淡江大學覺生紀念圖書館 (TKU Library)
進階搜尋


下載電子全文限經由淡江IP使用) 
系統識別號 U0002-1209201018055200
中文論文名稱 6RUS並聯式機械手臂之運動分析
英文論文名稱 Kinematic Analysis of 6RUS Parallel Manipulator
校院名稱 淡江大學
系所名稱(中) 機械與機電工程學系博士班
系所名稱(英) Department of Mechanical and Electro-Mechanical Engineering
學年度 98
學期 2
出版年 99
研究生中文姓名 許富凱
研究生英文姓名 Fu-Kai Hsu
學號 894340065
學位類別 博士
語文別 中文
口試日期 2010-07-15
論文頁數 105頁
口試委員 指導教授-劉昭華
委員-林鎮洲
委員-劉昭華
委員-陳正光
委員-楊智旭
委員-王銀添
中文關鍵字 並聯式機械手臂  正向位置分析  工作空間  正向奇異位置  剛性 
英文關鍵字 parallel manipulator  direct kinematic analysis  workspace analysis  direct singular position analysis  stiffness analysis 
學科別分類
中文摘要 本研究將HEXA並聯式機械手臂修改為6RUS並聯式機械手臂,使得正向位置分析的閉合解可以求出。本論文並從事此6RUS機構之工作空間、正向奇異位置以及剛性分析。在正向位置分析過程中,首先將6RUS機構簡化為等效3RS結構,利用活動平台之球窩接頭間的距離為已知長度,推導出三個多項式方程式,再使用席維斯透析消去法(Sylvester dialytic elimination method)求得正向位置之解。本論文利用逆向位置分析技巧求出此機構的定向工作空間與方向工作空間。
本研究使用螺旋理論,求出螺旋Jacobian矩陣,同時亦求出HEXA並聯式機械手臂螺旋Jacobian矩陣,利用此矩陣可得到6RUS與HEXA並聯式機械手臂的正向奇異位置與中心結構時的剛性。
英文摘要 In this dissertation, the structure of the 6 degree-of-freedom parallel manipulator HEXA is modified to take a 6RUS form so that closed-form solutions for direct kinematic analysis can be found. In addition, workspace analysis, direct singular position analysis, and stiffness analysis on this 6RUS manipulator are also performed. In direct kinematic analysis, the manipulator is first transformed into an equivalent 3RS structure, and then three polynomial equations are obtained by using the property of constant length between three spherical joints on the moving platform. Sylvester dialytic elimination method is used to obtain direct kinematic solutions. Constant orientation workspace and orientation workspace are found by performing inverse position analysis.
Jacobian matrices of HEXA and the 6RUS manipulator are obtained by using screw theory. Certain direct singular positions of the two manipulators are found from these matrices. Also determined from the Jacobian matrices is the stiffness of central configuration of the two manipulators.
論文目次 目 錄

中文摘要 I
英文摘要 II
目錄 III
圖目錄 V
表目錄 VIII
第一章 緒論 1
1.1 文獻回顧 1
1.2 研究動機 3
第二章 6RUS機構之組成 4
2.1 6RUS並聯式機械手臂之結構 4
2.2 機構之尺寸設計 4
第三章 正向位置分析 6
3.1 交圓圓心及交圓半徑 7
3.2 等效3RS結構 9
3.3 逆向位置分析 15
第四章 位置分析結果與討論 17
第五章 工作空間 21
5.1 工作空間方程式 23
5.2 定向工作空間與方向工作空間 24
第六章 工作空間結果與討論 26
6.1 定向工作空間 26
6.2 方向工作空間 27
第七章 正向奇異位置分析 28
7.1 螺旋Jacobian矩陣之推導(Screw-based Jacobian) 29
7.2 HEXA並聯式機械手臂之螺旋Jacobian矩陣 32
7.3 正向奇異位置 33
第八章 剛性分析 37
第九章 結論 44
參考文獻 46
附錄A 席維斯透析消去法 52
附錄B WAi、WBi與WCi 59

圖 目 錄

圖1 HEXA並聯式機械手臂 60
圖2 6RUS並聯式機械手臂 61
圖3 基座與驅動角度示意圖 62
圖4 兩圓球交圓所在之平面 63
圖5 等效3RS結構 64
圖6 與 座標系之座標轉換 65
圖7 驅動角40°-40°-40°-40°-40°-40°時之機構構形3 66
圖8 驅動角40°-40°-40°-40°-40°-40°時之機構構形4 67
圖9 驅動角40°-40°-40°-40°-40°-40°時之機構構形1 68
圖10 驅動角40°-40°-40°-40°-40°-40°時之機構構形2 69
圖11 驅動角40°-40°-40°-40°-40°-40°時之機構構形7 70
圖12 驅動角40°-40°-40°-40°-40°-40°時之機構構形5 71
圖13 驅動角80°-70°-90°-60°-110°-100°時之機構構形1 72
圖14 驅動角80°-70°-90°-60°-110°-100°時之機構構形2 73
圖15 驅動角80°-70°-90°-60°-110°-100°時之機構構形3 74
圖16 驅動角80°-70°-90°-60°-110°-100°時之機構構形4 75
圖17 兩組 解 76
圖18 Bryant Angles座標轉換 77
圖19 ( )=(0, 0, 0), =1, 關係圖 78
圖20 ( )=(0, 0, 0), =0.25, 關係圖 79
圖21 ( )=(0, 0, 0), =0.5, 關係圖 80
圖22 ( )=(0, 0, 0), =2, 關係圖 81
圖23 ( )=(0, 0, 0), =3, 關係圖 82
圖24 ( )=(0, 0, 0), =3.5, 關係圖 83
圖25 ( )=(0, 0.5, 3), , 關係圖 84
圖26 ( )=(0, 0.5, 3), , 關係圖 85
圖27 ( )=(0, 0.5, 3), , 關係圖 86
圖28 ( )=(0, 0.5, 3), , 關係圖 87
圖29 ( )=(0, 0.5, 3), , 關係圖 88
圖30 ( )=(0, 0.5, 3), , 關係圖 89
圖31 ( )=(0, 0.5, 3), , 關係圖 90
圖32 ( )=(0, 0.5, 3), , 關係圖 91
圖33 ( )=(0, 0.5, 3), , 關係圖 92
圖34 ( )=(0, 0.5, 3), , 關係圖 93
圖35 ( )=(0, 0.5, 3), , 關係圖 94
圖36 ( )=(0, 0.5, 3), , 關係圖 95
圖37 ( )=(0, 0.5, 3), , 關係圖 96
圖38 螺旋座標示意圖 97
圖39 (a)6RUS第一種位置示意圖 (b)YZ面側視圖 98
圖40 (a)HEXA第一種位置示意圖 (b)YZ面側視圖 99
圖41 6RUS第二種位置示意圖 100
圖42 HEXA第二種位置示意圖 101
圖43 HEXA第三種位置示意圖 102
圖44 6RUS第三種位置示意圖 103
圖45 (a)6RUS第四種位置示意圖 (b)YZ面側視圖 104
圖46 (a)HEXA第四種位置示意圖 (b)YZ面側視圖 105

表 目 錄

表1 6RUS機構尺寸表(位置分析) 17
表2 40°-40°-40°-40°-40°-40°活動平台位置表 18
表3 80°-70°-90°-60°-110°-100°活動平台位置表 19
表4 逆向位置分析數據表 20
表5 6RUS機構尺寸表(工作空間) 26

參考文獻 [1] Tsai, L-W., Robot Analysis : the Mechanics of Serial and Parallel Manipulators, John Wiley & Sons, Inc., New York, 1999.
[2] Merlet, J-P., Parallel Robots, 2nd ed., Springer, the Netherlands, 2006.
[3] Zhang, C-D., and Song, S-M., “Forward Position Analysis of Nearly General Stewart Platforms”, ASME Journal of Mechanical Design, Vol. 116, pp. 54-60, March, 1994.
[4] Merlet, J-P., “Direct Kinematics of Parallel Manipulators”, IEEE Transactions on Robotics and Automation, Vol. 9, No. 6, pp. 842-846, December, 1993.
[5] Pierrot, F., Dauchez, P., and Fournier, A., “HEXA: a fast six-DOF fully-parallel robot”, Proceedings of the 15th International Conference on Advanced Robotics, Pisa, Italy, pp. 1158-1163, June 19-22, 1991.
[6] Pierrot, F., Fournier, A., and Dauchez, P., “Towards a Fully-Parallel 6 Dof Robot for High-Speed Applications”, Proceedings of the 1991 IEEE International Conference on Robotics and Automation, Sacramento, Califomia, pp. 1288-1293, April, 1991.
[7] Kim, D., and Uchiyama, M., “A Force/Torque Sensor-less Realization of Fast and Dexterous Tasks with a Parallel Robot”, Proceedings of Industrial Electronics Conference(IECON 2000), 26th Annual Conference of the IEEE Electronics Society, Nagoya, Vol. 1, pp. 223- 228, October 22-28, 2000.
[8] Nenchev, D. N., and Uchiyama, M., “Singularity-Consistent Path Planning and Control of Parallel Robot Motion Through Instantaneous-Self-Motion Type Singularities”, Proceedings of the 1996 IEEE International Conference on Robotics and Automation, Minneapolis, Minnesota, pp. 1864-1870, April, 1996.
[9] Nenchev, D. N., and Uchiyama, M., “Singularity-Consistent Path Planning and Motion Control Through Instantaneous Self-Motion Singularities of Parallel-Link Manipulators”, Journal of Robotic Systems, Vol. 14, No.1, pp. 27-36, 1997.
[10] Sato, D., Ishii, Y., Shitashimizu, T., Kim, D., and Uchiyama, M., “3D Graphics-Based Off-line Task Teaching for a Force-Controlled High -Speed Parallel Robot”, Proceedings of the 4th IEEE International Symposium on Assembly and task Planning Soft Research Park, Fukuoka, Japan, pp. 122-127, May 28-29, 2001.
[11] Sato, D., Shitashimizu, T., and Uchiyama, M., “Task Teaching to a Force-Controlled High-Speed Parallel Robot”, Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan, pp. 4110-4115, September 14-19, 2003.
[12] 丘世昌,CaPaMan2 3-DOF並聯式機械手臂正向位置分析,淡江大學機械與機電工程學系碩士論文,2006年6月。
[13] Roth, B., “Computations in Kinematics”, in Computational Kinematics, edited by Angeles, J., Hommel, G., and Kovacs, P., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993, pp. 3-14.
[14] Wee, C. E., and Goldman, R. N., “Elimination and Resultants Part 1: Elimination and Bivariate Resultants”, IEEE Computer Graphics and Applications, Vol. 15, No. 1, pp. 69-77, January, 1995.
[15] Lee, K. M., and Shah, D. K., “Kinematic Analysis of a Three- Degrees-of-Freedom In-Parallel Actuated Manipulator”, IEEE Journal of Robotics and Automation, Vol. 4, No. 3, pp. 354-360, June, 1988.
[16] Pierrot, F., Reynaud, C., and Fournier, A., ‘‘DELTA: a simple and efficient parallel robot’’ , Robotica, Vol. 8, pp. 105-109, 1990.
[17] Callegari, M., Palpacelli, M., and Scarponi, M., “Kinematics of the 3-CPU Parallel Manipulator Assembled for Motions of Pure Translation”, Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain, pp. 4020 -4025, April, 2005.
[18] Li, Y., and Xu, Q., ”Kinematic Analysis and Dynamic Control of 3-PUU Parallel Manipulator for Cardiopulmonary Resuscitation”, 12th International Conference on Advanced Robotics, Seattle, United States, pp. 344-351, July, 2005.
[19] Liu, X-J., and Kim, J., “A New Spatial Three-DoF Parallel Manipulator With High Rotational Capability”, IEEE/ASME Transactions on Mechatronics, Vol. 10, No. 5, pp. 502-512, 2005.
[20] Nanua, P., Waldron, K. J., and Murthy, V., “Direct Kinematic Solution of a Stewart Platform”, IEEE Transactions on Robotics and Automation Vol. 6, No. 4, pp. 438-444, August, 1990.
[21] Tsai, M-S., Shiau, T-N., Tsai, Y-J., and Chang, T-H., “Direct kinematic analysis of a 3-PRS parallel mechanism”, Mechanism and Machine Theory, Vol. 38, pp. 71-83, January, 2003.
[22] Dunlop, G. R., and Jones, T. P., “Position Analysis of a 3-DOF Parallel Manipulator”, Mechanism and Machine Theory, Vol. 32, No. 8, pp. 903-920, November, 1997.
[23] Li, Y., and Xu, Q., “Kinematic Analysis and Design of a New 3-DOF Translational Parallel Manipulator”, ASME Journal of Mechanical Design, Vol. 128, pp. 729-737, July, 2006.
[24] Li, Y., and Xu, Q., “Kinematic analysis of a 3-PRS parallel manipulator”, Robotics and Computer-Integrated Manufacturing, Vol. 23, pp. 395-408, August, 2007.
[25] Kim, D. I., Chung, W. K., and Youm, Y., “Geometrical Approach for the Workspace of 6-DOF Parallel Manipulators”, IEEE International Conference on Robotics and Automation, Vol. 4, pp. 2986-2991, April, 1997.
[26] Merlet, J-P., Gosselin, C. M., and Mouly, N., “Workspaces of Planar Parallel Manipulators”, Mechanism and Machine Theory, Vol. 33, No. 1-2, pp. 7-20, 1998.
[27] Huang, T., Wang, J., Gosselin, C. M., and Whitehouse, D., “Determination of Closed Form Solution to the 2-D-Orientation Workspace of Gough-Stewart Parallel Manipulators”, IEEE Transactions on Robotics and Automation, Vol. 15, No. 6, pp. 1121- 1125, December, 1999.
[28] Rao, A. B. K., Rao, P. V. M., and Saha, S. K., “Workspace and Dexterity Analyses of Hexaslide Machine Tools”, Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan, pp. 4104-4109, September 14-19, 2003.
[29] Rao, A. B. K., Rao, P. V. M., and Saha, S. K., “Dimensional Design of Hexaslides for Optimal Workspace and Dexterity”, IEEE Transactions on Robotics, Vol. 21, No. 3, pp. 444-449, June, 2005.
[30] Li, Y., and Xu, Q., “Design and Development of a Medical Parallel Robot for Cardiopulmonary Resuscitation”, IEEE/ASME Transactions on Mechatronics, Vol. 12, No. 3, pp. 265-273, June, 2007.
[31] Wittenburg, J., Dynamics of Multibody Systems, 2nd ed., Berlin, New York : Springer, 2008.
[32] Gosselin, C., and Angeles, J., “Singularity Analysis of Closed-Loop Kinematic Chains”, IEEE Transactions on Robotics and Automation, Vol. 6, No. 3, pp. 281-290, 1990.
[33] Gosselin, C., and Wang, J., “Singularity loci of planar parallel manipulators with revolute actuators”, Robotics and Autonomous Systems, Vol. 21, No. 4, pp. 377-398, 1997.
[34] Ottaviano, E., Gosselin, C. M., and Ceccarelli, M., “Singularity Analysis of CaPaMan: A Three-Degree of Freedom Spatial Parallel Manipulator”, Proceedings of the 2001 IEEE International Conference on Robotics & Automation, Seoul, Korea, pp. 1295-1300, May 21-26, 2001.
[35] Wolf, A., Ottaviano, E., Shoham, M., and Ceccarelli, M., “Application of line geometry and linear complex approximation to singularity analysis of the 3-DOF CaPaMan parallel manipulator”, Mechanism and Machine Theory, Vol. 39, pp. 75-95, 2004.
[36] Liu, C. H., and Cheng, S., “Direct Singular Positions of 3RPS Parallel Manipulators”, ASME Journal of Mechanical Design, Vol. 126, pp. 1006-1016, November, 2004.
[37] Guan, L-W., Wang, J-S., and Wang, L-P., ‘‘Mobility Analysis of the 3-UPU Parallel Mechanism Based on Screw Theory’’ , Proceedings of the 2004 International Conference on Intelligent Mechatronics and Automation, pp. 309-314, August, 2004.
[38] Liu, C. H., and Chiu, J., “Direct kinematic singularities of 3-3 Stewart-Gough platforms”, Proceedings of the Institution of Mechanical Engineers, Part K, Journal of Multi-body Dynamics, Vol. 219, pp. 311-324, 2005.
[39] Liu, C. H., and Hsu, F-K., “Direct singular positions of the parallel manipulator Tricept”, Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science, Vol. 221, No. 1, pp. 109-117, 2007.
[40] Gosselin, C., “Stiffness Mapping for Parallel Manipulators”, IEEE Transactions on Robotics and Automation, Vol. 6, No. 3, pp. 377-382, June, 1990.
[41] Tahmasebi, F., and Tsai, L-W., “Jacobian and Stiffness Analysis of a Novel Class of Six-DOF Parallel Minimanipulators” , Proceedings of the 1992 ASME Design Technieal Conference and 22nd Biennial Mechanisms Conference, Scottsdale, Arizona, DE-Vol. 47, pp. 95- 102, September 13-16, 1992.
[42] Hashimoto, M., and Imamura, Y., “Design and Characteristics of a Parallel Link Compliant Wrist”, Proceedings IEEE International Conference on Robotics and Automation, Vol. 3, pp. 2457-2462, 1994.
[43] Tahmasebi, F., and Tsai, L-W., “On the Stiffness of a Novel Six- Degree-of-Freedom Parallel Minimanipulator”, Journal of Robotic Systems, Vol. 12, No.12, pp. 845-856, 1995.
[44] Yoon, W-K., Suehiro, T., Tsumaki, Y., and Uchiyama, M., “A Method for Analyzing Parallel Mechanism Stiffness including Elastic Deformations in the Structure”, IEEE International Conference on Intelligent Robots and Systems, Vol. 3, pp. 2875- 2880, 2002.
[45] Ceccarelli, M., and Carbone, G., “A stiffness analysis for CaPaMan (Cassino Parallel Manipulator)”, Mechanism and Machine Theory, Vol. 37, pp. 427-439, 2002.
[46] 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, April, 2003.
[47] Yoon, W-K., Suehiro, T., Tsumaki, Y., and Uchiyama, M., “A Compact Modified Delta Parallel Mechanism Design Based on a Stiffness Analysis”, Proceedings of the 2003 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Vol. 2, pp. 1262-1267, 2003.
[48] Kim, J-W., Kim, K-W., Kim, H-S., and Kyung, J-H., “Stiffness Analysis and Design of a 3-DOF Parallel Robot with One Constraining Leg (ICCAS 2007)”, International Conference on Control Automation and Systems, Seoul, Korea, pp. 2288-2293, October 17-20, 2007.
[49] Li, Y., and Xu, Q., “Stiffness analysis for a 3-PUU parallel kinematic machine”, Mechanism and Machine Theory, Vol. 43, No. 2, pp. 186- 200, February, 2008.
論文使用權限
  • 同意紙本無償授權給館內讀者為學術之目的重製使用,於2011-09-15公開。
  • 同意授權瀏覽/列印電子全文服務,於2012-09-15起公開。


  • 若您有任何疑問,請與我們聯絡!
    圖書館: 請來電 (02)2621-5656 轉 2281 或 來信