本文提出新的方法來設計可達到多個等向性構形之平面與空間3自由度機器人。首先提出一個基本的方法並應用於平面3R機器人，除了證明此類機器人最多可達到4個等向性位置之外，並找出能夠到達四個等向性位置連桿長度之範圍。其次推導出能直接以3R等向性機器人設計空間4R機器人之方法，此方法不需求解任何非線性方程式即可得到8個等向性位置之空間機器人。在並聯式機器人方面，本文亦提出一個新的方法，此方法將利用四連桿機構推導出5R並聯式等向性機器人，此類機器人最多可到達8個等向性位置。

This paper proposes methods for designing isotropic planar and 3-DOF spatial manipulators that can reach multiple isotropic positions. A general method is first presented to develop 3R planar manipulators. It shows that the obtained design can reach four isotropic positions. Furthermore, the ranges of link parameters with four isotropic positions are provided. Next, an efficient method in which a 4R spatial manipulator can be directly developed from a 3R planar manipulator is proposed. The method does not involve developing and solving any nonlinear equations. For parallel manipulators an alternative approach is proposed for developing 5R planar parallel manipulators. The manipulators are developed from four-bar mechanisms. The parallel and spatial designs can reach eight isotropic positions.

1.C. A. Klein and B. E. Blaho, “Dexterity measures for the design and control of kinematically redundant manipulators”, Int. J. Robot Res. 6(2), pp. 72-83 (1987).
2.C. M. Gosselin and J. Angeles, “The optimum kinematic design of a planar three-degree-of freedom manipulator”, J. Mech Trans Automat in Design 110, pp. 35-41 (1988).
3.M. Kircanski, Kinematic isotropy and optimal kinematic design of palnar manipulators and a 3-DOF spatial manipulator, Int J Robot Res 15: (1) pp. 61-77 (1996).
4.C. M. Gosselin and J. Angles, The optimum kinematic design of a spherical three-degree-of freedom manipulator, J Mech Trans Automat in Design, 111, pp. 202-207 (1989)
5.C. A. Klein and T. A. Miklos, Spatial robotic isotropy, Int J Robot Res 10: (4), pp. 426-437 (1991).
6.K. E. Zanganeh and J. Angeles, Kinematic isotropy and the optimum design of parallel manipulators, Int J Robot Res. 16: (2) pp. 185-196 (1997).
7.黃冠達，”六自由度等向性並聯式機器人設計之探討”，國立台灣科技大學機械工程技術研究所，2002年6月博士論文。
8.周世仁，”等向性產生器在六自由度並聯式機器人設計上之應用”，國立台灣科技大學工程技術研究所，2003年6月碩士論文。
9.J. Angeles, The design of isotropic manipulator architectures in the presence of redundancies, Int J Robot Res 11: (3) pp. 196-201 (1992).
10.王志偉，”多餘軸等向性機器人之設計”，國立台灣科技大學機械工程技術研究所，2004年6月碩士論文。
11.W. S. Burniside, A. W. panton, The theory of equations, Dublin University Press, 1886.
12.L. W. Tsai, Robot analysis, John Wiley & Sons, Inc, 1999.