本研究將HEXA並聯式機械手臂修改為6RUS並聯式機械手臂，使得正向位置分析的閉合解可以求出。本論文並從事此6RUS機構之工作空間、正向奇異位置以及剛性分析。在正向位置分析過程中，首先將6RUS機構簡化為等效3RS結構，利用活動平台之球窩接頭間的距離為已知長度，推導出三個多項式方程式，再使用席維斯透析消去法(Sylvester dialytic elimination method)求得正向位置之解。本論文利用逆向位置分析技巧求出此機構的定向工作空間與方向工作空間。
    本研究使用螺旋理論，求出螺旋Jacobian矩陣，同時亦求出HEXA並聯式機械手臂螺旋Jacobian矩陣，利用此矩陣可得到6RUS與HEXA並聯式機械手臂的正向奇異位置與中心結構時的剛性。

In this dissertation, the structure of the 6 degree-of-freedom parallel manipulator HEXA is modified to take a 6RUS form so that closed-form solutions for direct kinematic analysis can be found. In addition, workspace analysis, direct singular position analysis, and stiffness analysis on this 6RUS manipulator are also performed. In direct kinematic analysis, the manipulator is first transformed into an equivalent 3RS structure, and then three polynomial equations are obtained by using the property of constant length between three spherical joints on the moving platform. Sylvester dialytic elimination method is used to obtain direct kinematic solutions. Constant orientation workspace and orientation workspace are found by performing inverse position analysis.
    Jacobian matrices of HEXA and the 6RUS manipulator are obtained by using screw theory. Certain direct singular positions of the two manipulators are found from these matrices. Also determined from the Jacobian matrices is the stiffness of central configuration of the two manipulators.

目 錄

中文摘要	I
英文摘要	II
目錄	III
圖目錄	V
表目錄	VIII
第一章 緒論	1
1.1 文獻回顧	1
1.2 研究動機	3
第二章 6RUS機構之組成	4
2.1 6RUS並聯式機械手臂之結構	4
2.2 機構之尺寸設計	4
第三章 正向位置分析	6
3.1 交圓圓心及交圓半徑	7
3.2 等效3RS結構	9
3.3 逆向位置分析	15
第四章 位置分析結果與討論	17
第五章 工作空間	21
5.1 工作空間方程式	23
5.2 定向工作空間與方向工作空間	24
第六章 工作空間結果與討論	26
6.1 定向工作空間	26
6.2 方向工作空間	27
第七章 正向奇異位置分析	28
7.1 螺旋Jacobian矩陣之推導(Screw-based Jacobian)	29
7.2 HEXA並聯式機械手臂之螺旋Jacobian矩陣	32
7.3 正向奇異位置	33
第八章 剛性分析	37
第九章 結論	44
參考文獻	46
附錄A 席維斯透析消去法	52
附錄B WAi、WBi與WCi	59

圖 目 錄

圖1  HEXA並聯式機械手臂	60
圖2  6RUS並聯式機械手臂	61
圖3  基座與驅動角度示意圖	62
圖4  兩圓球交圓所在之平面	63
圖5  等效3RS結構	64
圖6   與 座標系之座標轉換	65
圖7  驅動角40°-40°-40°-40°-40°-40°時之機構構形3	66
圖8  驅動角40°-40°-40°-40°-40°-40°時之機構構形4	67
圖9  驅動角40°-40°-40°-40°-40°-40°時之機構構形1	68
圖10  驅動角40°-40°-40°-40°-40°-40°時之機構構形2	69
圖11  驅動角40°-40°-40°-40°-40°-40°時之機構構形7	70
圖12  驅動角40°-40°-40°-40°-40°-40°時之機構構形5	71
圖13  驅動角80°-70°-90°-60°-110°-100°時之機構構形1	72
圖14  驅動角80°-70°-90°-60°-110°-100°時之機構構形2	73
圖15  驅動角80°-70°-90°-60°-110°-100°時之機構構形3	74
圖16  驅動角80°-70°-90°-60°-110°-100°時之機構構形4	75
圖17  兩組 解	76
圖18  Bryant Angles座標轉換	77
圖19  ( )=(0, 0, 0)， =1， 關係圖	78
圖20  ( )=(0, 0, 0)， =0.25， 關係圖	79
圖21  ( )=(0, 0, 0)， =0.5， 關係圖	80
圖22  ( )=(0, 0, 0)， =2， 關係圖	81
圖23  ( )=(0, 0, 0)， =3， 關係圖	82
圖24  ( )=(0, 0, 0)， =3.5， 關係圖	83
圖25  ( )=(0, 0.5, 3)， ， 關係圖	84
圖26  ( )=(0, 0.5, 3)， ， 關係圖	85
圖27  ( )=(0, 0.5, 3)， ， 關係圖	86
圖28  ( )=(0, 0.5, 3)， ， 關係圖	87
圖29  ( )=(0, 0.5, 3)， ， 關係圖	88
圖30  ( )=(0, 0.5, 3)， ， 關係圖	89
圖31  ( )=(0, 0.5, 3)， ， 關係圖	90
圖32  ( )=(0, 0.5, 3)， ， 關係圖	91
圖33  ( )=(0, 0.5, 3)， ， 關係圖	92
圖34  ( )=(0, 0.5, 3)， ， 關係圖	93
圖35  ( )=(0, 0.5, 3)， ， 關係圖	94
圖36  ( )=(0, 0.5, 3)， ， 關係圖	95
圖37  ( )=(0, 0.5, 3)， ， 關係圖	96
圖38  螺旋座標示意圖	97
圖39  (a)6RUS第一種位置示意圖 (b)YZ面側視圖	98
圖40  (a)HEXA第一種位置示意圖 (b)YZ面側視圖	99
圖41  6RUS第二種位置示意圖	100
圖42  HEXA第二種位置示意圖	101
圖43  HEXA第三種位置示意圖	102
圖44  6RUS第三種位置示意圖	103
圖45  (a)6RUS第四種位置示意圖 (b)YZ面側視圖	104
圖46  (a)HEXA第四種位置示意圖 (b)YZ面側視圖	105

表 目 錄

表1  6RUS機構尺寸表(位置分析)	17
表2  40°-40°-40°-40°-40°-40°活動平台位置表	18
表3  80°-70°-90°-60°-110°-100°活動平台位置表	19
表4  逆向位置分析數據表	20
表5  6RUS機構尺寸表(工作空間)	26

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