本文系統的分析拓樸最佳化的相關技術及應用拓樸最佳化技術於順從機構設計。對於順從機構的拓樸狀態出現類接頭的不合理結構形態，從虛似剛體模型法的等效撓性接頭設計方向切入，以撓性接頭力學分析為基礎，研究此方法，發展順從機構的多目標最佳化數學模型，得到更佳的輸入位移與輸出位移增益比效果。接著本文再提出應用拓樸最佳化的結果為初始形態，發展撓性接頭多目標最佳化設計，整合成有效的順從機構設計方法，合理的將拓樸類接頭形態設計成明確而機械型撓性接頭，結果得知，結合拓樸最佳化及撓性接頭順從機構設計的方法優於傳統虛似剛體設計方法。經由比較後發現，類接頭拓樸形態中心位置實為本文之機械型撓性接頭對稱圓孔連心線中心位置。因此，本文提出簡化類接頭之再設計改善策略，發展簡化的撓性接頭最佳化。同時應用此簡化設計策略於本文發展的力致動與熱變形微機電順從機構上。本文提出的最佳化設計方法論，也成功地應用至不同的微機電順從機構元件設計。

A systematic analysis and study concerning the techniques of the topological optimization applying to compliant mechanisms synthesis are presented in this thesis. During the structural topology optimization, a singular hinge-like appears and then requires to be eliminated or be further modified. A pseudo-rigid-body model had been studied at first, then the typical flexural hinge analysis had been applied and transformed to a multiobjective optimization design model for improving the characteristics of flexural joints. The presented optimization process can obtain superior results than the conventional multi-stage optimization, particularly, the ratio of output motion to input motion on a compliant mechanism has been improved. This study adopts the outcome of the topological optimization as the initial model, then combines the proposed multiobjective optimization strategy for eliminating the unrealistic hinge-like phenomenon. This post-design process not only can deal with flexures but also can dramatically increase the overall performance of the compliant structure. It can be concluded that the geometrical center of a typical flexure exactly is the center of a hinge-like location that was observed and experimented from topology optimization. Eventually, this work continuously proposed a simplifying design model to redesign the flexures for promoting the overall performance. The proposed design method and process had been applied to several micro electro-mechanical structural design included a thermal-actuated amplifying compliant mechanism.

目錄	 
中文摘要                                       	Ⅰ
英文摘要                                          	II
目錄                                               	III
圖目錄                                              	Ⅴ
表目錄                                            	Ⅸ
符號說明                                         	Ⅹ
第一章 緒論                                         	1
1-1 研究動機與目的                                 	1
1-2 文獻回顧                                      	3
1-3 本文架構                                      	11
第二章 順從機構的拓樸最佳化設計           	         13
	2-1 順從機構與拓樸最佳化原理         	13
	2-2 拓樸機構最佳化的數值方法         	18
	2-2-1 結構有限元分析             	         18
	2-2-2 最佳近似方法 	                  24
	2-2-3 一階靈敏度解析方法        	         26
	2-2-4 棋盤現象與處理                       	28
	2-2-5 設計例題                             	35
	2-3 平面角致動順從機構拓樸最佳化設計 	48
	2-4 類接頭現象與處理                     	61
	2-5 結語                 	                  66
第三章 撓性接頭分析與最佳化設計                	67
	3-1 順從機構的學理分析與設計程序     	67
	3-1-1 撓性接頭力學分析                	67
	3-1-2 順從機構的設計程序              	72
	3-2 含撓性接頭順從機構的最佳設計        	83
	3-3 拓樸設計後類接頭改善設計         	99
	3-4 類接頭的簡化改善設計                	114
	3-5 結語                                   	121
第四章 微機電順從機構的最佳化設計              	122
	4-1 順從機構於微機電系統中的應用       	122
	4-2 微動平台的形變放大器的順從機構最佳設計	126
	4-3 力致動型微夾持器的順從機構最佳設計	135
	4-4 熱變形微夾持器的順從機構最佳設計 	143
	4-4-1熱變形微夾持器的拓樸最佳設計    	145
	4-4-2撓性接頭的簡化最佳化設計        	141
第五章 結論                                   	156
參考文獻	159
附錄 A  平面結構拓樸最佳化設計程式使用手冊    	165
附錄 B  撓性接頭簡化最佳化設計的ANSYS使用說明  	169
 
圖目錄
圖1-1  配置型元素拓樸結構成形示意圖            	5
圖1-2  連續型元素拓樸結構成形示意圖           	5
圖2-1  一般拓樸結構最佳設計模型示意圖         	15
圖2-2  懸臂結構自由端節點橫方向位移的軟體解比對	22
圖2-3  懸臂結構自由端節點縱方向位移的軟體解比對	22
圖2-4  拓樸設計用的懸臂樑幾何尺寸及受力圖     	29
圖2-5  類棋盤的拓樸結構形態圖                 	31
圖2-6  消除類棋盤現象的拓樸結構形態圖         	31
圖2-7  拓樸形態的分割與分析示意圖             	32
圖2-8  微夾持器拓樸設計領域，幾何尺寸及邊界圖  	37
圖2-9  微夾持器拓樸設計的對稱領域，幾何尺寸及邊界圖	37
圖2-10 微夾持器對稱領域的拓樸最佳化圖         	38
圖2-11 微夾持器的拓樸最佳化設計圖             	38
圖2-12 縮小微夾持器拓樸設計領域，幾何尺寸及邊界圖	40
圖2-13 縮小微夾持器拓樸設計的對稱領域，幾何尺寸及邊界圖40
圖2-14 縮小微夾持器對稱領域的拓樸最佳化圖     	41
圖2-15 縮小微夾持器的拓樸最佳化設計圖         	41
圖2-16 熱變形微致動器拓樸設計領域，幾何尺寸及邊界	43
圖2-17 熱變形微致動器拓樸設計的對稱領域，幾何尺寸及邊界43
圖2-18 熱變形微致動器對稱領域的拓樸最佳化圖   	44
圖2-19 熱變形微致動器的拓樸最佳化設計圖       	44
圖2-20 熱變形微致動器的拓樸結構形態與文獻[47]比較	46
圖2-21 熱變形微致動器的拓樸結構形態與文獻[48]比較	46
圖2-22 熱致動微順從致動器照片圖[48]           	47
圖2-23 平面S型角致動順從機構的微照片圖[49]     	49
圖2-24 平面S型角致動順從度機構示意圖          	50
圖2-25 平面S型機構旋轉平台的作動示意圖        	52
圖2-26 平面S型順從機構的連桿作動模型          	52
圖2-27 平面角致動順從機構的拓樸設計領域及幾何尺寸	54
圖2-28 平面角致動順從機構的拓樸設計形態圖      	54
圖2-29 光調變旋轉機構組合設計圖               	55
圖2-30平面角致動器順從機構的結果設計圖        	56
圖2-31 光調變旋轉機構的修整設計圖             	57
圖2-32 光調變旋轉機構的有限元位移分析圖       	58
圖2-33 光調變旋轉機構的有限元應力分析圖       	59
圖2-34 熱變形微致動器的拓樸形態類接頭標示圖   	62
圖2-35 三種類接頭形態放大圖                            62
圖2-36 小波修整類接頭形態舉例[31]               	64
圖2-37 複合過濾器修整類接頭形態舉例[32]        	64
圖3-1  等效四連桿順從機構示意圖[20]           	68
圖3-2  凹型撓性接頭幾何圖                         	68
圖3-3  凹型撓性接頭的圓弧部份的幾何圖         	70
圖3-4  凹型撓性接頭的等效虛似剛體模型         	74
圖3-5  微夾持器的連桿機構圖                   	74
圖3-6  微夾持器的虛似剛體模型                        	75
圖3-7  凹型撓性接頭的等效虛似剛體修正模型            	75
圖3-8  微夾持器的虛似剛體修正模型                    	76
圖3-9  微夾持器的虛似剛體更正模型                   	77
圖3-10 微夾持器的原設計結果圖[46]                  	79
圖3-11 微夾持器的原設計模型幾何關係圖           	80
圖3-12 微夾持器的設計模型幾何關係圖                	81
圖3-13 本文的微夾持器初始設計幾何關係圖         	84
圖3-14 兩個設計目標的設計解與理想解                	88
圖3-15 微夾持器設計完成圖                           	92
圖3-16 最佳化設計後的微夾持器有限元分析模型      	94
圖3-17 最佳化設計後的微夾持器有限元位移分析圖 	95
圖3-18 最佳化設計後的微夾持器有限元應力分析圖 	96
圖3-19 微夾持器多目標最佳化設計幾何關係圖     	101
圖3-20 微夾持器多目標最佳化設計變數圖         	103
圖3-21 微夾持器的目標結果設計圖               	108
圖3-22 微夾持器多目標最佳化設計有限元分析模型  	109
圖3-23 微夾持器多目標最佳化設計有限元位移分析圖	110
圖3-24 微夾持器多目標最佳化設計有限元應力分析圖	111
圖3-25 最佳化設計的微夾持器撓性接頭分析圖     	115
圖3-26 拓樸最佳化設計的微夾持器尺寸分析圖     	116
圖3-27 單點連接拓樸形態與區域坐標示意圖        	119
圖3-28 矩形結構與凹型接頭示意                      	119
圖4-1  短衝程微致動器機構[58]                     	123
圖4-2  短衝程微致動器之應用[58]                      	123
圖4-3  以壓電致動器為源輔以順從機構的微動平台[59]	124
圖4-4  電熱致動的夾持器順從機構的作動照片圖[62]	125
圖4-5  形變式微動平台的原設計示意圖[63]           	128
圖4-6  微動平台的形變放大器順從機構[63]       	128
圖4-7  形變放大器的拓樸設計領域，幾何尺寸及邊界圖	129
圖4-8  形變放大器的拓樸最佳化設計結果圖        	129
圖4-9  形變放大器的拓樸結果修整設計圖            	131
圖4-10 拓樸最佳化後的微動平台有限元分析模型     	132
圖4-11 拓樸最佳化後的微動平台有限元位移分析圖 	133
圖4-12 拓樸最佳化後的微動平台有限元應力分析圖 	134
圖4-13 微夾持器拓樸設計及撓性接頭簡化最佳化初始圖	136
圖4-14 撓性接頭簡化最佳化微夾持器的設計圖     	138
圖4-15 撓性接頭簡化最佳化的微夾持器有限元分析模型	139
圖4-16 撓性接頭簡化最佳化的微夾持器有限元位移分析	140
圖4-17 撓性接頭簡化最佳化的微夾持器有限元應力分佈	141
圖4-18 熱變形微夾持器拓樸設計領域，幾何尺寸及邊界圖	146
圖4-19 熱變形微夾持器拓樸對稱設計領域，幾何尺寸及邊界圖146
圖4-20 熱變形微夾持器對稱領域的拓樸最佳化圖    	147
圖4-21 熱變形微夾持器的拓樸最佳化設計圖       	147
圖4-22 熱變形微夾持器的撓性接頭簡化最佳化初始圖	150
圖4-23 熱變形微夾持器的設計圖結果                   	152
圖4-24 熱變形微夾持器的有限元模型                	153
圖4-25 熱變形微夾持器的有限元位移分析圖         	154
圖4-26 熱變形微夾持器的有限元應力分析圖         	155
 
表目錄
表2-1 自由端節點兩自由度位移的數值解             	23
表2-2 光調變器的設計性能                           	60
表3-1 微夾持器最佳化設計結果                         	91
表3-2 微夾持器最佳化限制條件值                     	91
表3-3 微夾持器的最佳化結果比較表                   	97
表3-4 微夾持器的相關目標函數及性能值              	97
表3-5 微夾持器最佳化設計結果                    	107
表3-6 微夾持器最佳化限制函數值                  	107
表3-7 微夾持器的最佳化結果比較表              	113
表3-8 微夾持器的相關目標函數及性能值              	113
表4-1 熱變形微夾持器拓樸類接頭的全域座標值           	149
表4-2 熱變形微夾持器撓性接頭簡化最佳化結果      	149

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