操控性與工作空間為目前機器人設計上經常使用之兩大參考指標。一般具最佳操控性之設計皆利用某一操控指數之平均值求得，但是此方法無法得知操控性之變化率，而以目前方法所得到具最大無奇異工作空間之最佳設計，在工作工間中可能存在相當大之子空間其操控性仍然非常不理想。本文提出方法求得具指定操控性指數值之相關曲線或曲面，並計算這些曲線所包圍之面積或曲面所包覆之體積，所得到之資料可用來判斷機器人之整體或局部操控性以及操控性之變化率，其次利用正位移分析之方法求得軸位移空間之操控性曲線或曲面在工作空間中對應的曲線或曲面，以決定工作空間中操控性大於某一設定值之範圍。所提出之方法適用於三自由度機器人及四自由度多餘軸串聯式機器人，亦可用來研究六自由度機器人之部分子空間之操控性。

Dexterity and workspace are two of the most important design criteria in developing manipulators. The design with optimum dexterity is obtained using the mean value of a dexterity measure that cannot determine the rates of changes of dexterity. The design with optimum singularity-free workspace developed by existing methods might have a relatively large subspace with dexterity close to zero. This thesis presents algorithms for developing contour surfaces with specified dexterities and evaluating the area of the surfaces or the volume of the enclosed regions. The obtained results can be utilized to evaluate the dexterity and the rate of change of dexterity. Any closed curve or surface can be used to determine the singularity-free workspace of a manipulator with better dexterity. The proposed algorithms can be employed to study the dexterity and singularity-free workspace of 3-DOF manipulators and 4-DOF redundant serial manipulators. The contour surfaces in some subspaces of 6-DOF manipulators can also be investigated.

[1] Merlet J. P., “Determination of 6D workspaces of Gough-type parallel manipulator and comparison between different geometries,’’ Int. J. Robot. Res., Vol. 18, No. 9, pp. 902-916 (1999)
[2] Luh C. M., Adkins F. A., Haug E. J., and Qiu C. C., “Working capability analysis of Stewart platforms,’’ Trans. ASME J. Mech. Des., Vol. 118, No. 2, pp. 220-227 (1996)
[3] Majid M. Z. A., Huang Z., and Yao Y. L., “Workspace analysis of a six-degrees of freedom, three-prismatic-prismatic-spheric-revolute parallel manipulator,” Int. J. Adv. Manuf. Technol., Vol. 16, No. 6, pp. 441-449 (2000)
[4] Masory O., and Wang J., “Workspace evaluation of Stewart platform,” Adv. Robotics, Vol. 9, No. 4, pp. 443-461 (1995)
[5] Gosselin C., “Determination of the workspace of 6-DOF parallel manipulators,” J. Mech. Trans. Automat. in Design, Vol. 112, No. 3, pp. 331-336 (1990)
[6] Bonev I. A., and Ryu J., “A geometrical method for computing the constant-orientation workspace of 6-PRRS parallel manipulators,” Mech. Mach. Theory, Vol. 36, No. 1, pp. 1-13 (2001)
[7] Merlet J. P., “Determination of the orientation workspaces of parallel manipulator,” J. Intelligent Robotic Syst., Vol. 13, No. 2, pp. 143-160 (1995)
[8] Bonev I. A., and Ryu J., “A new approach to orientation workspace analysis of 6-DOF parallel manipulators,” Mech. and Mach. Theory, Vol. 36, No. 1, pp. 15-28 (2001)
[9] Merlet J. P., “Designing a parallel manipulator for a specific workspace,” Int. J. Robot. Res., Vol. 16, No. 4, pp. 545-556 (1997)
[10] Hay A. M., and Snyman J. A., “Methodologies for the optimal design of parallel manipulators,” Int. J. Numer. Meth. Engin., Vol. 59, No. 3, pp. 131-152 (2004)
[11] Klein, C. A., and Blaho, B. E., “Dexterity measures for the design and control of kinematically redundant manipulators,” Int. J. Robot. Res., Vol. 6, No. 2, pp. 72-83 (1987)
[12] Gosselin C. M., and Angeles J., “The Optimum Kinematic Design of a Planar Three-Degree-of-Freedom Manipulator,” J. Mech. Trans. Automat. in Design, Vol. 110, No. 1, pp. 35-41 (1988)
[13] Gosselin C. M., and Angeles J., “The optimum kinematic design of a spherical three-degree-of freedom manipulator,” J. Mech. Trans. Automat. in Design, Vol. 111, No. 2, pp. 202-207 (1989)
[14] Angeles J., and Lopez-Cajun, C. S., “Kinematic isotropy and the conditioning index of serial robotic manipulators,” Int. J. Robot. Res., Vol. 11, No. 6, pp. 560-571 (1992)
[15] Kircanski M., “Kinematic isotropy and optimal kinematic design of planar manipulators and a 3-DOF spatial manipulator,” Int. J. Robot. Res., Vol. 15, No. 1, pp. 61-77 (1996)
[16] Pittens K. H., and Podhorodeski R. P., “A family of Stewart platforms with optimal dexterity,” J. of Robot. Sys., Vol. 10, No. 4, pp. 463-479 (1993)
[17] Stoughton R. S., and Arai T., “A modified Stewart platform manipulator with improved dexterity,” IEEE Trans. Robot. and Autom., Vol. 9, No. 2, pp. 166-173 (1993)
[18] Bhattacharya S., Hatwal H., and Ghosh A., “On the optimum design of Stewart platform type parallel manipulators,” Robotica, Vol. 13, No. 2, pp. 133-140 (1995)
[19] Lee, J., Duffy J., and Hunt K.H., “A practical quality index based on the octahedral manipulator,” Int. J. Robot. Res., Vol. 17, No. 10, pp. 1081-1090 (1998)
[20] Khan W. A., and Angeles J., “The kinetostatic optimization of robotic manipulators: the inverse and the direct problems,” ASME J. Mech. Des., Vol. 128, No. 1, pp. 168-178 (2006)
[21] Angeles J., “The design of isotropic manipulator architectures in the presence of redundancies,” Int. J. Robot. Res., Vol. 11, No. 3, pp. 196-201 (1992)
[22] Zanganeh K. E., and Angeles J., “Kinematic isotropy and the optimum design of parallel manipulators,” Int. J. Robot. Res., Vol. 16, No. 2, pp. 185-197 (1997)
[23] Fattah A., and Ghasemi A. M. H., “Isotropic design of spatial parallel manipulators,” Int. J. Robot. Res., Vol. 21, No. 9, pp. 811-824 (2002)
[24] Fassi I., Legnani G., and Tosi D., “Geometrical conditions for the design of partial or full isotropic hexapods,” J. of Robot. Sys., Vol. 22, No. 10, pp. 507-518 (2005)
[25] Klein C. A., and Miklos T. A., “Spatial robotic isotropy,” Int. J. Robot. Res., Vol. 10, No. 4, pp. 426-437 (1991)
[26] Tsai K. Y., and Huang K. D., “The design of isotropic 6-DOF parallel manipulators using isotropy generators,” Mech. and Mach. Theory, Vol. 38, No. 11, pp. 1199-1214 (2003)
[27] Tsai K. Y., and Wang Z. W., “The design of redundant isotropic manipulators with special link parameters,” Robotica, Vol. 23, No. 2, pp. 231-237 (2005)
[28] Tsai K. Y., and Lee T. K., “6-DOF isotropic parallel manipulator with three PPSR or PRPS chains,” 12th IFToMM Conference, Besancon (France), June 18-21, 2007.
[29] Tsai K. Y., and Lee T. K., “6-DOF parallel manipulators with better dexterity, rotatability, or singularity-free workspace,” Vol. 27, No. 4, pp. 599-606 (2009)
[30] Tsai K. Y., and Zhou S. R., “The optimum design of 6-DOF isotropic parallel Manipulators,” J. of Robot. Sys., Vol. 22, No. 6, pp. 333-340 (2005)
[31] Gosselin C. M., and Angeles J., “A global performance index for the kinematic optimization of robotic manipulators,” ASME J. Mech. Des., Vol. 113, No. 3, pp. 220-226 (1991)
[32] Liu, X.-J., Wang, J., and Pritschow, G., “Performance atlases and optimum design of planar 5R symmetrical parallel mechanisms,” Mech. Mach. Theory, Vol. 41, No. 2, pp. 119-144 (2006)
[33] Merlet, J. P., “Jacobian, manipulability, condition number, and accuracy of parallel robots,” ASME J. Mech Des., Vol. 128, No. 1, pp. 199-208 (2006)
[34] Liu, X.-J., Jin, Z.-L., and Gao, F., “Optimum design of 3-DOF spherical parallel manipulators with respect to the conditioning and stiffness indices,” Mech. Mach. Theory, Vol. 35, No. 9, pp. 1257-1267 (2000)
[35] Liu, X.-J., Wang, J., and Zheng, H.-J., “Optimum design of the 5R symmetrical parallel manipulator with a surrounded and good-condition workspace,” Robot. Auton. Syst., Vol. 54, No. 3, pp. 221-233 (2006)
[36] Tsai, K. Y., Hsu, I. P., and Kohli, D., “Admissible motions of special manipulators,” IEEE Trans. Rob. Automa., Vol. 10, No. 3, pp. 386-391 (1994)
[37] Tsai, K. Y., Lin, P. Y., and Lee, T. K., “4R spatial and 5R parallel manipulators that can reach maximum number of isotropic positions” Mech. Mach. Theory, Vol. 43, No. 1, pp. 68-79 (2008)
[38] Tsai, L. W., Robot analysis, John Wiley & Sons, NY (1999)
[39] 趙英宏、趙元和 合著，「數值分析」，五南圖書出版股份有限公司，2008年7月初版，第63-68頁。