並聯機器人為過去三十年來機器人學術研究上之一個焦點，但是大部份之研究皆集中於史都華型機器人。本文探討3-PRSR並聯式機器人之方位工作空間，與其他類型之並聯式機器人相比，決定3-PRSR並聯式機器人之方位工作空間相對較為困難，其主要原因為此類機器人球窩接頭不位於工作平台上而使得運動等分析較為複雜，本文提出兩種方法求得方位工作空間之邊界曲面。第一個方法在並聯機器人上面建立三個運動學分析較為容易之虛擬三自由度串聯機器人，這些機器人之反位移分析解可輕易的解二次式求得，而並聯式機器人之方位工作空間則可藉由虛擬機器人之反位移分析解、座標變換以及一些搜尋步驟求得。另一個方法是以解三個非線性聯立方程式求得方位工作空間，此方法不需使用任何座標變換及搜尋步驟。

Parallel manipulators have been intensively studied over the past three decades, but most research works focused on Stewart manipulators. This thesis investigates the orientation workspace of a 3-PRSR parallel manipulator. Comparing to different types of parallel manipulators, the determination of orientation workspace of a 3-PRSR manipulator is a more difficult task because of the complexity in kinematics caused by the positions of the spherical joints (that are not on the platform). This work presents two methods to develop the orientation workspace. The first method introduces three virtual 3-DOF serial manipulators with simple kinematics on the parallel manipulator. The inverse kinematic solutions of the virtual manipulators can be easily obtained by solving quadratics, and the orientation workspace can be determined using the inverse kinematic solutions, coordinate transformations and some searching processes. The other method directly develops the orientation workspace by solving three non-linear equations, no coordinate transformation and searching process is needed by this approach.

[1]Fichter,E.F. “Stewart platform-based manipulator: general theory and practical construction” International Journal of Robotics Research, Volume 5, Issue 2, June 1986, Pages 157-182.
[2]Behi,Fariborz “Kinematic analysis for a six-degree-of-freedom 3-PRPS parallel mechanism” IEEE journal of robotics and automation, Volume 4, Issue 5, October 1988, Pages 561-565.
[3]Gosselin,C. “Determination of the workspace of 6-DOF parallel manipulators” Journal of mechanisms, transmissions, and automation in design, Volume 112, Issue 3, September 1990, Pages 331-336.
[4]Tahmasebi,Farhad , Tsai,Lung-Wen “Closed-form direct kinematics solution of a new parallel minimanipulator” Journal of Mechanical Design, Volume 116, 1993, Pages 1141-1147.
[5]Merlet,J.-P. “Determination of the orientation workspace of parallel manipulators” Journal of Intelligent and Robotic Systems, Volume 13, Issue 2, June 1995, Pages 143-160.
[6]Gosselin,C.M. , Jean,M. “Determination of the workspace of planar parallel manipulators with joint limits” Robotics and Autonomous Systems, Volume 17, Issue 3, May 1996, Pages 129-138.
[7]Byun,Y.K. , Cho,H.S. “Analysis of a novel 6-DOF, 3-PPSP parallel manipulator” International Journal of Robotics Research, Volume 16, Issue 6, 1997, Pages 859-872.
[8]Merlet,J.-P. , Gosselin,C.M. , Mouly,N. “Workspaces of planar parallel manipulators” Mechanism and Machine Theory, Volume 33, Issue 1-2, January 1998, Pages 7-20.
[9]Sima'an,N. , Glozman,D. , Shoham,M. “Design considerations of new six degrees-of-freedom parallel robots” IEEE International Conference on Robotics and Automation, Volume 2, 1998, Pages 1327-1333.
[10]Merlet,J.-P. “Determination of 6D workspaces of Gough-type parallel manipulator and comparison between different geometries” International Journal of Robotics Research, Volume 18, Issue 9, September 1999, Pages 902-916.
[11]Majid,M.Z.A. , Huang,Z. , Yao,Y.L. “Workspace analysis of a six-degrees of freedom, three-prismatic-prismatic-spheric-revolute parallel manipulator” International Journal of Advanced Manufacturing Technology, Volume 16, Issue 6, 2000, Pages 441-449.
[12]陳建中 「衡量並聯式機器人方向性工作空間之方法」 碩士論文，國立臺灣科技大學機械工程研究所，臺北，2002。
[13]Yang,Guilin “Design and Analysis of a 3-RPRS Modular Parallel Manipulator for Rapid Deployment” IEEE Advanced Intelligent Mechatronics, Volume 2, 2003, Pages 1250-1255.
[14]邱鈞鉦 「六自由度並聯式機器人方向性工作空間之研究」 碩士論文，國立臺灣科技大學機械工程研究所，臺北，2003。
[15]Tsai,K.Y. , Lin,J.C. “Determining the compatible orientation workspace of Stewart-Gough parallel manipulators” Mechanism and Machine Theory, Volume 41, Issue 10, October 2006, Pages 1168-1184.
[16]Hwang,Y.-K. , Yoon,J.-W. , Christiand , Ryu,J.-H. “The optimum design of a 6-DOF parallel manipulator with large orientation workspace” IEEE International Conference on Robotics and Automation, 2007, Article number 4209086, Pages 163-168.
[17]陳俊宏 「三鏈六自由度並聯式機器人方位工作空間之研究」 碩士論文，國立臺灣科技大學機械工程研究所，臺北，2009。
[18]Arrouk,K.A. , Bouzgarrou,B.C. , Gogu,G. “CAD based techniques for workspace analysis and representation of the 3-CRS parallel manipulator” 19th International Workshop on Robotics in Alpe-Adria-Danube Region, RAAD, 2010, Article number 5524591, Pages 155-160.
[19]Gan,Dongming “Design and kinematics analysis of a new 3-CCC parallel mechanism” Robotica, Volume 28, 2010, Pages 1065-1072.
[20]施宗佑 「特殊六自由度並聯式機器人方位工作空間之研究」 碩士論文，國立臺灣科技大學機械工程研究所，臺北，2010。