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研究生: 張筱萱
Hsiao-Hsuan Chang
論文名稱: 機械求積儀之研究
A Study on the Mechanical Planimeters
指導教授: 鄧昭瑞
Geo-Ry Tang
郭進星
Chin-Hsing Kuo
口試委員: 郭進星
Chin-Hsing Kuo
陳羽薰
Yu-Hsun Chen
鄧昭瑞
Geo-Ry Tang
學位類別: 碩士
Master
系所名稱: 工程學院 - 機械工程系
Department of Mechanical Engineering
論文出版年: 2020
畢業學年度: 108
語文別: 中文
論文頁數: 179
中文關鍵詞: 求積儀面積量測Green定理機構設計機械式積分器計算連桿機構
外文關鍵詞: Planimeter, area measurement, Green’s theorem, mechanism design, mechanical integrators, computing linkages
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  • 摘要 I Abstract II 致謝 III 目錄 IV 表目錄 VII 圖目錄 VIII 第一章 緒論 1 1.1. 研究動機與目的 1 1.2. 文獻回顧 3 1.2.1. 多邊形面積之求解 3 1.2.2. 求積儀 4 1.2.3. 求積儀誤差來源 5 1.2.4. 論文架構 6 第二章 求積儀歷史 8 2.1. 時間軸 8 2.2. 前期發明 10 2.3. 後期發明 12 第三章 求積儀分類 16 3.1. 原理分類 16 3.2. 機構分類 17 第四章 求積儀數學原理 20 4.1. 微積分基本定理 20 4.2. Green定理 21 第五章 雙線性式求積儀 24 5.1. 定義 24 5.2. 原理 25 5.3. 小結 27 第六章 線性式求積儀 28 6.1. 定義 29 6.2. 原理及證明 29 6.2.1. Green定理證明 29 6.2.2. 機構原理證明 32 6.3. 使用方式 37 6.3.1. 測量矩形面積 37 6.3.2. 測量地圖上的面積 40 6.4. 線性式求積儀之變化類型 43 第七章 極座標式求積儀 56 7.1. 定義 57 7.2. 原理 57 7.2.1. Green定理之應用 57 7.2.2. 機構原理證明 63 7.3. 使用方式 65 7.3.1. 測量矩形面積 65 7.3.2. 測量地圖上的面積 68 7.4. 極座標式求積儀之變化類型 70 第八章 斧型式求積儀 94 8.1. 定義 98 8.2. 原理 99 8.2.1. 面積差定理 99 8.2.2. 斧型式求積儀證明 100 8.3. 使用方式 102 8.3.1. 測量矩形面積 102 8.3.2. 測量地圖上的面積 106 8.4. 斧型式求積儀之變化類型 109 第九章 平均半徑求積儀 114 9.1. 定義 115 9.2. 原理 115 9.3. 使用方式 117 9.3.1. 測量簡單圓形圖表平均半徑 117 9.3.2. 測量實際圖表的平均半徑 120 9.4. 平均半徑求積儀之變化類型 123 第十章 平方根求積儀 130 10.1. 定義 130 10.2. 原理 131 10.3. 使用方式 135 10.4. 平方根求積儀之變化類型 137 第十一章 討論 145 11.1. 誤差實驗分析 146 11.1.1. 測量面積用求積儀的準確度與操作穩定度 146 11.1.2. 不同測量平面的比較實驗 151 11.2. 小結 155 第十二章 結論與未來規畫 156 12.1. 結論與建議 156 12.2. 未來展望 159 參考文獻 160 附錄A 163 版權聲明 165

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