本論文主要在探討與發展線驅動平台初始設定之方法與進行線驅動平台之誤差分析。首先，建立平面式線驅動平台初始設定方法的理論基礎。在不使用外加感測器的情況下，將平面式平台初始設定之方法分為使用輔具與不使用輔具兩種方式，發展其初始設定進行的步驟。在使用輔具時，分為使用平移式輔具以及使用旋轉式輔具兩種方法，在不使用輔具時，則以三線連接平台或以四線連接平台兩種方式，利用幾何限制與數學方法對平台進行初始設定。其次，探討線驅動平台的誤差來源，以一實際平台機構為例，提出補償的方法。最後，對於無法補償之誤差，例如線長誤差，則推導分析線長誤差造成平台的位置誤差與姿態誤差，並以一實際平台為例進行數值範例探討，經由分析的結果，提出減小平台於操作過程所產生之誤差的建議。本研究所發展的線驅動平台初始設定方法與誤差分析，雖然只適用於平面式平台，但應該可以進一步應用在空間式平台上，對於線驅動平台之實際使用應有助益。

This research focuses on the initial setup and error analysis of wire-driven platforms（WDP）. Firstly, methods without using external sensors are proposed for the initial setup of planer type WDP, which includes using assisting devices or using special geometric restrictions of WDP, and the procedures of initial setup are also developed. Then, the sources of errors and their effects while in a real operating WDP are discussed and investigated. The compensations are proposed in order to eliminate the errors caused by the apparatus of the platform mechanism. As to the effects of the errors, which cannot be avoided, such as the length error of the wire, to the position and posture of the platform are considered and analyzed. Finally, some practical cases are studied numerically, and the suggestions to reduce the effects of errors are purposed. Although, this study only takes the planar type WDP into consideration, the methods and the analysis developed in this study should be able to extend for the spatial type WDP, and could be useful for the application of WDP.

中文摘要 I
Abstract II
誌謝 III
目錄 IV
圖目錄 VII
表目錄 X
符　號　表 XI
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.3研究動機與目的 4
1.4 研究方法與步驟 5
第二章 線驅動平台基礎理論 7
2.1逆向運動學 7
2.2平台之可工作點 9
2.2.1 力學分析 10
2.2.2 幾何分析 12
2.3順向運動學 14
2.3.1 Freudenstein equation 14
2.3.2 極心曲線 17
2.3.3 耦點曲線 20
第三章 平台位置之初始設定 23
3.1 平台初始設定理論 23
3.1.1 平台平移與線長變化量 24
3.1.2 平台旋轉與線長改變量 25
3.2使用輔具之初始設定方法 26
3.2.1 使用平移式輔具之初始設定方法 26
3.2.2 使用旋轉式輔具之初始設定方法 31
3.3 不使用輔具之平台初始設定方法 36
3.3.1 平台線長與位置之關係 37
3.3.2 三線連接之平台的初始設定方法 41
3.3.3 四線連接之平台的初始設定方法 44
第四章 平台之誤差分析 52
4.1 誤差分析理論 52
4.2 機構誤差分析 54
4.2.1 基座出線口裝置 54
4.2.2 捲線裝置 57
4.3 平台位置與姿態誤差分析 59
4.3.1 線長對平台誤差之影響 63
4.3.2 平台位置對平台誤差之影響 66
4.3.3 連接線接近共線時對平台誤差之影響 73
4.3.4 平台尺寸對平台誤差之影響 75
4.4 小結 83
第五章 結論 85
5.1 結論 85
5.2 未來研究建議 86
參考文獻 88
附錄A 三線連接之平台位置唯一性 91
附錄B 運算程式 93

[1] Stewart, D., 1965, “A Platform with Six Degree of Freedom,” Proc. Institute of Mechanical Engineers, Vol. 108, No. 15, pp. 371-386.
[2] Garrett, W. B., 1986, “Suspension System for Supporting and Conveying Equipment, such as a Camera,” United States Patent, No. 4625938.
[3] Zhuang, H. and Liu L., 1996, “Self-calibration of a class of parallel manipulators,” Proceedings of IEEE International Conference on Robotics and Automation Minneapolis, Minnesota, Vol. 2, pp. 994-999.
[4] Khalil, W. and Besnard, S., 2001, “Identifiable parameters for parallel robots kinematic calibration,” IEEE International Conference on Robotics and Automation, v 3, p 2859-2866.
[5] Yang, G., Chen, I. M., Lim, W. K. and Yeo, S. H., 2002, “Simultaneous base and tool calibration for self-calibrated parallel robots,” Robotica , Vol. 20, pp. 367-374.
[6] Jeong, J. W., Kim, S. H. and Kwak, Y. K., 1998, “ Design and kinematic analysis of the wire parallel mechanism for a robot pose measurement,” Proceedings - IEEE International Conference on Robotics and Automation, v 4, p 2941-2946.
[7] Masory, O., Wang, J. and Oren, H. Z., 1993, “On the Accuracy of a Stewart Platform,” IEEE International Conference on Robotics and Automation, v 1, p 725-731.
[8] Ali, N., John M. H. and Vincent, H., 1994, “Calibration of a Parallel Robot Using Multiple Kinematic Closed Loops,” IEEE International Conference on Robotics and Automation pt 1, May 8-13, pp. 407-412, pp. 1050-4729.
[9] Lintott, A. B. and Dunlop, G. R., 1997, “Parallel Topology Robot Calibration,” Robotica, v 15, n 4, July-Aug, p 395-398.
[10] 鄭中緯, 1999, 並聯機構平台機構參數自我校正之研究, 國立中正大學碩士論文.
[11] Dixon, W. E., Walker, I. D., Dawson, D. M. and Hartranft, J. P., 2000, “Fault detection for robot manipulators with parametric uncertainty: A prediction error based approach,” Proceedings of the IEEE International Conference on Robotics and Automation, Vol. 16, No. 6, pp. 3628-3634.
[12] Wang, S. M. and Ehmann, K. F., 2002, “Error model and accuracy analysis of a six-dof stewart platform,” Transaction of the ASME Journal of Manufacturing Science and Engineering, Vol. 124, pp. 286-295.
[13] Roberts, R. G., Graham, T. and Lippitt, T., 1998, “On the inverse kinematics, statics, and fault tolerance of cable-suspended robots,” Journal of Robotic Systems, Vol. 15, No. 10, p 581-597.
[14] 黃友權, 2004, 平面線驅動平台在重力場下之驅動順序調控, 台灣大學機械工程學研究所碩士論文.
[15] 楊文珍, 2001, 腱驅動平台機構之線型態設計, 台灣大學機械工程學研究所碩士論文.
[16] Freudenstein, F., 1955, “Approximate Synthesis of Four-Bar Linkages,” Trans. ASME 77, p 853-61.
[17] Kawamura, S. and Ito, K., 1993, “A new type of master robot for teleoperation using a radial wire drive system,” Proceedings of the 1993 International Conference on Intelligent Robots and Systems, pp. 55–60.
[18] 陳俍鈞, 2002, 腱驅動平台之多餘度及張力調配, 台灣大學機械工程學研究所碩士論文.
[19] Orzech, G. and Orzech, M., 1981, Plane Algebraic Curves, pp. 174-178.
[20] Chung, W. Y., 2003, “The Order and Circularity of a Coupler Curve,” 第二十屆機械工程研討會論文集.