臺灣博碩士論文加值系統

靜平衡機構(static balancing mechanism)為一利用彈簧以平衡物件重量的機構，在日常生活中已被廣泛應用於支撐或取放(pick and place)，如監視器支撐架、手術燈等。對一個搬運的動作而言，能夠確保工件的安全是最基本的要求，而靜平衡機構的利用，即在於能夠使機器在工件搬運過程中的任何停駐位置均達成靜力平衡，亦可以使搬運的過程不需其他動力機械的輔助，而可靠地完成搬運工作，不須擔心物件掉落或因突然的震動而損壞。對於此類靜平衡機構之設計，可分為兩個部分，一為機構本身的構型，另一則為彈簧的使用，然而現今對於平衡機構之構型部分仍未有一套系統化的設計方法，乃停滯於四桿機構，使應用的範圍更受到限制。
為能提出一套完整之設計方法，本論文擬先利用原有之靜平衡機構，在限定彈簧之彈性係數為常數下找出基本之二桿靜平衡機構的構型特徵及彈簧參數化設計公式；藉由此構型特徵而由基本之二桿平衡機構找出構型之條件去推導單自由度四至六桿平衡機構之構型特徵，再以此特徵推得四桿及六桿之單自由度平衡機構之可行構型，最後根據彈簧設計公式設計得出之四、六桿構型之彈簧彈性係數，即可得到一個簡單的單自由度六桿彈簧平衡機構；最後，可將此單自由度之平衡機構視為一個單元，以兩種不同之方法－串連與並聯－予以合成，將各個單元結合起來，即可得到一多自由度之平衡機構，或可將原來平面中桿件的關係延伸至空間中面的關係，而合成為一空間中的多自由度機構。
因此，可利用本研究所提出之設計方法方便設計出一平衡機構，即可符合工作搬運的各項需求，如所需構型設計、可靠的搬運、、複雜的動作、簡單的動力設計等，亦可使設計的過程正確而快速。

The static balancing mechanism is a mechanism, which balances the weight of objects via springs. Such as supporting frames and surgical lights, SCM is broadly applied to support and pick-and-place objects. To ensure the safety of the objects in manufacture process, the static balancing mechanism can be balanced at arbitrary rest configuration and moves objects stably without aids of actuators.
The design of SCM can be separated into two sections, the configuration synthesis and the spring-design. Since there is no systematic procedure about the configuration synthesis, the configuration is always four-bar parallelogram mechanism.
A systematic design procedure for one-dof four- and six-link static balancing mechanisms is developed in this study. Structural characteristics for the two-link static balancing mechanism are investigated, from which general structural characteristics for up-to-six link static balancing mechanisms can be generated. According to these structural characteristics, an atlas of valid configurations for up-to-six link static balancing mechanisms is obtained. It will be shown that a static balancing mechanism can be synthesized by connecting multiple one-dof static balancing mechanisms to adapt to versatile design requirements. It is believed that the proposed approach provides better physical comprehension in the design process and is beneficial to extent the application of static balancing mechanisms.

CONTENTS
Chapter 1 Introduction 1
1.1 Background 1
1.2 Overview of related works 5
1.3 Motivation and preview 7
Chapter 2 Generalized Structural Characteristics 12
2.1 Introduction 12
2.2 Spring installation in two-link
static balancing mechanism 12
2.3 Admissible graphs for up-to-six link mechanisms 19
2.4 The properties of links 23
2.5 Summary 24
Chapter 3 Configuration Synthesis for Four-link Parallel Mechanism 26
3.1 Introduction 26
3.2 Configuration synthesis for
four-link parallel mechanism 26
3.3 Summary 30
Chapter 4 Configuration Synthesis for One-dof Six-link Parallel Mechanism 31
4.1 Introduction 31
4.2 General steps 31
4.3 Graph w-1 33
4.4 Graph w-2 41
4.5 Graph s-1 46
4.6 Graph s-2 52
4.7 Summary 55
Chapter 5 One-dof Six-link Static Balancing Mechanism 60
5.1 Introduction 60
5.2 Spring arrangement 60
5.3 Design example 63
5.4 Summary 66
Chapter 6 Multi-unit Static Balancing Mechanism 67
6.1 Introduction 67
6.2 Requirements 67
6.3 Serial connection 68
6.4 Parallel connection 71
6.5 Summary 74
Chapter 7 Conclusions and Future Works 76
7.1 Conclusions 76
7.2 Future works 78
Reference 79
Appendix A 81
Appendix B 82
Appendix C 84
Appendix D 87
Appendix E 90
List of Figures
Figure 1-1 A supporting arm 2
Figure 1-2 A surgical light 2
Figure 1-3 Anglepoised lamp 3
Figure 1-4 PGV 3
Figure 1-5 Basic model of a two-link
static balancing mechanism 5
Figure 2-1 A two-link pick-and-place mechanism 13
Figure 2-2 A two-link static balancing mechanism with only
a R-joint 15
Figure 2-3 A two-link static balancing mechanism with only
a P-joint 17
Figure 2-4 An up-to-six link static
balancing mechanism 20
Figure 2-5 A four-link kinematic chain 21
Figure 2-6 An admissible four-link graph 22
Figure 2-7 Six-link kinematic chains 22
Figure 2-8 Admissible six-link graphs 23
Figure 3-1 Schematic representation of admissible
four-link graph 27
Figure 3-2 Functional representation of four-link
parallel mechanism 30
Figure 4-1 Schematic representation of graph w-1 33
Figure 4-2 Schematic representation of graph w-1
for case (ii) 39
Figure 4-3 Schematic representation of graph w-2 42
Figure 4-4 Schematic representation of graph s-1 47
Figure 4-5 Schematic representation of graph s-1 with coincident joints 49
Figure 4-6 Schematic representation of graph s-2 52
Figure 5-1 One-dof six-link static balancing mechanism from graph w-1 64
Figure 5-2 One-dof six-link static balancing mechanism from graph s-2 65
Figure 6-1 An n-unit serial static balancing mechanism 68
Figure 6-2 An 2-unit serial static balancing mechanism 71
Figure 6-3 Topview of a p-unit parallel static balancing
mechanism 72
Figure 6-4 A 3-unit serial static balancing mechanism 74
(a) Frontview 74
(b) Topview 74
List of Tables
Table 1 Admissible configurations for graph w-1 40
(a) For case (i) 40
(b) For case (ii) 40
(c) For case (iii) 40
(d) For case (iv) 40
Table 2 Admissible configurations for graph w-2 46
(a) For case (i) 46
(b) For case (ii) 46
(c) For case (iii) 46
(d) For case (iv) 46
Table 3 Admissible configurations for graph w-1 57
(a) For case (i) 57
(b) For case (ii) 57
(c) For case (iii) 58
(d) For case (iv) 58

Bonora, A. C., Richardson, B. A., Brain, M. D., Cortez, E. J. and Huang, B. H., 1996, “Human Guided Mobil Loader Stocker,” US Patent, No. 5570990
Ebert-Uphoff, I., Gosselin, C. M. and Laliberte, T., 2000, “Static Balancing of Spatial Parallel Platform Mechanisms- Revisited,” Journal of Mechanical Design, Vol. 122, pp. 43-51.
Fisher, K. J., 1992, “Counterbalance Mechanism Positions a Light with Surgical Precision,” Mechanical Engineering, pp. 76-80.
French, M. J. and Widden, M. B., 2000, “The Spring-And-Lever Balancing Mechanism, George Carwardine and the Anglepoise lamp,” Proceedings of the Institution of Mechanical Engineers, Vol. 214, Part C, pp. 501-508.
Idlani, S., Streit, D. A., and Gilmore, B. J., 1993, “Elastic Potential Synthesis — A Generalized Procedure for Dynamic Synthesis of Machine and Mechanism Systems,” Journal Mechanical Design, Vol. 115, pp.568-575.
Nathan, R. H., 1985, “A Constant Force Generation Mechanism,” Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 107, pp. 508~512.
Rahman, T., Ramanathan, R., Seliktar, R. and Harwin, W., 1995, “A Simple Technique to Passively Gravity-Balance Articulated Mechanisms,” Journal Mechanical Design, Vol. 117, pp. 655-658.
Souder, Jr. J. J., Scarborough, Jr. E. D., Fox, M. D., Rettich, D. R. and Mason, R. L., 1984, “Spring Counterbalanced Support Arm System,” US Patent, No. 4447031.
Streit, D. A., 1989, “Perfect Spring Equilibrators for Rotatable Bodies,” Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 111, pp. 451~458.
Shin, E. and Streit, D. A., 1991, “Spring Equilibrator Theory for Static Balancing of Planar Pantograph Linkages,” Mech. & Mach. Theory, Vol. 26, No. 7, pp. 645-657.
Streit, D. A. and Shin, E., 1993, “Equilibrators for Planar Linkages,” Journal Mechanical Design, Vol. 115, pp. 604-611.
Soper, R. R., Mook, D. T. and Reinholtz, C. F., 1997, “Vibration of Nearly Perfect Spring Equilibrators,” in Proceedings of the 1997 ASME Design Engineering Technical Conference, number DAC-3768.
Wang, J. and Gosselin, C. M., 1998, “Static Balancing of Spatial Six-Degree-Of-Freedom Parallel Mechanisms with Revolute Actuators,” In Proceedings of the 1998 ASME Design Engineering Technical Conference, number DETC98/MECH-5961.