臺灣博碩士論文加值系統

因為史都華平台的幾何結構，使其機械效能隨end-effector在空間中位置的不同而大幅變化，所以增大工作空間中機械性能較好的區域成為設計史都華平台的首要之務。到目前為止雖然有不少的文獻對史都華平台的構型做最佳化設計，但大部分的研究不是所使用的性能指標其物理意義不明確，就是只在工作空間中的部分區域進行最佳化設計。2000年[17] 雖然解決了以上兩個問題，但其提出的方法在作機械性能分析時，均採用離散方法，亦即格子點法(Grid method)。並假設在單一格子內史都華平台的機械性能為單調(monotonic)變化，也就是機械性能的極值出現在格子點上。如此雖然可以簡化分析的過程，但結果是設計出的機器無法保證在工作空間內機械性能決對符合規格的要求。
為了改進上述方法的缺點，本研究將提出一套檢查的程序，以保證利用上述方法設計出的機器在工作空間內機械性能決對符合規格的要求，或是找出機械性能不符合規格要求的區域。本文將以三角形對稱簡化型（TSSM）的史都華平台為主要研究對象，並假定該機構在應用上使用平台機構的三個平移自由度。

第1章 簡介
1.1史都華平台簡介
1.2文獻回顧
1.2.1史都華平台的發展背景
1.2.2機械性能相關文獻回顧
1.2.3區間演算法與擾動法的發展背景
1.3研究動機
1.4論文內容概要
第2章 區間演算法與擾動法簡介
2.1機械性能指標簡介
2.1.1從機械效能看機械性能指標
2.1.2從剛性看機械性能指標
2.1.3從奇異位置看機械性能指標
2.1.4各項性能指標與最佳化問題陳述
2.2區間演算法簡介
2.2.1區間數學之基本定義及定理
2.2.2建立區間函數的方法
2.3擾動法簡介
2.4區間演算法與擾動法的定性比較
第3章 二維機械性能分析
3.1問題的定義與假設
3.2演算法的主要架構
3.3估算次模組的演算法
3.4切分次模組的演算法
3.5停止條件次模組的演算法
3.6二軸性能指標圖形
第4章 三維機械性能分析
4.1問題的定義與假設
4.2演算法的主要架構
4.3 軸檢查次模組的演算法
4.4切分次模組的演算法
4.5停止條件次模組的演算法
4.6三軸性能指標圖形
第5章 結論
5.1結論
5.2未來展望
參考文獻

[1] Yang, D. C. H., and Lee, T. W., 1984, “Feasibility study of a platform type of robotic manipulator form a kinematic view point,” ASME J. of mechanisms, Transmissions and Automation in Design, Vol. 106, pp. 191-198.
[2] Heisel, U., and Gringel, M., 1996, “Machine tool design requirements for high-speed machining,” Annals of th CIRP, Vol. 45/1, pp. 389-392.
[3] Warnecke, H. J., Neugebauer, R., and wieland, F., 1998, “Development of Hexapod based machine tool,” Annals of th CIRP, Vol. 47/1, pp. 337-340.
[4] Allcock, A., 1995, “A Machine for the 21st century,” Machinery and production Engineering, Vol. 108, No. 15, pp. 371-386.
[5] Stewart, D., 1993, “Stewart platform of general geometry has 40 configurations,” Trans. ASME, J. Mechanical Design, Vol. 115, No. 2, pp. 277-280.
[6] C. Gosselin and J. Angeles, 1988, “The optumum kinematic design of a planar three-degree-of —freedom parallel manipulator,” ASME J. of mechanisms, Transmissions and Automation in Design, Vol. 110, pp. 35-41.
[7] C. Gosselin and J. Angeles, 1989, “The optumum kinematic design of a spherical three-degree-of —freedom parallel manipulator,” ASME J. of mechanisms, Transmissions and Automation in Design, Vol. 111, pp. 202-207.
[8] K. H. Pittens and R. P. Podhorodeski, 1993, “A family of Stewart platforms with optimal dexterity,” Journal of robotic systems, Vol. 10, No. 2, pp. 463-479.
[9] K. E. Zanganeh and J. Angeles, 1997, “Kinematic isotropy and the optimum design of parallel manipulators,” Int. J. Robotics Res., Vol. 16, No. 2, pp. 185-197.
[10] J. Lee, J. Duffy, and K. H. Hunt, 1998, “A practical quality index based on the octahedral manipulator,” Int. J. Robotics Res., Vol. 17, No. 10, pp. 1081-1090.
[11] W. Khalil and D. Murareci, 1996, “Kinematic analysis and singular configurations of a class of parallel robots,” Mathematics and computers, Vol. 41, pp. 377-390.
[12] T. Huang, D. J. Whitehouse, and J. Wang, 1998, “The local dexterity, optimal architecture and design criteria of parallel machine tools,” Annals of the CIRP, Vol. 47, No. 1, pp. 347-351.
[13] D. Kim and W. Chung, 1999, “Analytic singularity equation and analysis of six-DOF parallel manipulators using local structurization method,” IEEE transactions on robotics and automation, Vol. 15, No. 4, pp. 612-622.
[14] B. M. St-Onge and C. M. Gosselin, 2000, “Singularity analysis and representation of the general Gough-Stewart platform,” Int. J. Robotics Res., Vol. 19, No. 3, pp. 271-288.
[15] R. S. Stoughton and T. Arai, 1993, “A modified Stewart platform manipulator with improved dexterity,” IEEE transactions and automation, Vol. 9, No. 2, pp. 166-173.
[16] S. Bhattacharya, H. Hatwal and A. Ghosh, 1995, “On the optimum design of Stewart platform type parallel manipulators,” Robotica, Vol. 13, pp. 133-140.
[17] 蔡永生，2000，”史都華平台五軸機械性能分析與設計程序”，國立清華大學動力機械工程學系碩士論文。
[18] R. E. Moore, 1966, Interval analysis, Prentice-Hall, Englewood Cliffs, New Jersey.
[19] H. Ratschek, 1980, “Centered forms,” SIAM J. Numer. Anal., Vol. 17, No. 5, pp. 656-662.
[20] J. G. Rokne, 1986, “Low complexity k-dimensional centered forms,” Computing, Vol. 37, pp. 247-253.
[21] E. R. Hansen, 1968, “On solving systems of equations using interval arithmetic,” Math. Comput., Vol. 22, pp. 374-384.
[22] J. G. Rokne and P. Bao, 1987, ”Interval taylor forms,” Computing, Vol. 39, pp. 247-259.
[23] C. Cargo and O. Shiska, 1966, “The Berstein form of a polynomial,” J. Res. Nat. Bureau Standards, Vol. 70B, pp. 79-81.
[24] J. Rokne, 1977, “Bounds for an interval polynomial,” Computing, Vol. 18, pp. 225-240.
[25] T. W. Sederberg and R. T. Farouki, 1992, “Approximation by interval Bezier curves,” IEEE Comput. Graph. Appl. Vol. 12, pp. 87-95.
[26] Q. Lin and J. G. Rokne, 1995, “Methods for bounding the range of a polynomial,” J. Comp. Appl. Math., Vol. 58, pp. 193-199.
[27] Q. Lin and J. G. Rokne, 1995, “Interval approximation of higher order to the ranges of functions,” Computers Math. Applic., Vol. 31, No. 7, pp. 101-109.
[28] F. L. Bauer and C. T. Fike, 1960, “Norms and exclusion theorems,” Numerische Mathematik, Vol. 2, pp. 137-141.
[29] A. S. Deif, 1995, “Rigorous perturbation bounds for eigenvalues and eigenvectors of a matrix,” J. Comp. Appl. Math., Vol. 57, pp. 403-412.
[30] E. Jiang, 1998, “Challenge eigenvalue perturbation problems,” Linear Algebra and its Applications, Vol. 278, pp. 303-307.
[31] J. Demmel and W. Kahan, 1990, “Accurate singular values of bidiagonal matrices,” SIAM J. Sci. Statist. Comput., Vol. 11, pp. 873-912.
[32] J. Barlow and J. Demmel, 1990, “Computing accurate eigensystems of scaled diagonally dominant matrices,” SIAM J. Numer. Anal., Vol. 27, No. 3, pp. 762-791.
[33] F. M. Dopico, J. Moro and J. M. Molera, 2000, “weyl-type relative perturbation bounds for eigensystems of hermitian matrices,” Linear Algebra and its Applications, Vol. 309, pp. 3-18.
[34] 黃耀德，2001，”廣義史都華平台五軸改良型工具機性能分析與設計程序” ，國立清華大學動力機械工程學系碩士論文。
[35] M. H. Perng and L. Hsiao, 1999, “Inverse kinematic solutions for a fully parallel robot with singularity avoidance,” Int. J. Robotics Res., Vol. 18, No. 6, pp. 575-583.
[36] P. Lancaster and M. Tismenetsky, 1985, The Theory of Matrices, New York: Academic Press.
[37] B. S. El-Khasawneh and P. M. Ferreira, 1999, “Computation of stiffness and stiffness bounds for parallel link manipulators,” Int. J. Machine Tools & Manufacture, v39, n2, pp. 321-342.
[38] O. Didrit, M. Petitot and E. Walter, 1998, “Guaranted solution of direct kinematic problems for general configurations of parallel manipulators,” IEEE transactions on robotics and automation, Vol. 14, No. 2, pp. 259-266.
[39] J. P. Merlet, 1999, “Determination of 6D workspaces of Gough-type parallel manipulator and comparison between different geometries,” Int. J. Robotics Res., Vol. 18, No. 9, pp. 902-916.
[40] E. Hanson, 1992, Global optimization using interval analysis, Marcel Dekker, New york.
[41] E. R. Moore, 1979, Methods and applications of interval analysis, SIAM Publ., Philadelphia, Pennsylvania.
[42] H. Ratschek and J. Rokne, 1984, Computer methods for the range of functions, Chichester, Ellis Horwood.
[43] G. W. Stewart and J. G. Sun, 1990, Matrix perturbation theory, Academic Press, San Diego.