Structural Synthesis of Non-fractionated and Fractionated Kinematic Chains Classified According to Their Contracted Graphs and Applications to Articulated Manipulators
축약그래프로 분류되는 비분절 및 분절 기구의 형태합성과 수직 다관절 로봇에 대한 응용
- 주제(키워드) Structural Synthesis , Non-fractionated Kinematic Chain , Fractionated Kinematic Chain , Graph Theory , Contracted Graph , Articulated Manipulator
- 발행기관 고려대학교 대학원
- 지도교수 심재경
- 발행년도 2022
- 학위수여년월 2022. 2
- 학위구분 박사
- 학과 대학원 기계공학과
- 원문페이지 168 p
- UCI I804:11009-000000257248
- DOI 10.23186/korea.000000257248.11009.0001250
- 본문언어 영어
초록/요약
새로운 기계를 개발함에 있어서, 기구학적 구조가 그 기계의 기구학적 그리고 동역학적 특성에 영향을 주기 때문에, 컨셉 설계 단계에서 다양한 기구 후보를 열거하는 것이 중요하다. 또한, 축약그래프로 분류된 기구 후보지는 기계 설계의 유용한 도구로 활용될 수 있고, 기구의 동형을 판별하는데 유용하다. 이 논문은 축약그래프로 분류되는 1~3자유도 비분절 기구와 2~3자유도 분절 기구의 모든 그래프를 중복 없이 생성하기 위한 방법을 제안한다. 1~3자유도 비분절 기구의 그래프는 최대 3개의 독립 루프 수까지, 2~3자유도 분절 기구의 그래프는 최대 4개의 독립 루프 수까지 열거되고, 생성된 그래프 수는 기존 연구의 결과와 일치함이 확인된다. 또한, 본 논문은 수직 다관절 로봇의 그래프를 체계적으로 열거하는 방법을 제안한다; 일반적으로 수직 다관절 로봇은 고정 베이스, 엔드 이펙터, 그리고 그 둘을 연결하는 중간 기구로 구성된다. 먼저, 기존 수직 다관절 로봇의 구조를 분석하여 해당 로봇이 적절한 자유도를 갖기 위한 기구학적 조건을 판별한다. 그리고, 그래프의 대칭성 개념을 기반으로 그래프를 중복 없이 생성하는 방법을 제안하고, 생성된 그래프의 수를 계산하는 공식을 유도한다. 그 결과, 2자유도 비분절 중간 기구를 갖는 969개의 그래프와 2자유도 분절 중간 기구를 갖는 1,919개의 그래프가 생성된다. 그리고 그 결과에 실제 산업에서 활용되는 수직 다관절 로봇이 포함되어 있는 것이 확인된다. 마지막으로, 축약그래프와 일반그래프의 정보를 기반으로 팔레타이징 로봇을 컨셉 설계하는 방법과 그 알고리즘 선도가 제안된다. 결과적으로, 앞서 생성한 축약그래프로 분류된 수직 다관절 로봇의 그래프를 활용하여 팔레타이징 작업을 위한 개념 설계 로봇이 제시된다.
more초록/요약
When developing a new machine, it is important to enumerate various candidates of kinematic structures in the conceptual design phase because the kinematic structure influences the machine's kinematic and dynamic characteristics. Furthermore, an atlas of kinematic chains classified according to the corresponding contracted graphs provides a handy tool for the design of machinery and identification of isomorphic structures. This paper proposes an isomorphism-free method to generate the entire graphs of planar one- to three-degree-of-freedom (DOF) non-fractionated kinematic chains and two- to three-DOF fractionated kinematic chains (FKCs) classified by the contracted graphs. The entire graphs of one- to three-DOF planar non-FKCs with up to 3 independent loops and graphs of two- to three-DOF planar FKCs with up to 4 independent loops which are sorted by the contracted graphs are enumerated, and it is confirmed that the numbers of generated graphs conform to previous research. In addition, this paper proposes a method for systematically enumerating the graphs of articulated manipulators. An articulated manipulator consists of a fixed base, an end-effector, and an intermediate KC that connects the two. By analyzing the structure of existing manipulators, the kinematic conditions for an articulated manipulator to have an appropriate DOF are identified. Then, based on the concepts of symmetry of a graph, graph generation methods without isomorphism are proposed, and the number of generated graphs is determined. As a result, 969 graphs of articulated manipulators having two-DOF non-fractionated intermediate KCs and 1,919 graphs having two-DOF fractionated intermediate KCs are generated. In addition, it is confirmed that the results include practical articulated manipulators that are used in general. Finally, a concept design method for palletizing robots and its algorithm flowchart is proposed based on the information of contracted and conventional graphs. As a result, conceptually designed robots for the palletizing task are presented using the enumerated conventional graphs of articulated manipulators classified by the contracted graphs.
more목차
ABSTRACT ⅰ
CONTENTS v
LIST OF FIGURES x
LIST OF TABLES xiii
1. INTRODUCTION 1
1.1 Research Background 1
1.2 Research Purpose 5
1.3 Thesis Overview 6
2. THEORETICAL BACKGROUND 7
2.1 Kinematic Chains and Mechanisms 8
2.2 Kinematics of Mechanisms 8
2.2.1 Kinematic Analysis 8
2.2.2 Kinematic Synthesis 9
2.2.2.1 Type Synthesis 9
2.2.2.2 Number Synthesis 9
2.2.2.3 Dimensional Synthesis 9
2.3 Structural Representations of Mechanisms or Kinematic Chains 10
2.3.1 Structural Representation 10
2.3.2 Graph Representation 11
2.3.3 Matrix Representation: Adjacency Matrix 13
2.4 Classification of Kinematic Chains or Graphs 14
2.4.1 Closed-, Open-, and Hybrid Kinematic Chains 14
2.4.2 Non-fractionated and Fractionated Kinematic or Graphs 14
2.4.3 Conventional Graphs and Contracted Graphs 16
2.4.3.1 Definition of Contracted Graph and its Expression 16
2.4.3.2 Advantages of Classifying Conventional Graphs by Contracted graphs 19
3. A Method for Generating Non-fractionated Graphs Classified According to Contracted Graphs 21
3.1 A Method for Generating Non-fractionated Graphs Classified by Contracted Graphs 21
3.1.1 Determination of the Number of Links and Joints in Kinematic Chains having Specific Degrees of Freedom 21
3.1.2 Lower and Upper Bounds of Degree of Vertex 22
3.1.3 Link Assortment 23
3.1.4 Enumeration of Contracted Graph 24
3.1.5 Partition of Binary Link Chains 28
3.1.6 Enumeration of Conventional Graphs 29
3.2 Enumeration of 1- to 3-DOF Graphs Classified by Contracted Graphs 31
3.2.1 Determination of the Number of Links and Joints in Kinematic Chains Having 3 DOFs 31
3.2.2 Link Assortment 31
3.2.3 Enumeration of Contracted Graph 32
3.2.4 Partition of Binary Link Chains 34
3.2.5 Enumeration of Conventional Graphs 36
3.2.6 Synthesis Results 39
4. A Method for Generating 2-DOF Fractionated Graphs Classified According to Contracted Graphs 40
4.1 Number Synthesis of 2-DOF Fractionated Kinematic Chains 40
4.2 Combining Method of Two Non-fractionated Graphs to Generate Non-isomorphic FKCs Having Identical Contracted Graphs 42
4.2.1 Concepts and Notations in Graphs 42
4.2.1.1 Vertex-symmetry or Vertex-asymmetry Sets 44
4.2.1.2 Edge-symmetry or Edge-asymmetry Sets 46
4.2.1.3 Vertex-edge-asymmetry Sets 47
4.2.2 Notations in Conventional Graphs Expanded From a Contracted Graph 49
4.2.3 Condition for Different Fractionated Graphs to Have the Same Contracted Graph 50
4.2.4 Connecting Rules for Generating All Fractionated Graphs Having the Same Contracted Graphs 52
4.2.4.1 Connecting Two Non-fractionated Graphs Expanded From an Identical Contracted Graph 54
4.2.4.2 Connecting Two Non-fractionated Graphs Expanded From Different Contracted Graphs 59
4.3 Procedure for Generating the Whole Family of 2-DOF Fractionated Kinematic Chains Classified According to the Contracted Graphs 63
4.4 Synthesis Results 69
5. A Method for Generating 3-DOF Fractionated Graphs Classified According to Contracted Graphs 75
5.1 Number Synthesis of 3-DOF Fractionated Kinematic Chains 75
5.1.1 One Fractionated Link 75
5.1.2 One Fractionated Joint 76
5.1.3 Two Fractionated Links or One Multiple Fractionated Link 78
5.2 Combining Method of Non-fractionated Graphs to Generate 3-DOF Non-isomorphic FKCs Having Identical Contracted Graphs 79
5.2.1 Connecting Methods for One Fractionated Vertex 79
5.2.1.1 Two Non-fractionated Graphs from an identical Contracted Graph 79
5.2.1.2 Two Non-fractionated Graphs from Two Different Contracted Graphs 82
5.2.1.3 Three Non-fractionated Graphs from an identical Contracted Graph 83
5.2.1.4 Three Non-fractionated Graphs from Two Identical Contracted Graphs and a Different Third One 88
5.2.1.5 Three Non-fractionated Graphs from Three Different Contracted Graphs 90
5.2.2 Concepts of Pairs 92
5.2.2.1 Symmetrical or Asymmetrical Pair Sets 92
5.2.2.2 Symmetrical or Asymmetrical Pair Sets of Contracted Graphs 94
5.2.2.3 Notations of Pairs in Conventional Graphs Expanded from a Contracted Graph 94
5.2.3 Connecting Methods for Two Different Fractionated Vertices 97
5.2.3.1 Two Side Graphs from an Identical Contracted Graph 97
5.2.3.1.1 A Symmetrical Pair of a Contracted Graph 97
5.2.3.1.2 An Asymmetrical Pair of a Contracted Graph 101
5.2.3.2 Two Side Graphs from Different Contracted Graphs 102
5.2.3.2.1 A Symmetrical Pair of a Contracted Graph 102
5.2.3.2.2 An Asymmetrical Pair of a Contracted Graph 104
5.3 Synthesis Results 107
6. A Method for Generating Articulated Manipulator Graphs Classified According to Contracted Graphs and Its Application on the Conceptual Design of Palletizing Robots 109
6.1 Articulated Manipulator 109
6.1.1 Basic Concepts of Articulated Manipulators 110
6.1.2 Analysis of the Kinematic Structures of Articulated Manipulators 112
6.2 A Method for Generating Articulated Manipulator Graphs Classified According to Contracted Graphs 113
6.2.1 Number Synthesis of Articulated Manipulator Mechanisms 113
6.2.2 A Procedure for Generating Articulated Manipulator Graphs Classified According to Contracted Graphs 114
6.2.3 Synthesis Results 122
6.2.3.1 Using 2-DOF Non-Fractionated Intermediate Graphs 122
6.2.3.2 Using 2-DOF Fractionated Intermediate Graphs 126
6.3 Determination of the Conceptual Design Direction of the Palletizing Robot Based on Graph Information 130
6.3.1 Determination of an End-effector Type 131
6.3.2 Determination of Actuator Mountable Joints 133
6.3.3 Integrated Algorithm Flow Chart to Determine the Palletizing Robot Type 136
6.3.4 Examples of conceptual design of palletizing robots 137
7. CONCLUSIONS 141
REFERENCES 144
CURRICULUM VITAE 148
ACKNOWLEDGEMENT 150
