使用齒輪彈簧模組之機械臂操縱器重力補償設計與剛性分析

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研究生：	阮武陵 Nguyen Vu Linh
論文名稱：	使用齒輪彈簧模組之機械臂操縱器重力補償設計與剛性分析 Gravity Compensation Design and Stiffness Analysis of Robotic Manipulators Using Gear-Spring Modules
指導教授：	林其禹 Chyi-Yeu Lin 郭進星 Chin-Hsing Kuo
口試委員:	林其禹 Chyi-Yeu Lin 林柏廷 Po Ting Lin 郭進星 Chin-Hsing Kuo 藍兆傑 Chao-Chieh Lan 詹魁元 Kuei-Yuan Chan Térence Essomba Térence Essomba
學位類別：	博士 Doctor
系所名稱：	工程學院 - 機械工程系 Department of Mechanical Engineering
論文出版年：	2020
畢業學年度：	108
語文別：	英文
論文頁數：	178
中文關鍵詞：	重力補償、靜平衡、齒輪滑塊機構、機器人、剛性分析、性能指標、人機互動
外文關鍵詞：	Gravity compensation, Static balancing, Gear-slider mechanism, Robotic manipulator, Stiffness analysis, Performance index, Physical human-robot interaction
相關次數：	點閱：212 下載：5
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工業機械臂操控器（簡稱「機械手臂」）一般皆需消耗大量能源以承載自身重量與負載，重力補償（Gravity compensation）使用機械能源元件（例如彈簧與配重）消除機械手臂之重力效應，藉以減少機械手臂的驅動能源並提高機械手臂之運動準確度、安全性與工作性能。本論文提出一種新型的重力補償設計，該設計由一個五桿齒輪滑塊機構與一個壓縮彈簧組成，此機構具一個運動自由度，且可模組化與機械手臂之旋轉接頭搭配，因此於本論文中稱為「齒輪彈簧模組」（Gear-spring module, GSM）。此齒輪彈簧模組設計具有構造緊湊、安裝簡單、易於模組化、與具良好之重力補償性能等特點。
本論文首先介紹使用齒輪彈簧模組於串聯式機械手臂重力補償之設計。在給定齒輪滑塊機構尺寸下，壓縮彈簧的剛性係數可藉由最佳化重力補償性能或簡化理論模型之解析法求得。本論文並提供數個1至3個自由度的串聯式手臂來闡述設計概念，且分析其重力補償設計性能。本研究亦建構了一個具齒輪彈簧模組的單自由度機械手臂與實驗，實驗結果顯示該手臂在齒輪彈簧模組協助下，其驅動力矩功率可降低86.5%。
基於在串聯式機械手臂的成功嘗試下，本論文進一步將齒輪彈簧模組應用至並聯式機械手臂的重力補償設計，以著名之Delta並聯機器人（Delta parallel robot）為設計範例。論文中提供了一個Delta並聯機器人的理論設計模型與一個工業實際模型（FANUC M-3iA/12H），說明齒輪彈簧模組於該模型下的設計方式與性能。再者，本研究並比較本設計與其他常見的扭力彈簧與張力彈簧的重力補償性能差異。研究結果顯示，本設計雖結構精簡，但仍能在不影響機械手臂運動空間的情形下提供理想的重力補償功能。
另一方面，本研究也提出了具彈簧元件機械手臂在重力與任意方向負載作用下的剛性（Stiffness）分析方法。此方法使用一順從性（Compliance）模型描述剛性、定位誤差、與準確度在靜態撓曲（Static deflection）下的關係，分析範例包含具單自由度與雙自由度的串聯型機械手臂、以及具齒輪彈簧模組的串聯型機械手臂與Delta並聯型機器人。與其他現有理論相較，本方法探討鉸接於接地端與遠端連桿的多重彈簧效應，而其他可用方法僅考慮接地端連桿的彈簧效應。
綜之，本論文提供了一種緊湊而有效的機械手臂重力補償設計和一種彈簧鉸接機械手臂的剛性分析方法。這些創新的發現將有助於具彈性元件鉸接的機構與機器人的設計與分析，本論文成果期有助發展節能與高效率之機械手臂。

Industrial robotic manipulators in general spend significant energy on carrying the weights of themselves and their payloads. Gravity compensation is one popular strategy that employs mechanical energy elements, e.g., springs and counterweights, to eliminate the gravitational effect on robotic manipulators, which leads to reducing the actuation energy and improving the accuracy, safety, and robot performance. In this thesis, a novel gravity compensation design based on a five-bar gear-slider mechanism with a compression spring is presented. The one-degree-of-freedom (1-DOF) design can be modulized for installing on each rotational joint of the robot arm, so it is called a “gear-spring module (GSM)” in this thesis. The proposed GSM-based design is characterized by structure compactness, less assemblage effort, ease of modularization, and high performance of gravity compensation.
The thesis firstly introduces the design of multi-DOF serial manipulators for gravity compensation using a series of GSMs. Based on a predefined geometrical dimension of the geared five-bar, the stiffness coefficient of the compression spring in the GSM is determined through either a design optimization or an analytical approximation to perfect balancing. Several 1-, 2-, and 3-DOF GSM-based robot arms are adopted for illustrating the design concept and design performance. An experimental study on a single-DOF GSM-based robot arm was performed, which shows that a power reduction rate of 86.5% is attained when the GSM is installed on the robot arm.
Based on the success of the GSM used on serial-type manipulators, the thesis further applies this balancing module for gravity compensation of parallel manipulators, particularly for the renowned Delta parallel robots. Design examples are implemented through a theoretical model and a real industrial Delta robot, the FANUC M-3iA/12H. Then, a comparative study between the uses of the gear-spring modules, torsion springs, and tension springs for gravity compensation is provided. As a result, the proposed GSM design suggests a compact mechanical solution for gravity compensation of the Delta robots without a compromise of the compensation performance and the robot workspace.
This research also puts forward a general method for the stiffness analysis of spring-articulated robotic manipulators under gravity and arbitrary load. In this method, a stiffness model of such spring-articulated manipulators is established for relating the positioning errors and accuracy of the manipulator in static deflection. The method is then applied to analyze the stiffness of several 1- and 2-DOF spring-articulated planar serial manipulator as well as the GSM-based serial manipulators and Delta parallel robots. The major significance of the proposed method is that it considers multiple springs attached to the robot’s proximal and distal links, while other available methods only take the spring effect on the proximal links into account.
In summary, this thesis shows a compact and effective gravity compensation design for robotic manipulators and an analytical stiffness method for spring-articulated robotic manipulators. These novel findings directly contribute to the design and analysis of mechanisms and robots with inherent compliance for gravity compensation. It is anticipated that the thesis outcomes are contributive to the development of energy-efficient and high-performance robotic manipulators.

摘要    I
ABSTRACT    III
ACKNOWLEDGMENT    V
TABLE OF CONTENTS    VI
LIST OF FIGURES    IX
LIST OF TABLES    XIV
Chapter 1.    Introduction    1
1.    Motivation    1
2.    Objectives    3
3.    State of the Art    4
3.1.    Gravity compensation of serial robotic manipulators    4
3.2.    Gravity compensation of parallel robotic manipulators    7
3.3.    Stiffness analysis of robotic manipulators    10
4.    Problem Statement    12
4.1.    Gravity compensation design    13
4.2.    Stiffness analysis method    14
5.    Organization and Contributions    15
5.1.    Organization    15
5.2.    Contributions    16
Chapter 2.    Fundamentals    18
1.    Design for Gravity Compensation    18
1.1.    A single-DOF rotating link    19
1.2.    A 2-DOF articulated robotic manipulator    22
1.3.    Multi-DOF articulated robotic manipulators    27
1.4.    Spring characteristics    29
2.    Method for Stiffness Analysis    30
Chapter 3.    A Gear-Spring Module for Gravity Compensation    34
1.    The Design Concept    34
2.    Design Approaches    35
2.1.    An optimization-based torque minimization    36
2.2.    An analytical approximation to perfect balancing    38
3.    Gear Friction Effect    40
3.1.    Power loss    40
3.2.    Spring stiffness correction    41
3.3.    Power reduction rates    42
4.    Design Examples    43
4.1.    Performance of gravity compensation    43
4.2.    Gear power loss    45
5.    Experimental Verification    47
5.1.    Passive test: Manual operation    49
5.2.    Active test: Motor actuation    50
6.    Chapter Conclusion    53
Chapter 4.    Gravity Compensation Design of Serial and Quasi-Serial Robotic Manipulators    54
1.    Design for Serial Robotic Manipulators    54
2.    Design for Quasi-Serial Robotic Manipulators    57
3.    Performance Evaluation    62
3.1.    A 2-DOF serial robotic manipulator    62
3.2.    A 3-DOF serial robotic manipulator    65
3.3.    A 2-DOF quasi-serial robotic manipulator    68
3.4.    Summary of the results    69
4.    Chapter Conclusion    70
Chapter 5.    Gravity Compensation Design of Delta Parallel Robots    72
1.    The Design Concept    72
1.1.    Description of the robot structure    72
1.2.    Geometry of the gear-spring modules (GSMs)    74
2.    Design Formulation    75
2.1.    The gravitational torques imposed on the actuation joints    75
2.2.    The balancing-spring torques    78
2.3.    The spring stiffness and installation angles    79
3.    Performance Indices    82
3.1.    Torque reduction rates (TRRs)    82
3.2.    Gravity compensation density (GCD)    83
3.3.    Energy reduction rate (ERR)    83
4.    Design Examples    84
4.1.    Example I: Delta robot with prescribed parameters    85
4.2.    Example II: FANUC M-3iA/12H Delta robot    89
5.    Discussion: Uses of torsion and tension springs    97
5.1.    Designs with torsion and ZFL-tension springs    98
5.2.    Performance comparison    99
6.    Chapter Conclusion    102
Chapter 6.    Stiffness Analysis of Spring-Articulated Robotic Manipulators    103
1.    Analytical Stiffness Method    103
1.1.    Planar serial (or quasi-serial) articulated manipulators    104
1.2.    The Delta parallel robotic manipulator    109
2.    Criteria for Performance Evaluation    110
2.1.    Positioning errors    110
2.2.    Compliant uniformity index (CUI)    114
2.3.    Accuracy measure of static deflection (AMSD)    117
3.    Illustrative Examples    118
3.1.    A 1-DOF spring-articulated planar serial manipulator    118
3.2.    A 2-DOF spring-articulated planar serial manipulator    121
3.3.    A 2-DOF spring-articulated planar quasi-serial manipulator    125
3.4.    A 2-DOF planar serial manipulator with GSMs    130
3.5.    A 3-DOF Delta parallel robot with GSMs    132
4.    Chapter Discussion and Conclusion    136
4.1.    Discussion    136
4.2.    Conclusion    138
Chapter 7.    Conclusion and Perspective    139
1.    Conclusion    139
2.    Perspective    140
2.1.    The significance of the thesis    140
2.2.    Future works and challenges    142
Bibliography    147
Appendix. Publications From The Thesis    158

                                

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