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本論文電子全文於2011-03-10起於校外公開使用
本論文紙本於2011-03-10起公開使用

系統識別號	U0002-0903201109200800
DOI	10.6846/TKU.2011.00281
論文名稱(中文)	兩指抓取位置分析
論文名稱(英文)	An Analysis on Two-fingered Grasping Positions
第三語言論文名稱
校院名稱	淡江大學
系所名稱(中文)	機械與機電工程學系碩士班
系所名稱(英文)	Department of Mechanical and Electro-Mechanical Engineering
外國學位學校名稱
外國學位學院名稱
外國學位研究所名稱
學年度	99
學期	1
出版年	100
研究生(中文)	陳偉恩
研究生(英文)	Wei-En Chen
學號	697370111
學位類別	碩士
語言別	繁體中文
第二語言別
口試日期	2011-01-17
論文頁數	126頁
口試委員	指導教授 - 劉昭華委員 - 陳正光委員 - 王銀添委員 - 林鎮洲委員 - 楊智旭委員 - 劉昭華
關鍵字(中)	抓取接觸分析庫倫摩擦定律
關鍵字(英)	Grasping Contact analysis Coulomb Friction Law
第三語言關鍵字
學科別分類
中文摘要	論文提要內容：本文針對兩指抓取剛體的情況，每個抓取點都是摩擦點接觸的狀態。這情況下提出尋找最理想抓取位置的技巧。本文僅針對剛性球體從事分析，分析過程是利用逆向動力學會產生一階的不確定性，因此可選擇一個接觸力當作未定力，其他所有接觸力（抓取力）數值皆由此力決定，接觸點是否發生滑動也是由此力決定。因此藉由此單一的力可定義出最理想的抓取位置，也就是僅需要最小的正向力就可以避免滑動的位置。此外，本文亦藉由此未定力找出剛好無法抓取球體的位置，在這位置之內區域都是可以抓取的區域。
英文摘要	Abstract: A technique to determine the best grasping positions for a two-fingered grasping is suggested in this thesis. We utilize the fact that there is one degree of indeterminacy in an inverse dynamics problem; implying that one contact force may be chosen as the unspecified force, from which values of all other forces may be determined. Hence the condition for slipping can be expressed in terms of this force. We define the best grasping position as the one that requiring the minimum normal force, whose value is also determined by this unspecified force. In this thesis we only treated the case of grasping a spherical object. Results show that the best grasping position is always on the opposite sides of a great circle. The graspable region can also be determined by locating its boundary, which corresponds to the case that the discriminant of a quadratic equation becomes zero.
第三語言摘要
論文目次	目錄中文摘要......................................................................................................................I 英文摘要......................................................................................................................II 目錄.............................................................................................................................III 表目錄..........................................................................................................................V 圖目錄.........................................................................................................................XI 第一章序論.................................................................................................................1 1.1 前言.................................................................................................................1 第二章工件運動方程式之推導.................................................................................2 2.1 簡介.................................................................................................................2 2.2 運動方程式.....................................................................................................2 2.3 情況1：當phi不等於二分之pi,theta不等於二分之pi的狀況.................................................................6 2.4 情況2：當phi等於二分之pi,theta不等於二分之pi的狀況................................................................10 2.5 情況3：當phi不等於二分之pi,theta等於二分之pi的狀況................................................................12 2.6 情況4：當phi等於二分之pi,theta等於二分之pi的狀況................................................................14 2.7 情況5：當phi不等於二分之pi,theta等於負二分之pi的狀況................................................................16 2.8 情況6：當phi等於二分之pi,theat等於負二分之pi的狀況................................................................17 第三章滑動情況之接觸力.......................................................................................20 3.1 最理想的抓取位置.......................................................................................20 3.1.1 情況1：當phi不等於二分之pi,theta不等於二分之pi的狀況........................................................20 A 點產生滑動時的T4..................................................................................20 B 點產生滑動時的T4..................................................................................21 3.1.2 情況2：當phi等於二分之pi,theta不等於二分之pi的狀況........................................................22 A點產生滑動時的T4..................................................................................22 B點產生滑動時的T4..................................................................................22 3.1.3 情況3：當phi不等於二分之pi,theta等於二分之pi的狀況....................................................... 23 A 點產生滑動時的T3 .................................................................................23 B 點產生滑動時的 T3 .................................................................................23 3.1.4 情況4：當phi等於二分之pi,theta等於二分之pi的狀況........................................................24 A 點產生滑動時的 N1..................................................................................24 B 點產生滑動時的 N1..................................................................................24 3.1.5 情況5：當phi不等於二分之pi,theta等於負二分之pi的狀況........................................................25 A 點產生滑動時的 T3..................................................................................25 B 點產生滑動時的 T3..................................................................................25 3.1.6 情況6：當phi等於二分之pi,theat等於負二分之pi的狀況........................................................26 3.1.7 求出最理想抓取位置的數值程序....................................................................................................................26 3.2 可抓取區域....................................................................................................................27 第四章結果與討論....................................................................................................................30 第五章結論....................................................................................................................33 參考文獻....................................................................................................................34 表目錄表一當ax-gx=1;ay=gy;az=gz,αx有加速度，αz=0情況下的最理想抓取位置…………………………………………………………………………………35 表二當ax-gx=1;ay=gy;az=gz,αx=0，αz有加速度情況下的最理想抓取位置…………………………………………………………………………………36 表三當ax-gx=1;ay=gy;az=gz,x αx與αz有加速度情況下的最理想抓取位置…………………………………………………………………………………37 表四當ax-gx=1;ay=gy;az=gz,αx=αz情況下的最理想抓取位置…………………………………………………………………………………38 表五當ax=gx;ay-gy=1;az=gz,αx有加速度,αz=0情況下的最理想抓取位置…………………………………………………………………………………39 表六當ax=gx;ay-gy=1;az=gz,αx=0,αz有加速度情況下的最理想抓取位置…………………………………………………………………………………40 表七當ax=gx;ay-gy=1;az=gz,αx與αz有加速度情況下的最理想抓取位置…………………………………………………………………………………41 表八當ax=gx;ay-gy=1;az=gz,αx=αz情況下的最理想抓取位置…………………………………………………………………………………42 表九當ax=gx;ay-gy=-1;az=gz,αx有加速度，αz=0情況下的最理想抓取位置..........................................................................................................................43 表十當ax=gx;ay-gy=-1;az=gz,αx=0,αz有加速度情況下的最理想抓取位置..........................................................................................................................44 表十一當ax=gx;ay-gy=-1;az=gz,αx與αz有加速度情況下的最理想抓取位置..........................................................................................................................45 表十二當ax=gx;ay-gy=-1;az=gz,αx=αz情況下的最理想抓取位置..........................................................................................................................46 表十三當ax=gx;ay=gy;az-gz=1,αx有加速度,αz=0情況下的最理想抓取位置..........................................................................................................................47 表十四當ax=gx;ay=gy;az-gz=1,αx=0,αz有加速度情況下的最理想抓取位置..........................................................................................................................48 表十五當ax=gx;ay=gy;az-gz=1,αx與αz有加速度情況下的最理想抓取位置..........................................................................................................................49 表十六當ax=gx;ay=gy;az-gz=1,αx=αz情況下的最理想抓取位置..........................................................................................................................50 表十七當ax-gx=1;ay-gy=1;az=gz,αx有加速度,αz=0情況下的最理想抓取位置..........................................................................................................................51 表十八當ax-gx=1;ay-gy=1;az=gz,αx=0,αz有加速度情況下的最理想抓取位置..........................................................................................................................52 表十九當ax-gx=1;ay-gy=1;az=gz,αx與αz有加速度情況下的最理想抓取位置..........................................................................................................................53 表二十當ax-gx=1;ay-gy=1;az=gz,αx=αz情況下的最理想抓取位置..........................................................................................................................54 表二十一當ax-gx=1;ay-gy=-1;az=gz,αx有加速度,αz=0情況下的最理想抓取位置................................................................................................................................55 表二十二當ax-gx=1;ay-gy=-1;az=gz,αx=0,αz有加速度情況下的最理想抓取位置................................................................................................................................56 表二十三當ax-gx=1;ay-gy=-1;az=gz,αx與αz有加速度情況下的最理想抓取位置................................................................................................................................57 表二十四當ax-gx=1;ay-gy=-1;az=gz,αx=αz情況下的最理想抓取位置................................................................................................................................58 表二十五當ax=gx;ay-gy=1;az-gz=1,αx有加速度αz=0情況下的最理想抓取位置................................................................................................................................59 表二十六當ax=gx;ay-gy=1;az-gz=1,αx=0,αz有加速度情況下的最理想抓取位置................................................................................................................................60 表二十七當ax=gx;ay-gy=1;az-gz=1,αx與αz有加速度情況下的最理想抓取位置................................................................................................................................61 表二十八當ax=gx;ay-gy=1;az-gz=1,αx=αz情況下的最理想抓取位置................................................................................................................................62 表二十九當ax=gx;ay-gy=-1;az-gz=1,αx有加速度,αz=0情況下的最理想抓取位置................................................................................................................................63 表三十當ax=gx;ay-gy=-1;az-gz=1,αx=0,αz有加速度情況下的最理想抓取位置................................................................................................................................64 表三十一當ax=gx;ay-gy=-1;az-gz=1,αx與αz有加速度情況下的最理想抓取位置................................................................................................................................65 表三十二當ax=gx;ay-gy=-1;az-gz=1,αx=αz情況下的最理想抓取位置................................................................................................................................66 表三十三當ax-gx=1;ay=gy;az-gz=1,αx有加速度,αz=0情況下的最理想抓取位置................................................................................................................................67 表三十四當ax-gx=1;ay=gy;az-gz=1,αx=0,αz有加速度情況下的最理想抓取位置................................................................................................................................68 表三十五當ax-gx=1;ay=gy;az-gz=1,αx與αz有加速度情況下的最理想抓取位置................................................................................................................................69 表三十六當ax-gx=1;ay=gy;az-gz=1,αx=αz情況下的最理想抓取位置................................................................................................................................70 表三十七當ax-gx=1;ay-gy=1;az-gz=1,αx有加速度,αz=0情況下的最理想抓取位置................................................................................................................................71 表三十八當ax-gx=1;ay-gy=1;az-gz=1,αx=0,αz有加速度情況下的最理想抓取位置................................................................................................................................72 表三十九當ax-gx=1;ay-gy=1;az-gz=1,αx與αz有加速度情況下的最理想抓取位置................................................................................................................................73 表四十當ax-gx=1;ay-gy=1;az-gz=1,αx=αz情況下的最理想抓取位置................................................................................................................................74 表四十一當ax-gx=1;ay-gy=-1;az-gz=1,αx有加速度,αz=0情況下的最理想抓取位置................................................................................................................................75 表四十二當ax-gx=1;ay-gy=-1;az-gz=1,αx=0,αz有加速度情況下的最理想抓取位置................................................................................................................................76 表四十三當ax-gx=1;ay-gy=-1;az-gz=1,αx與αz有加速度情況下的最理想抓取位置................................................................................................................................77 表四十四當ax-gx=1;ay-gy=-1;az-gz=1,αx=αz情況下的最理想抓取位置................................................................................................................................78 表四十五當ax=gx;ay=gy;az=gz,αx有加速度,αz=0情況下的最理想抓取位置................................................................................................................................79 表四十六當ax=gx;ay=gy;az=gz,αx=0,αz有加速度情況下的最理想抓取位置................................................................................................................................80 表四十七當ax=gx;ay=gy;az=gz,αx與αz有加速度情況下的最理想抓取位置................................................................................................................................81 表四十八當ax=gx;ay=gy;az=gz,αx=αz情況下的最理想抓取位置................................................................................................................................82 表四十九當ax=gx;ay-gy=1;az=gz,αx=0,αz有加速度情況下的最理想抓取位置................................................................................................................................83 X 圖目錄圖1 一個半徑為r的實心球受到在A點的抓取力N1、T1及T2和受到在B 點的抓取力N2、T3及T4 ................................................................................................................................84 圖2 所有的力對AB所產生的力矩等於慣性力ma及慣性力矩Iα對AB所產生的合力矩.................................................................................................................................85 圖3 A點或B點的接觸力.................................................................................................................................86 圖4 當ax-gx=1;ay=gy;az=gz,αx=1,αz=5情況下的可抓取區域.................................................................................................................................87 圖5 當ax-gx=1;ay=gy;az=gz,αx=5,αz=1情況下的可抓取區域................................................................................................................................88 圖6 當ax-gx=1;ay=gy;az=gz,αx=2.5,αz=2.5情況下的可抓取區域................................................................................................................................89 圖7 當ax=gx;ay-gy=1;az=gz,αx=1,αz=5情況下的可抓取區域................................................................................................................................90 圖8 當ax=gx;ay-gy=1;az=gz,αx=5,αz=1情況下的可抓取區域................................................................................................................................91 圖9 當ax=gx;ay-gy=1;az=gz,αx=2.5,αz=2.5情況下的可抓取區域................................................................................................................................92 圖10 當ax=gx;ay-gy=-1;az=gz,αx=1,αz=5情況下的可抓取區域................................................................................................................................93 圖11 當ax=gx;ay-gy=-1;az=gz,αx=5,αz=1情況下的可抓取區域................................................................................................................................94 圖12 當ax=gx;ay-gy=-1;az=gz,αx=2.5,αz=5.5情況下的可抓取區域................................................................................................................................95 圖13 當ax=gx;ay=gy;az-gz=1,αx=1,αz=5情況下的可抓取區域................................................................................................................................96 圖14 當ax=gx;ay=gy;az-gz=1,αx=5,αz=1情況下的可抓取區域................................................................................................................................97 圖15 當ax=gx;ay=gy;az-gz=1,αx=2.5,αz=2.5情況下的可抓取區域................................................................................................................................98 圖16 當ax-gx=1;ay-gy=1;az=gz,αx=1,αz=5情況下的可抓取區域................................................................................................................................99 圖17 當ax-gx=1;ay-gy=1;az=gz,αx=5,αz=1情況下的可抓取區域...............................................................................................................................100 圖18 當ax-gx=1;ay-gy=1;az=gz,αx=2.5,αz=2.5情況下的可抓取區域...............................................................................................................................101 圖19 當ax-gx=1;ay-gy=-1;az=gz,αx=1,αz=5情況下的可抓取區域...............................................................................................................................102 圖20 當ax-gx=1;ay-gy=-1;az=gz,αx=5,αz=1情況下的可抓取區域...............................................................................................................................103 圖21 當ax-gx=1;ay-gy=1;az=gz,αx=2.5,αz=2.5情況下的可抓取區域...............................................................................................................................104 圖22 當ax=gx;ay-gy=1;az-gz=1,αx=1,αz=5情況下的可抓取區域...............................................................................................................................105 圖23 當ax=gx;ay-gy=1;az-gz=1,αx=5,αz=1情況下的可抓取區域...............................................................................................................................106 圖24 當ax=gx;ay-gy=1;az-gz=1,αx=2.5,αz=2.5情況下的可抓取區域...............................................................................................................................107 圖25 當ax=gx;ay-gy=-1;az-gz=1,αx=1,αz=5情況下的可抓取區域...............................................................................................................................108 圖26 當ax=gx;ay-gy=-1;az-gz=1,αx=5,αz=1情況下的可抓取區域...............................................................................................................................109 圖27 當ax=gx;ay-gy=1;az-gz=1,αx=2.5,αz=2.5情況下的可抓取區域...............................................................................................................................110 圖28 當ax-gx=1;ay=gy;az-gz=1,αx=1,αz=5情況下的可抓取區域...............................................................................................................................111 圖29 當ax-gx=1;ay=gy;az-gz=1,αx=5,αz=1情況下的可抓取區域...............................................................................................................................112 圖30 當ax-gx=1;ay=gy;az-gz=1,αx=2.5,αz=2.5情況下的可抓取區域...............................................................................................................................113 圖31 當ax-gx=1;ay-gy=1;az-gz=1,αx=1,αz=5情況下的可抓取區域...............................................................................................................................114 圖32 當ax-gx=1;ay-gy=1;az-gz=1,αx=5,αz=1情況下的可抓取區域...............................................................................................................................115 圖33 當ax-gx=1;ay-gy=1;az-gz=1,αx=2.5,αz=2.5情況下的可抓取區域...............................................................................................................................116 圖34 當ax-gx=1;ay-gy=-1;az-gz=1,αx=1,αz=5情況下的可抓取區域...............................................................................................................................117 圖35 當ax-gx=1;ay-gy=-1;az-gz=1,αx=5,αz=1情況下的可抓取區域...............................................................................................................................118 圖36 當ax-gx=1;ay-gy=1;az-gz=1,αx=2.5,αz=2.5情況下的可抓取區域...............................................................................................................................119 圖37 當ax=gx;ay=gy;az=gz,αx=1,αz=5情況下的可抓取區域 .................................................................................................................................120 圖38 當ax=gx;ay=gy;az=gz,αx=5,αz=1情況下的可抓取區域 .................................................................................................................................121 圖39 當ax=gx;ay=gy;az=gz,αx=2.5,αz=2.5情況下的可抓取區域...............................................................................................................................122 圖40 當ax-gx=1;ay-gy=1;az=gz,αx=1,αz=1情況下的可抓取區域 (μ = 0.5) ............................................................................................................................123 圖41 當ax-gx=1;ay-gy=1;az=gz,αx=1,αz=1情況下的DB 數值 (phi= 0.15pi).........................................................................................................................124 圖42 當ax-gx=1;ay-gy=1;az=gz,αx=1,αz=1情況下的DB數值 (phi= 0.2pi)..........................................................................................................................125 圖43 當ax-gx=1;ay-gy=1;az=gz,αx=1,αz=1情況下的DA數值 (phi=0.25*pi)....................................................................................................................126
參考文獻	參考文獻 [1] Faverjon, B., and Ponce, J., On Computing Two-finger Force-closure Grasps of Curved 2D Objects, Proceedings - IEEE International Conference on Robotics and Automation, v 1, p 424-429, 1991. [2] Chen, I-M., and Burdick, J.W., Finding Antipodal Point Grasps on Irregularly Shaped Objects, IEEE Transactions on Robotics and Automation, v 9, n 4, p 507-512, 1993. [3] Nguyen, V., Constructing Force-Closure Grasps, International Journal of Robotics Research, v 7, n 3, pp 3-16, 1988. [4] Adán, A., Vázquez, A.S., and Molina, F., 3D Grasping Solutions Through MWS Models, Proceedings of 2005 International Conference on Advanced Robotics, v 2005, p 186-193, 2005. [5] Walker, I. D., Freeman, R. A., and Marcus, S.I., Analysis of Motion and Internal Loading of Objects Grasped by Multiple Cooperating Manipulators, International Journal of Robotics Research, v 10, n 4, p 396-409, 1991. [6] Park, J, Determining Contact Force Distribution for Enveloping Grasps: Subspace Structure and Dynamic Balance, Proceedings of the 2002 IEEE International Conference on Robotics and Automation, pp. 2912-2917, 2002. [7] Cheng, F-T., and Orin, D. E., Efficient Algorithm for Optimal Force Distribution-The Compact-dual LP Method, IEEE Transactions on Robotics and Automation, v 6, n 2, p 178-187, 1990.
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