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 本文針對一種由三條皆可推拉之超彈性纜線與雙平板所組成的可彎曲圓管機構，進行其順、逆向運動學、速度與工作空間分析。該可彎曲圓管機構可藉由三條超彈性纜線的同時推拉，控制其中一平板之運動；並且，由於纜線的特殊材料性質，機構驅動時會呈現一彎曲狀。本文首先推導該機構之逆向運動學解析解，即當移動平板之位置為已知，求得三條超彈性纜線之長度。接著，分析該機構於一般構形下之擬順向運動學(Quasi-forward kinematics)解析解以及於特殊構形下之順向運動學解析解。再者，我們並進行該機構之速度分析，探討三條纜線伸縮速度與移動平板速度之關聯性。並且，利用給定超彈性纜線長度之限制範圍，研究該機構末端平板工作空間(Workspace)。最後，實作加工該機構模型，測試以超彈性纜線組成的多段可彎曲圓管機構之可行性。與其它相關文獻相較，本研究主要貢獻有三：第一，成功求得該機構於一般構形下之擬順向以及特殊構形下之順向運動學解析解；第二，順利推導得到當三條超彈性纜線為均勻分布且長度皆可變化下之Jacobian矩陣；第三，完整演繹由三條超彈性纜線驅動之可彎曲圓管機構的工作空間，說明該機構之可行性。本文之產出，可為超彈性纜線驅動之可彎曲機構的運動分析與控制提供完整理論基礎。
 This thesis studies the position, velocity and workspace analyses of a flexible tube mechanism. The mechanism is composed of two plates, one being fixed to ground and the other being movable, and three superelastic wires. When the three wires are being pushed and/or pulled respectively, the mechanism will be actuated, forming a bending shape from which the motion of the movable plate is fully defined. First, we derive the analytical solutions for the inverse kinematics problem of the mechanism. Then, we solve for the quasi-forward kinematics problem of the mechanism at general configuration and derive the analytical solutions for its forward kinematics problem at a special configuration at which the three wires are equally distributed. Next, we derive the Jacobian matrix to relate the pushing/pulling speeds of the three wires to the velocity of the movable plate. Then, given by specific motion ranges of the wires, we illustrate the reachable workspace of the mechanism. Finally, a prototype is constructed for verifying the concept of the multi-flexible mechanism driven by superelastic wires. As a result, the major contributions of this work are three holds: (1) The analytical solutions for the quasi-forward/forward kinematics problems of the mechanism at general/special configurations are obtained, respectively; (2) The Jacobian matrix of the mechanism with three equally distributed and pullable wires is derived; and (3) The reachable workspace of a three-wire-actuated tube mechanism is verified. In conclusion, this work provides a solid theoretical background for the motion analysis and control of the three-wire-acctuated tube mechanisms and its combination.
 摘要 IAbstract III致謝 V目錄 VI表目錄 X圖目錄 XI符號表 XV第一章 緒論 11.1 研究動機 21.2文獻回顧 51.3 研究目的 81.4 論文架構 9第二章 內置超彈性纜線可彎曲圓管機構 122.1 超彈性纜線 122.2 可彎曲圓管機構之構造 132.3 機構自由度與纜線個數 132.4 問題敘述與基本假設 142.5 可彎曲圓管機構運動學求解流程 17第三章 逆向運動學分析 213.1一般構形逆向運動解分析 213.2 數值範例 323.3 小結 34第四章 順向運動學分析 354.1 一般構形之擬順向運動解 354.1.1 構形函數 364.1.2 位置與方位函數 464.1.3 纜線弧長 494.2特殊構形之順向運動解 504.2.1 擬順向運動解 ( ) 504.2.2 順向運動解 ( ) 514.3 數值範例 544.3.1 一般構形數值範例 544.3.2特殊構形數值範例 604.4小結 65第五章 速度分析 675.1 一般構形之速度分析 675.1.1上平板位置相對於構形函數之變化率 695.1.2構形函數相對於纜線端點距離之變化率 735.1.3 纜線端點距離相對於纜線長度之變化率 745.2特殊構形之速度分析 745.2.1 方法一：由纜線端點距離求特殊構形速度分析 755.2.1 方法二：由纜線弧長長度求特殊構形速度分析 785.3 奇異構形 795.4 數值範例 805.4.1以纜線端點距離求特殊構形末端點速度 805.4.2以超彈性纜線長度求特殊構形末端點速度 815.4.3 上平板角速度與纜線速度之關係 825.5 討論 895.6 小結 92第六章 工作空間分析 936.1工作空間邊界 936.1.1最大曲率 946.1.2 、 與 976.2 纜線長度極值 1036.3 數值範例 1066.4 討論 1086.4.1 中心弧長S與旋轉角φ產生之曲率κ 1086.4.2 曲率κ與旋轉角φ產生之中心弧長S 1096.5 小結 111第七章 模型實作 1137.1 概念設計 1137.2 實作加工 117第八章 結論與未來展望 1218.1結論 1218.2未來展望 122參考文獻 124作者簡歷 133
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