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研究生:林書弘
研究生(外文):Lin, Shu-Hong
論文名稱:具限制條件的特殊化機構之生成函數研究
論文名稱(外文):On the Generating Function of Specialized Mechanisms with Design Constraints
指導教授:黃以文黃以文引用關係
指導教授(外文):Hwang, Yii-Wen
口試委員:許正和劉霆馮展華劉德騏林榮信
口試委員(外文):Hsu, Cheng-HoLiu, TyngFong, Zhang-HuaLiu, De-ShinLin, Rong-Shine
口試日期:2011-12-08
學位類別:博士
校院名稱:國立中正大學
系所名稱:機械工程學系暨研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2011
畢業學年度:100
語文別:中文
論文頁數:131
中文關鍵詞:生成函數特殊化
外文關鍵詞:Generating FunctionSpecialization
相關次數:
  • 被引用被引用:1
  • 點閱點閱:369
  • 評分評分:
  • 下載下載:25
  • 收藏至我的研究室書目清單書目收藏:2
本研究提出一個創新方法來產生特殊化機構,過程中以數學方式計算,且不須判斷同構。首先,利用組合理論找出編碼後運動鏈之排列群,再依排列群內之元素互換方式與排列數找出運動鏈之複合排列群,複合排列群是由本文所提之基本排列群與運算子組合而得。本文針對八桿以下運動鏈進行分析,觀察排列群內之元素互換關係與排列數,共定義六個基本排列群及四個運算子,每一個基本排列群擁有自身的生成函數,再經運算子搭配計算可得複合排列群的生成函數,生成函數以多項式表示,呈現的結果即為特殊化過程中分配連桿或接頭種類的依據。
類型合成中,設計限制的定義是用來篩選數目合成所得之運動鏈。經由與類型合成相關文獻的收集與分類,將設計限制分類成三種,分別為鄰接、附隨及路徑限制條件。本方法經求得複合排列群之生成函數後,再考慮設計限制條件,並對複合排列群之生成函數篩選,最後獲得符合設計限制條件之特殊化機構。
過去,特殊化過程是以人為觀察進行連桿、接頭分配,過程中對於同構檢查也是倚靠人為方式檢查,因而難免因人為因素的疏忽而產生錯誤。但本研究所提之方法,過程中以數學運算得到特殊化機構,不但提高效率且免除同構判斷,再者,本文收集過去創造性機構設計方法之應用例,再以本文所提之方法操作計算,並比較所得結果的正確性,以證明本文所提方法之可行性與可靠性。
This research proposes an innovative methodology to generate specialized mechanism, without having to check for an isomorphic mechanism. The first step in this methodology is the derivation of a permutation from a labeled kinematic chain, according to the combinatorial theory. Then, the permutation is analyzed to obtain a composite permutation group. The composite permutation group contains basic permutation groups and operators. In this thesis, six basic permutation groups and four operators explained and defined by the permutations. Every basic permutation group has its own generating function and computation, using the operators derives the generating function of the kinematic chain. The generating function is a polynomial, which allots a name to links, or joints of the kinematic chain, in specialization.
Type synthesis defines a design constraint to sieve the solution from the kinematic chain. Three design constrains are discussed in this thesis; adjacent, incident and path constraints. The generating function of the kinematic chain is sieved by the design constrains and a specialized generating function is obtained, which shows the result of the specialization process.
The innovative mathematical method proposed here uses the generating function and coefficient to efficiently and accurately identify specialized mechanisms, thereby solving the problem of specialization in type synthesis. Being systematic, the method avoids the disadvantages of the observation method in the specialization process, and, as the numerical results show, eliminates the need to inspect for isomorphism in order to identify the exact mechanisms.
摘 要 I
ABSTRACT II
目 錄 III
圖目錄 V
符號說明 VIII
第一章 前言 1
1.1 研究動機與目的 1
1.2 文獻回顧 2
1.3 研究方法 4
第二章 基本名詞說明 5
2.1 連桿(接頭)的鄰接與非鄰接矩陣 5
2.2 附隨矩陣 5
2.3 路線、路徑與迴路 6
2.4 排列群 6
2.5 路徑群 7
2.6 相似類別 9
2.7 POLYA理論 9
2.8 生成函數 10
第三章 基本排列群與運算子 12
3.1 單位群 12
3.2 對稱群 13
3.3 對偶群 14
3.4 迴路群 15
3.5 拘束迴路群 18
3.6 座標群 20
3.7 聯集運算子 21
3.8 附著運算子 22
3.9 組合運算子 24
3.10 組合附著運算子 26
第四章 受限制之生成函數 29
4.1 倒置機構 29
4.2 鄰接與非鄰接限制條件 31
4.3 附隨限制條件 34
4.4 路徑限制條件 35
第五章 方法流程及應用 38
5.1 分配迴轉對與滑行對於(6,7)運動鏈 38
5.2 分配旋轉對與滑行對於(8,10)運動鏈 46
5.3 輪子避震機構 58
5.4 電梯的雙安全防夾機構 60
5.5 可變行程的內燃引擎機構 63
5.6 沖床滑體驅動機構 67
第六章 結論與建議 73
REFERENCE 75
附錄 I 79
附錄 II 112
附錄 III 115
附錄 IV 117


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