
Gough robot 6SPS in IKP ................................................................................................ 116

XVI


Table 3-43 The actual computational time of the three method ............................................ 117
Table3-44 Trajectory tolerance of 3RRR parallel robot ........................................................ 118
Table3-45 Trajectory tolerance of Stewart Gough Robot 6SPS ............................................ 118
Table3-46 Trajectory tolerance of TPM robot detailed development of right limb............... 118
Table 4-1 Coordinates of points belong to experimental controlled trajectory ...................... 123
Table 4-2 Interface of declaration of IKP of parallel Scara robot .......................................... 124
Table 4-3 IKP results of parallel Scara robot ........................................................................ 125
Table 4-4 FKP results of parallel Scara robot ....................................................................... 127
Table 4-5 The error of controlled trajectory of parallel Scara robot ..................................... 128
Table 4-6 The value of intermediate velocity at the displacement point of variable 1 ....... 133
Table 4-7 The model of each segment of the variable 1 joint space (state variable t) ........ 134
Table 4-8 The model of each segment of variable 1 in the joint space (actual time variable )
......................................................................................................................................... 135
Table 4-9 The value of intermediate velocity at the displacement points of variable  2 ..... 141
Table 4-10 The model of each segment of variable  2 in joint space (state variable t)......... 142
Table 4-11 The model of each segment of variable  2 in the joint space (actual time
variable)…. ...................................................................................................... ………..143
Table 4-12 The results of kinematic problems of parallel scara robot in AutoCAD ............. 149
Table 4-13 Comparision results of kinematic problems of parallel scara robot in AutoCAD with
in novel method ............................................................................................................... 150

Table 4-14 Comparision of the results of displacement control of novel method and Adams
software ........................................................................................................................... 153
Table 4-15 Error of displacement control of novel method and Adams software ................. 153
Table 4-16 Average experimental values and errors of controlled trajectory........................ 171
Table 4-17 Average experimental value and error of angles 1 &  2 ................................... 172
Table 4-18 Average experimental value and error of angles 1 & 2 ................................... 173
Table 4-19 The average experimental value and error of translational joint in the original
configuration L1 & L2 ....................................................................................................... 174
Table 4-20 The degree of accuracy of the formula of variable change ................................. 175
Table 5-1 Kinematic parameters of robot Fanuc S900W ...................................................... 208
Table 5-2 Extracted results of measured tolerances of built-up links in robot Fanuc S900W

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......................................................................................................................................... 209
Table 5-3 The results of dimension tolerances in built-up links of robot Fanuc S900W ...... 210
Table 5-4 Extracted results of measured tolerances in built-up links of 3RRR parallel robot ....
......................................................................................................................................... 211
Table 5-5 The tolerance results of built-up link dimensions of 3RRR parallel robot ........... 213

XVIII


Chapter 1 Introduction

Chapter 1 Introduction
1.1 Methods for information initialization of robot
How to have a machine with the skills of human which can replace human to do whatever
they want, it is a legitimate demand that attract many scientists. Today, the machine is becoming

more compact and smart because its function is not only determined by the hardware but also
mainly by the software. The software itself has many different levels from the lowest which is
merely a hard command sequence to implement to advanced software which is more popular in
the industry today expressed, it forms different layer of control according to situations. Despite
the origin of the software level, the nature of information given in appropriate time or more
detailed is the result of the survey describing a control lever system. The root of the lower level
software no matter what nature is giving information to the appropriate time, or it is more
detailed results from the survey give a model to describe the control system.
This study only discusses about the robot, which is a special product of the mechatronics,
and also talk about how to build or initiate information to control it, more specifically, the
kinematic information, data ensuring the accuracy of the controlling process according to a
predetermined trajectory.
At current levels, the robot inputs often initialized according to the method as follow:
-

Manual programming (code G);

-

From the limit switch or sample displacement (adjust gauge, contact…)

-

Programming by PC (APT or APT, or APT like);

-

Retrieved from another system via external links (CAD/CAM);

-

From artificial vision (Camera, sensor);

-

From auditory (voice)

-

From neurobiology (bioelectric impulses of the living body);

-

From sensors equipped on the robot (encoder + teach-in technique)

Each method has its own advantages and disadvantages:
-

Manual programming with G code is appropriated with simple program, easy to
implement and easy to learn, but not available for complex interpolation, especially the
curves, most commercial robot has straight or curve interpolation or a combination of
such objects only.

-

The information provided by the limit switch is only suitable for simple systems.

1