MIPS平台之正向奇異位置分析

Direct Kinematic Singularity Analysis of the Parallel Manipulator MIPS

馬智明(Chih-Ming Ma)

指導教授 ： 劉昭華

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2005年)

https://doi.org/10.6846/TKU.2005.00714

摘要

本研究的目的是說明機構速度分析的圖形法(graphical method for mechanism velocity analysis)可以用來尋找限制自由度(limited-DOF)並聯式機械手臂的正向奇異位置；限制自由度並聯式機械手臂是指從事空間運動的機械手臂但其自由度低於6。本研究是以三自由度MIPS並聯式機械手臂為對象，首先推導出此機械手臂的6×6 Jacobian矩陣，但由於尋找6×6矩陣行列式為零的位置較為不易，因此本研究中此矩陣是用來檢驗結果。本研究利用速度分析圖形法推導出當驅動器靜止時而活動平台速度不必為零的條件，此條件成立的位置即正向奇異位置，本文利用此條件尋找出數個機構的正向奇異位置，並代入6×6Jacobian矩陣以驗證結果。

關鍵字

MIPS並聯式機械手臂 ； 正向奇異位置 ； 速度分析圖形法

並列摘要

It is shown in this study the graphical method in velocity analysis may be used to locate direct singular positions of a limited-DOF parallel manipulator. The three DOF parallel manipulator MIPS is treated for illustration. The 6×6 Jacobian matrix for this manipulator is first derived. Since it is hard to deal with a 6×6 matrix, the Jacobian matrix is only used to verify solutions. In using the graphical method for velocity analysis, the conditions for the moving platform to become movable under zero driving speeds can be obtained. Manipulator configurations satisfying these conditions are direct singular positions. Several direct singular positions are found in this study and all these positions can make the 6×6 Jacobian matrix singular.

並列關鍵字

MIPS parallel manipulator ； Direct kinematic singularity ； graphical method in velocity analysis

參考文獻

[1] Merlet, J-P.,”First esperiments with MIPS 1(Mini IN-Parallel Positioning System)”, In ISER(International Symposium on Experimental Robotics), page 372-379, Barcelona, 15-18 Juan 1997.

[2] Merlet, J-P.,“Micro Parallel robot MIPS for medical applications”, Proceedings of the 2001 IEEE International Conference on Robotics 8 Automation Washington, DC 2001

[3] Merlet, J-P.,”Optimal design for the micro parallel robot MIPS”, Proceedings of the 2002 IEEE International Conference on Robotics 8 Automation Washington, DC May 2002

[4] Gosselin, C., and Angeles, J., “Singularity Analysis of Closed-Loop Kinematic Chains”, IEEE Transactions of Robotics and Automation, Vol. 6, pp. 281-290, 1990.

[5] Tsai, L-W., Robot Analysis：the Mechanics of Serial and Parallel Manipulators, John Wiley & Sons, Inc., New York, 1999.