臺灣博碩士論文加值系統

3D 列印技術在近年來獲得了相當多的關注,其發展也更臻成熟。然而關於高自由度機械手臂和3D 列印技術互相結合的相關研究卻不多見。有鑒於此，在此論文中,我們結合了這兩個主題, 除了控制理論的探討以外,我們也延伸了運用機械手臂高自由度及其工作空間廣大的特性來呈現在非水平面的列印等以增加其應用層面的廣度及深度。
此篇論文主要分為兩部分。 在第一部分, 為了解決在3D列印時可能會遇到的關節極限或奇異點等問題,我們設計了三個勢場及使用核空間控制以防止在3D列印的過程中上述問題的發生。針對避開奇異點的處理,我們提出了一個簡單且能夠快速計算出操作性的方法,比起傳統的計算方式具有在高自由度機構上更好的擴展性。另外對於最小化位於末端執行器列印噴頭的角度誤差以避免噴頭翻轉過大,我們也提出了另一個勢場函數的設計,使得僅以雅可比位置矩陣即可達到旋轉角度的控制。在第二部分,我們針對NTU六軸機械手臂設計了縮小版本的haptic device, 使得在以機械手臂進行3D列印的過程中使用者的直接參與變得可行。在此haptic device的協助下,可以呈現出更多樣化的列印應用,其實驗結果將會在第五章進行呈現。
所提出的理論及機械手臂3D 列印系統，經模擬及實驗驗證，成效良好。

Though 3D printing has received great attention, only few researches carries out the topic of combining robotic manipulators and 3D printing. This thesis, we integrate the robot with 3D printing. The proposed system utilizes the feature of high degrees of freedom and large workspace of a robot to extend the application level of 3D printing.
We divided into 2 parts. In the first part, for solving problems like joint limit avoidance and singularity avoidance, 3 potential fields have been constructed in null-space control. In addition, a faster and easier way of calculating manipulability for singularity avoidance has been developed. Another potential field designed for minimizing the orientation error of the extruder using only the Jacobian position matrix also has been illustrated and testified in the first part. In the second part of this thesis, a haptic device for human direct participation in 3D printing is designed. In assistance with such haptic device, versatile applications can be shown, more straightforward and easier human control during the 3D printing are justified.
The proposed robot 3D printing system and related theories have been justified and demonstrated through simulations and experiments. The results are promising.

Contents

致謝 iv
摘要 vi
Abstract viii
Contents x
List of Tables xii
List of Figures xiii
Nomenclature xvi
Chapter 1 Introduction to 3D Printing 1
1.1 Motivation 6
1.2 Contribution 8
1.3 Organization of Thesis 9
Chapter 2 Kinematic Analysis 11
2.1 Forward Kinematics 12
2.2 Inverse Kinematics 14
2.3 Jacobian Matrix 16
2.4 Euler Rotation and Quaternions 19
2.4.2 Gimbal Lock 22
2.4.3 Quaternion 23
Chapter 3 Null Space Control 25
3.1 Redundant Solution 25
3.1.1 Velocity-based Control 28
3.1.2 Acceleration-based Control 28
3.2 Joint Limit Avoidance 28
3.3 Singularity Avoidance 30
3.3.1 Singular Avoidance using Robot Manipulability 33
3.3.2 Calculation of Manipulability using SVD Method 35
3.3.3 A Novel SVD-based Method for Maximizing Manipulability 36
3.4 Orientation Representation Methods 39
3.4.1 Orientation Error Representation 41
3.4.2 Orientation Error Minimization 43
3.5 Multi-Priority using Null Space Control 45
3.5.1 Gradient Projection Method 48
Chapter 4 3D-Printing with Human Participation 51
4.1 Human Robot Interaction 51
4.2 Haptic Devices and Teleoperation 53
4.3 Design Concept 55
4.3.1 Mechanism 58
4.3.2 Hardware Connection 62
4.3.3 Software Connection 65
4.4 Trajectory Generation 68
4.4.1 Moving Average Filter 68
4.4.2 Trajectory Generation from Image Input 70
Chapter 5 Simulations and Experiments 75
5.1 Hardware Platform 75
5.1.1 NTU Robot Arm 75
5.1.2 Extruder and Heating System 78
5.1.3 Material Selection 80
5.2 Software Platform 80
5.2.1 NTU Robot Arm GUI 81
5.2.2 Pronterface GUI for Controlling Extruder 82
5.3 Simulation Results 83
5.3.1 Joint Limits Avoidance 83
5.3.2 Maximizing Manipulability 85
5.3.3 Reducing Orientation Error 87
5.4 Experiments 89
5.4.1 Basic Object Printing 89
5.4.2 Trajectory Generated by Robot Junior 92
5.4.3 Printing on Single Tilted Surface 95
5.4.4 Double Tilted Surface Printing 96
5.4.5 Trajectory Generation from Image Input 98
5.4.6 Large Scale Printing 103
5.4.7 Human Robot Cooperation - Post Manufacturing 104
5.4.8 Direct 3D printing using Robot Junior 109
5.5 Summary 111
Chapter 6 Conclusions and Future Works 113
6.1 Conclusions 113
6.2 Future Works 115
References 119

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