多餘軸機器人理論上有無限多之構形可到達一指定之位置及方位，因此機器人可輕易的避開障礙物及奇異點，而且在軌跡規劃時可選擇最短路徑、最少能量等各種最佳路徑。目前在學術研究上有相當多關於多餘軸機器人方面之論文，但是絕大多數之論文集中於控制領域，藉由控制之方法使機器人避開奇異點或障礙物，增加操控性或產生各種最佳路徑。本文將提出方法設計具有較佳操控性以及較不易接近奇異點之四自由度多餘軸機器人。
　　工業機器人之構造較為簡單，不但可減少連桿間干涉現象而且運動學分析相對較為容易，因此以工業機器人為基礎設計多餘軸機器人為一個相當理想之方法。本文將利用此方法提出四種多餘軸機器人之設計並進行奇異點分析，由分析結果發現此類機器人只要少數幾個軸位移到達某些固定角度即到達奇異點，因此只要給予適當軸位移限制即可避開相當多之奇異點而減少機器人到達奇異點之機率。此外本文亦求得各種不同尺寸機器人之整體操控性並將所得結果列表整理以供為設計具較佳操控性多餘軸機器人之參考。

A redundant manipulator, in theory, has infinite number of configurations to reach a point in task space, so the manipulator can easily get around singular positions or obstacles, and different types optimal paths(such as minimum distance or minimum energy) can be used in trajectory planning. Redundant manipulators have been intensively investigated, but most research interests focus on presenting control techniques to avoid singularity or obstacles, to increase dexterity, or to generate different types of optimal paths. This thesis proposes methods to develop 4-DOF redundant manipulators with better dexterity and less singular surfaces.
An industrial manipulator usually has simple kinematics and less link interactions due to its special link parameters, so it is a good method to develop redundant manipulators from industrial manipulators. This work employs this approach to develop four redundant manipulators and studies their singularities. The results show that many singular surfaces are generated by a few joints at some specific displacements. Therefore, properly choosing joint ranges can significantly reduce the number of singular surfaces. The global dexterities of a lot of manipulators with different link dimensions are also evaluated, and the obtained data are tabulated that can be used to develop redundant manipulators with better dexterity.

[1]　Denavit, J. and Hartenberg, R.S., 1955, “A Kinematic Notation for Lower Pair Mechanisms Based on Matrices,” ASME J. Appl. Mech., Vol. 77, pp.215-221.
[2]　Ziqiang Mao and T.C. Hsia, 1997, “Obstacle avoidance inverse kinematics solution of redundant robots by neural networks”, Robotica, Vol. 15, No. 1, pp. 3-10.
[3]　J. A. Kuo and D. J. Sanger, 1997, “Task planning for serial redundant manipulators”, Robotica, Vol. 15, No. 1, pp. 75-83.
[4]　Arati S. Deo and Ian D. Walker, 1997, “Minimum Effort Inverse Kinematics for Redundant Manipulators”, IEEE Transactions on Robotics and Automation, Vol. 13, No. 5, pp. 767-775.
[5]　Chieh-Li Ghen and Chih-Jer Lin, 1997, “Motion planning of Redundant Robots”, Journal of Robotic Systems, Vol. 14, No. 12, pp. 839-850.
[6]　Tzu-Chen Liang and Jing-Sin Liu, 1999, “An Improved Trajectory Planner for Redundant Manipulators in Constrained Workspace”, Journal of Robotic Systems, Vol. 16, No. 6, pp. 339-351.
[7]　V. Perdereau, C. Passi, and M. Drouin, 2002, “Real-time control of redundant robotic manipulators for mobile obstacle avoidance”, Robotics and Autonomous Systems, Vol. 41, No. 1, pp. 41-59.
[8]　Rene V. Mayorga and Pronnapa Sanongboon, 2005, “Inverse kinematics and geometrically bounded singularities prevention of redundant manipulators: An Artificial Neural Network approach”, Robotics and Autonomous Systems, Vol. 53, No. 3-4, pp. 164-176.
[9]　Bhaskar Dasgupta, Akhil Gupta, and Ekta Singla, 2009, “A variational approach to path planning for hyper-redundant manipulators”, Robotics and Autonomous Systems, Vol. 57, No. 2, pp. 194-201.
[10]　Swagat Kumar, Laxmidhar Behera, and T.M. McGinnity, 2010, “Kinematic control of a redundant manipulator using an inverse-forward adaptive scheme with a KSOM based hint generator”, Robotics and Autonomous Systems, Vol. 58, No. 5, pp. 622-633.
[11]　Michael Kauschke, 1996, “Closed form solutions applied to redundant serial link manipulators”, Mathematicas and Computers in Simulation, Vol. 41, No. 5-6, pp. 509-516.
[12]　Iman Ebrahimi, Juan A. Carretero, and Roger Boudreau, 2008, “Kinematic analysis and path planning of a new kinematically redundant planar parallel manipulator”, Robotica, Vol. 26, No.3, pp. 405-413.
[13]　Masayuki Shimizu, Hiromu Kakuya, Woo-Keun Yoon, Kosei Kitagaki, and Kazuhiro Kosuge, 2008, “Analytical Inverse Kinematic Computation for 7-DOF Redundant Manipulators With Joint Limits and Its Application to Redundancy Resolution”, IEEE Transactions on Robotics, Vol. 24, No. 5, pp. 1131-1142.
[14]　J Gallardo-Alvarado and J M Rico-Martinez, 2009, “Kinematics of a hyper-redundant manipulator by means of screw theory”, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, Vol. 223, No. 4, pp. 325-334.
[15]　Yunfeng Wang and Gregory S. Chirikjian, 2004, “Workspace generation of hyper-redundant manipulators as a diffusion process on SE(N) ”, IEEE Transactions on Robotics and Automation, Vol. 20, No. 3, pp. 399-408.
[16]Mircea Badescu and Constantinos Mavroidis, 2004, “New Performance Indices and Workspace Analysis of Reconfigurable Hyper-Redundant Robotic Arms”, The International Journal of Robotics Research, Vol. 23, No. 6, pp. 643-659.
[17]　Samer Yahya, M. Moghavvemi, and Haider A.F. Mohamed, 2011, “Geometrical approach of planar hyper-redundant manipulators: Inverse kinematics, path planning and workspace”, Simulation Modelling Practice and Theory, Vol. 19, No. 1, pp. 406-422.
[18]　Yanming Li, Peisun Ma, Changjun Qin, Xueguan Gao , Jianbin Wang, and Haihong Zhu, 2003, “Design and study of a novel hyper-redundant manipulator”, Robotica, Vol. 21, No. 5, pp. 505-509.
[19]　K. Y. Tsai and Z. W. Wang, 2005, “The design of redundant isotropic manipulators with special link parameters”, Robotica, Vol. 23, No. 2, pp. 231-237.
[20]　Maher G. Mohamed and Clément M. Gosselin, 2005, “Design and analysis of kinematically redundant parallel manipulators with configurable platforms”, IEEE Transactions on Robotics, Vol. 21, No. 3, pp. 277-287.
[21]　KeJun Ning and Florentin Worgotter, 2009, “A Novel Concept for Building a Hyper-Redundant Chain Robot”, IEEE Transactions on Robotics, Vol. 25, No. 6, pp. 1237-1248.
[22]　Jaime Gallardo-Alvarado, Raul Lesso-Arroyo, and J. Santos Garcia-Miranda, 2011, “A worm-inspired new spatial hyper-redundant manipulator”, Robotica, Vol. 29, No. 4, pp. 571-579.
[23]　Charles W. Wampler, 1986, “Manipulator inverse kinematic solutions based on vector formulations and damped least-squares methods”, IEEE Transactions on Systems, Man and Cybernetics, Vol. 16, No. 1, pp.93-101.
[24]　Jon Kieffer, 1991, “A view of singularities in manipulator inverse kinematics”, Fifth International Conference on Advanced Robotics, Robots in Unstructured Environments, vol. 1, pp. 668 - 671.
[25]　Manja V. Kircanski, 1993, “Inverse kinematic problem near singularities for simple manipulators: Symbolical damped least-squares solution”, IEEE International Conference on Robotics and Automation, Vol. 1, pp.974-979.
[26]　Fan-Tien Cheng, Tzung-Liang Hour, York-Yin Sun, and Tsing-Hua Chen, 1997, “Study and Resolution of Singularities for a 6-DOF PUMA Manipulator”, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol. 27, No. 2, pp. 332-343.
[27]　Fan-Tien Cheng, Jeng-Shi Chen, and Fan-Chu Kung, 1998, “Study and Resolution oF Singularities for 7-DOF Redundant Manipulator”, IEEE Transactions on Industrial Electronic, Vol. 45, No. 3, pp. 469-480.
[28]　歐陽妏青，2011，“工業機器人之奇異點分析”，國立臺灣科技大學機械工程研究所，碩士論文。
[29]　余汯育，2010，“機器人操控性曲面及應用”，國立臺灣科技大學機械工程研究所，7月碩士論文。
[30]　呂易達，2009，“七軸機器人反位移分析之研究”，國立臺灣科技大學機械工程研究所，7月碩士論文。