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系統識別號 U0002-2907200520281000
中文論文名稱 機械手臂Tricept的正向奇異位置
英文論文名稱 Direct Singular Positions of the Tricept Robot
校院名稱 淡江大學
系所名稱(中) 機械與機電工程學系碩士班
系所名稱(英) Department of Mechanical and Electro-Mechanical Engineering
學年度 93
學期 2
出版年 94
研究生中文姓名 許富凱
研究生英文姓名 Fu-Kai Hsu
學號 692341141
學位類別 碩士
語文別 中文
口試日期 2005-07-12
論文頁數 37頁
口試委員 指導教授-劉昭華
委員-陳正光
委員-王銀添
中文關鍵字 並聯式機械手臂  正向奇異位置 
英文關鍵字 direct singular positions  Tricept  parallel manipulator 
學科別分類 學科別應用科學機械工程
中文摘要 本研究尋找出Tricept並聯式機械手臂的正向奇異位置。首先推導出較為簡單的3×3 Jacobian矩陣,並且利用此矩陣尋找此機構的正向奇異位置。針對任何一個活動平台方向,都必定會有至少一個活動平台伸長量,造成機構的正向奇異位置,而這伸長量可由3次多項式方程式解出。本文找出在活動平台工作空間之內,有2個區域的正向奇異位置會出現在無法到達的位置,因此當活動平台在此2個區域內時不必考慮正向奇異位置。
英文摘要 In this research the direct singular positions of the parallel manipulator Tricept are determined. An alternative 3×3 Jacobian matrix, simpler than the existing one, is obtained in this study. For a given moving platform’s orientation, the determinant of the Jacobian matrix may be expressed as a cubic polynomial in moving platform’s extension. Direct singular positions may thus be obtained by solving cubic polynomial equations. For an arbitrarily chosen moving platform’s orientation, there exists at least one moving platform’s extension that causes direct kinematic singularity. It is found that in two regions within the moving platform’s workspace direct kinematic singularities can only occur at positions impossible to reach.
論文目次 目 錄
中文摘要 I
英文摘要 II
目錄 III
圖目錄 IV
第一章 緒論 1
1.1 文獻回顧與研究動機 1
第二章 機構之特性與運動限制 4
2.1 平台之結構 4
2.2 機構之運動限制 4
第三章 機構之Jacobian矩陣與工作空間 5
3.1 Jacobian矩陣之推導 5
3.2 機構之工作空間 9
第四章 正向奇異位置之推導 10
4.1 正向奇異位置時的伸長量r 10
4.2 正向奇異位置 12
第五章 結果與討論 13
第六章 結論 16
參考文獻 17
附錄A Jacobian矩陣 19

圖 目 錄
Figure 1 An illustrative diagram of the hybrid kinematic machine-Tricept 21
Figure 2 An illustrative diagram of Tricept 22
Figure 3 The illustrative diagrams of base and moving platform 23
Figure 4 The revolving angle of U joint 24
Figure 5 The workspace of moving platform 25
Figure 6 Direct singular position for the case 26
Figure 7 Direct singular position for the case 27
Figure 8 Direct singular position for the case 28
Figure 9 Direct singular positions distribution (b=1.5);roots r1, r2, and r3 [see eqs.(12a)~(12c)] are denoted by x, +, and o respectively 29
Figure 10 Direct singular positions distribution (top view) 30
Figure 11 Direct singular position for the case 31
Figure 12 Direct singular position for the case 32
Figure 13 Direct singular position for the case 33
Figure 14 Direct singular position for the case 34
Figure 15 Direct singular position for the case 35
Figure 16 Direct singular positions distribution (top view) 36
Figure 17 D-H coordinate frames for the passive leg of the Tricept manipulator 37
參考文獻 [1] Joshi, S., and Tsai, L.W., “A Comparison Study of Two 3-DOF Parallel Manipulators: One With Three and the Other With Four Supporting Legs”, IEEE Transactions on Robotics and Automation, Vol. 19, No. 2, pp. 200-209, 2003.
[2] Joshi, S., and Tsai, L.W., “The Kinematics of a Class of 3-DOF, 4-Legged Parallel Manipulators”, ASME Journal of Mechanical Design, Vol. 125, pp. 52-60, March 2003.
[3] Giddings & Lewis, Home page at http://www.giddings.com/
[4] Toyoda Machine Works, Home page at http://www.toyoda-kouki.co.jp
[5] Comau, Home page at http://www.comau.com/
[6] Neos Robotics, Home page at http://www.neosrobotics.com/
[7] Baroncelli, A., “Il robot fa carriera” (in Italian), Automazione e Robotica, 14, (Oct., 1996).
[8] Neumann, K. E., 2002, “Tricept Application,” Proc. of the 3rd Chemnitz Parallel Kinematics Seminar, pp.547-551, Zwickau, Germany.
[9] Siciliano, B., “The Tricept robot: Inverse kinematics, manipulability analysis and closed-loop direct kinematics algorithm”, Robotica, Vol. 17, pp. 437-445, 1999.
[10] Gosselin, C., and Angeles, J., “Singularity Analysis of Closed-Loop Kinematic Chains”, IEEE Transactions of Robotics and Automation, Vol. 6, pp. 281-290, 1990.
[11] Tsai, L-W., Robot Analysis : the Mechanics of Serial and Parallel Manipulators, John Wiley & Sons, Inc., New York, 1999.
[12] Liu, C. H., and Cheng, S., "Direct Singular Positions of 3RPS Parallel Manipulators", ASME Journal of Mechanical Design, in print.
[13] Joshi, S. A., and Tsai, L-W., “Jacobian Analysis of Limited-DOF Parallel Manipulators”, ASME Journal of Mechanical Design, Vol. 124, pp.254-258, 2002.
[14] Tsai, L-W., and Joshi, S., “Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator”, ASME Journal of Mechanical Design, Vol. 122, pp.439-446, 2000.
[15] Wang, J., and Gosselin, C. M., “Singularity Loci of a Special Class of Spherical 3-DOF Parallel Mechanisms With Prismatic Actuators”, ASME Journal of Mechanical Design, Vol. 126, pp.319-326, 2004.
[16] Wang, J., and Gosselin, C. M., “Kinematic Analysis and Design of Kinematically Redundant Parallel Mechanisms”, ASME Journal of Mechanical Design, Vol. 126, pp.109-118, 2004.
[17] Parviz, E.N., “Computer-Aided Analysis of Mechanical Systems”, Prentice-Hall International, 1988.
[18] Spiegel, M. R., and Liu, J., “Mathematic Handbook of Formulas and Tables Second Edition”, McGraw-Hill, NY, 1999.
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