臺灣博碩士論文加值系統

可重構方塊機構(Reconfigurable cube mechanism)為一個由2x2x2個正方體組成的益智玩具，該機構可循環變化構形，以展示正方體上的組合圖畫。本研究首先探討可重構方塊機構之奇異構形，應用螺旋理論判認各操作狀態下之靜對構形(Stationary configuration)與不定構形(Uncertainty configuration)，並據此分析機構於每個狀態之可動度(Mobility)。接著，我們合成該可重構方塊機構之所有可行初始構形，驗證現有設計為具循環轉換特性之唯一可行構形。此外，本研究亦探討一與可重構方塊機構具相似重構特性與圖畫展示能力之可重構紙板機構(Reconfigurable panel mechanism)，提出可避免紙板干涉而又能達到可重構特性之新型可重構紙板機構設計。

Reconfigurable cube mechanism (RCM) is a puzzle toy made by 23 sub-cubes. The mechanism can transform its configuration cyclically, and it can demonstrate drawings on the surfaces of the sub-cubes with variable configurations. First, we discussed singular configurations of the RCM, identifying stationary configurations and uncertainty configurations by screw theory. We also analyzed the mobility at every operable stage. Next, we synthesized all feasible initial topological configurations of the RCM and verified that the existing RCM is the only feasible design which can transform its configuration cyclically. In addition, we also studied a reconfigurable panel mechanism (RPM), which is a variant of the RCM with different shape profile and possesses similar reconfigurability to the RCM. We also came up with a new RPM that can avoid interference of the links. It is expected that the outcome of this work can contribute to creative design of reconfigurable cube and/or panel mechanisms.

Chapter 1 Introduction 1
1.1 Introduction to RCM 1
1.2 Motivations and Objectives 4
1.3 Literature Review 5
1.3.1 RCM Review 5
1.3.2 Stationary Configuration and Uncertainty Configuration 5
1.3.3 Configuration Synthesis 6
1.3.4 Shape Profile Design 7
1.3.5 Origami Mechanisms 8
1.3 Thesis Organization 10
Chapter 2 Configuration Singularity Analysis of the RCM 12
2.1 Stationary Configuration and Uncertainty Configuration 12
2.2 Mobility 13
2.3 Stationary Configuration Analysis 15
2.4 Uncertainty Configuration Analysis 18
2.5 Summary and Discussions 21
Chapter 3 Configuration Synthesis for RCMs with 23 Sub-Cubes 22
3.1 Enumerating the Topological Configurations of RCM 22
3.1.1 Connecting Sequence for RCM 22
3.1.2 Enumerating All Possible Topological Configurations 25
3.2 Eliminating the Topological Configurations of RCM 26
3.2.1 Repeated joint rule 27
3.2.2 One co-axial joint pair rule 30
3.2.3 Configuration isomorphism detection 31
3.2.4 Inside joint rule 37
3.2.5 Cyclic reconfiguration verification 38
3.3 Summary and Discussions 44
Chapter 4 Shape Profile Design: From Reconfigurable Cube Mechanism to the Reconfigurable Panel Mechanism (RPM) 45
4.1 Introduction to RPM 45
4.2 Topological Configuration and Transforming 47
4.3 Configuration Characteristics 53
4.4 Drawings Revealing Analysis 55
4.5 Summary and Discussions 61
Chapter 5 Conclusions and Suggestions 62
5.1 Conclusions 62
5.2 Suggestions 63
REFERENCES 64

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