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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 李志中 | zh_TW |
| dc.contributor.advisor | Jyh-Jone Lee | en |
| dc.contributor.author | 張元 | zh_TW |
| dc.contributor.author | Yuan Chang | en |
| dc.date.accessioned | 2024-06-03T16:06:07Z | - |
| dc.date.available | 2024-06-04 | - |
| dc.date.copyright | 2024-06-03 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-05-29 | - |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/92668 | - |
| dc.description.abstract | 在機構設計領域，連桿機構的尺度合成對於精確控制機械運動至關重要。本研究將聚焦於平面與球面四連桿機構的尺度合成。傳統的傅立葉描述子 (Fourier Descriptors, FD) 的複數坐標在描述空間曲線時存在限制。因此，我們引入橢圓傅立葉描述子 (Elliptical Fourier Descriptors, EFD) 作為新的形狀表示法，以提高描述的準確性和通用性。EFD通過本研究改良後的正規化係數取得幾何不變性，使用傅立葉功率分析自動選擇諧波數，並可擴展至空間曲線。本研究採用圖集與差分進化法進行數值最佳化，對機構尺度進行最佳化設計。通過各種耦桿曲線和合成條件的測試，我們實現了更精確的路徑生成與剛體導引。以平面與球面四連桿機構為例，多種案例分析表明，EFD能有效解決開放曲線與空間曲線的描述問題，驗證了方法的有效性。研究創新點在於首次將EFD應用於機構合成領域，解決了FD在描述複雜曲線時的局限性。此外，本研究還提出了一種新的開放曲線描述方法，其精確性和效率相較於過往方法有顯著提升。 | zh_TW |
| dc.description.abstract | In mechanism design, dimensional synthesis of linkages is crucial for precisely controlling mechanical motion. This study focuses on the dimensional synthesis of planar and spherical four-bar linkages. The complex coordinates of conventional Fourier Descriptors (FD) have limitations in describing spatial curves. Therefore, we introduce Elliptical Fourier Descriptors (EFD) as a new shape representation to enhance accuracy and generality. EFD achieves geometric invariance through improved normalization coefficients in this study, automatically selects the number of harmonics using Fourier power analysis, and can be extended to spatial curves. Numerical optimization of linkage dimensions is conducted using atlas-based and differential evolution methods. Through tests on various coupler curves and synthesis conditions, we verified path generation and rigid body guidance can be achieved efficiently and precisely through EFD. Using planar and spherical four-bar linkages as examples, multiple case studies demonstrate that EFD effectively addresses the description issues of open and spatial curves, validating the method’s effectiveness. The innovation of this research lies in the first application of EFD in the field of linkage synthesis, overcoming the limitations of FD in describing complex curves. Additionally, a new method for describing open curves is proposed in this study, which significantly improves accuracy and efficiency compared to previous methods. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-06-03T16:06:07Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-06-03T16:06:07Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 口試委員審定書 i
誌謝 ii 摘要 iii Abstract iv 圖次 viii 表次 xi 符號表 xiii 第1章 緒論 1 1.1 前言 1 1.2 文獻回顧 2 1.2.1 傅立葉分析方法 2 1.2.2 數值最佳化方法 5 1.3 研究動機與目的 6 1.4 論文架構 7 第2章 橢圓傅立葉描述子 8 2.1 封閉曲線描述 8 2.2 圖形正規化 11 2.3 空間描述與正規化 13 2.4 傅立葉功率分析 15 2.5 開放曲線描述 17 2.5.1 三角函數多項式曲線擬合法 18 2.5.2 往復描述法 22 2.6 係數比較 25 2.7 小結 27 第3章 平面與球面四連桿機構 29 3.1 平面四連桿機構 29 3.1.1 耦桿曲線計算 30 3.1.2 連桿分類 31 3.1.3 去正規化 32 3.1.4 剛體導引機構 33 3.2 球面四連桿機構 34 3.2.1 耦桿曲線計算 34 3.2.2 等效連桿分類 37 3.2.3 去正規化 39 3.3 小結 40 第4章 合成方法 41 4.1 圖集資料庫 41 4.2 數值最佳化 43 4.2.1 差分進化法 45 4.3 改良距離誤差法 48 4.3.1 正規化時間參數 48 4.3.2 目標函數設計 50 4.4 平面剛體導引 51 4.4.1 時間導引與運動標記 53 4.4.2 多目標最佳化 56 4.4.3 距離誤差法 59 4.5 小結 60 第5章 案例探討 61 5.1 實驗架構 61 5.2 封閉曲線路徑生成 62 5.2.1 範例1-1 62 5.2.2 範例1-2 64 5.2.3 範例1-3 66 5.2.4 範例1-4 68 5.2.5 範例1-5 69 5.3 開放曲線路徑生成 71 5.3.1 範例2-1 72 5.3.2 範例2-2 73 5.4 封閉曲線片段路徑匹配 74 5.4.1 範例3-1 74 5.4.2 範例3-2 76 5.4.3 範例3-3 77 5.5 改良距離誤差合成 78 5.6 平面四連桿剛體導引 80 5.6.1 改良距離誤差剛體導引 85 第6章 結論與未來展望 90 6.1 結論 90 6.2 未來展望 91 參考文獻 92 附錄 I 離散點坐標近似至EFD係數推導 98 附錄 II 往復開放曲線簡化EFD係數證明 100 | - |
| dc.language.iso | zh_TW | - |
| dc.subject | 傅立葉分析 | zh_TW |
| dc.subject | 橢圓傅立葉描述子 | zh_TW |
| dc.subject | 路徑生成 | zh_TW |
| dc.subject | 四連桿機構 | zh_TW |
| dc.subject | 剛體導引 | zh_TW |
| dc.subject | Four-Bar Linkages | en |
| dc.subject | Fourier Analysis | en |
| dc.subject | Elliptical Fourier Descriptors | en |
| dc.subject | Rigid-Body Guidance | en |
| dc.subject | Path Generation | en |
| dc.title | 基於橢圓傅立葉描述子之平面與球面四連桿機構運動合成 | zh_TW |
| dc.title | Kinematic Synthesis of Planar and Spherical Four-Bar Linkages Using Elliptical Fourier Descriptors | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-2 | - |
| dc.description.degree | 博士 | - |
| dc.contributor.oralexamcommittee | 詹魁元;徐冠倫;蘇偉儁;張秉純;謝文賓 | zh_TW |
| dc.contributor.oralexamcommittee | Kuei-Yuan Chan;Kuan-Lun Hsu;Wei-Jiun Su;Biing-Chwen Chang;Win-Bin Shieh | en |
| dc.subject.keyword | 橢圓傅立葉描述子,傅立葉分析,四連桿機構,路徑生成,剛體導引, | zh_TW |
| dc.subject.keyword | Elliptical Fourier Descriptors,Fourier Analysis,Four-Bar Linkages,Path Generation,Rigid-Body Guidance, | en |
| dc.relation.page | 100 | - |
| dc.identifier.doi | 10.6342/NTU202401033 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2024-05-29 | - |
| dc.contributor.author-college | 工學院 | - |
| dc.contributor.author-dept | 機械工程學系 | - |
| 顯示於系所單位： | 機械工程學系 | |
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