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系統識別號 U0002-0903201109200800
中文論文名稱 兩指抓取位置分析
英文論文名稱 An Analysis on Two-fingered Grasping Positions
校院名稱 淡江大學
系所名稱(中) 機械與機電工程學系碩士班
系所名稱(英) Department of Mechanical and Electro-Mechanical Engineering
學年度 99
學期 1
出版年 100
研究生中文姓名 陳偉恩
研究生英文姓名 Wei-En Chen
電子信箱 a0922335857@yahoo.com.tw
學號 697370111
學位類別 碩士
語文別 中文
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
中文關鍵字 抓取  接觸分析  庫倫摩擦定律 
英文關鍵字 Grasping  Contact analysis  Coulomb Friction Law 
學科別分類 學科別應用科學機械工程
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.
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= 0.15*pi).........................................................................................................................124
圖42 當ax-gx=1;ay-gy=1;az=gz,αx=1,αz=1情況下的DB數值
(phi= 0.2*pi)..........................................................................................................................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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