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详细说明：工业机器人机构误差分析pdf,工业机器人机构误差分析肾部
腕部
腰部
机座
5
∧BB6自由度型机器人本体结构由回转的机体、大臂、小臂和腕部等部分组
成,共有6个自由度,属于关节型机器人,每个关节均有角度零位与正负方向限
位开关。机器人的回转机体实现机器人机体绕轴的回转(角01),它由固定底座
和回转工作台组成。安装在轴中心的驱动电机经传动装置,可实现工作台回转
大臂、小臂的平衡由机器人屮的平衡装置控制,在机器人的回转工作台上安装有
大臂台应,将大臂下端关节支承在台座上,大臂的上端关节用于支承小臂。大臂
臀体的下端安有直流伺服电机,可控制人臀上下摆动(角θ2)。小臂支承于人臀
臂体的上关节处,其驱动电机可带动小臂做上下俯仰(角θ3),以及小臂的回转
(角θ4)。机器人旳腕部位于小臂臂体前端,通过伺服电动机传动,可实现腕部
摆动(角θ5和转动(角θ6)。各关节处均安装有传感器,可输出关节的位置信号,
并反馈给控制系统,实现各部分协同⊥作。
从而使DH法建立运动方程,如下图1所示。主要有以下几个参数:
1连杆长度记为a
2杆打转角记为a
3连杆偏移量记为d
4.关节角记为θ
Z
2
(图1)
为了运动分析的方便,建立如图2所示的丛标系。其中所有坐标系均遵守
右手定则。ABB6R型机器人各杆件的结构参数和运动参数如表1所示。
5
4
66
v6
21A
日?
1
1
(图2)
根据资料所得的该机器人结构参数和运动参数如表1所示。
表1结构参数和运动参数
a1(ge)d28(ge)关节变量范围()
00
90
-180~180
2
-90
90
90-110
0
230~50
3
90
d
200~200
5o 90
0
120~120
6
90
400-400
其中ar=70mm,a2=360mm,a3=0mm,d4=380mm。
2运动学方程的建立
连朴坐标系{相对于{i-1}的齐次变换称为连村变换,可以把它分解为坐标系{
的四个基本子变换问题,每个子变换只依赖于一个连杆参数,这四个子变换是:
(1)绕x1转列l11
2)沿x1移动a
(3)绕x转动O
(4)沿移动d
在D-H法中相邻坐标间的矩阵即DH矩阵如下式:
COS
SIn
A
sin 8, cos a- cos 8, cos a--sin a -d, sin a-1
sin e, sin a_ cos 6, sin a- cos a- d cos a_
从而求得A1-A6分别为:
cos
B - 0 0
A==
sin
Cos
010
001
COS
-sIn
马==/0
SIlL
18,-cos 82
0
0
cos
s B3 - sin e3 0
COS
10
COs a4-sin B4 0 a3
0
0
sIn
164-cos400
0
0
cos 8. - e,00
0-10
sin e cose 00
00
cos 86-sin 86 00
SIne
6-cos6600
由此可得A-A6,从而得到运动学方程为
4=”P
6
0.a.D.|=4414,44
0001
其中a,on三个矢量描述机器人空间的姿态;p为手部位置在基准参考系中的坐
标
利用 MATLAB软件编稈求得A为(xi=θ;):
>> sym2 x1 x2 x3 x5 x6 al a2 a3 d4
A1=[Co(x1)-sin(x1)00;sin(x1}cos(x1】00;0010;0001
A2=[Cs(x2)-s⊥n(x2)0a1;0010;-sin1(x2}=Cus(x2)00;0031
A3=LCos(x3)sin(x3)0a2;sn(x3)c3sx3)00;310;0001」
24=[coa(x4)-sin(x4)0a3;001d4;-sin(x4)-cos(x4)00;0001
A5=[c。a(5)-5n(X5)00;00-10;3inix5)cos(x5)00;0001]
A6-[Coa(X6)-sin(x5)00;0010;-sinx6)-ccs(x6)00;00011
A=A1大A2A3+A4+A5+A5
Sp(A);
Al
[=sx-);-sin(x1),
0]
sinix
0
0
1
A?
2),-sin(x2)
0
0,
0
[ -sin(x2),-cos(x2)
0]
0
A3
I cos (x3)-sin(x3),
a21
nix
x3)
0
0
A4=
cos:x4)r-sin(x4)
a31
I -sin(x4)
⊙s(x4)
0
1
As
cos(x5)r-sin(x5),
0,
0]
0
5),cs(x5)
Au
「cog{x6)r-sin(x6),
0
0
[-sin(x6)
s(x5)
0]
0
1
L(((c。s(x1)+coS(x2)+cos(3)C;x1)s1n(x2)s1n(x3))C5x4)+B1n(x1
)*sir.(x4))*COs(x5)+(-cos(x1)*cos(x2)*sin(x3)-cos(xl)*sin(x2)*Cos(x3)
9in(K5))*c。3(x6)-((⊙3(x1)c3(x2)*c3(x3)-C(X1)*sin(K2)*sin(x3))
sin(x4)-sin(x1,*cos(x4))*sin(x6)
(((c0a(81)+cos(82)*08(3)-c08(X1)+s1n(x2)*s⊥r(x3))teos(4)+sin(x1)
sin(x4))*cos(x5)I( co8(x1)*cos(x2)*sin(x3: CCs(x1)*sin(x2)*C08(x3))*s
in(x5))sin(x6}-((CUs(×1)*Cos(x2)*C:s!x3)-Cos(x1)*s⊥n(x2)*sin(×3))*s⊥
n(x)-Ein(x1)*Cos(x4))*cos(x6
(cs(x1)+cos(x2)*c。s(x3)-cs(x1)*sin(x2}*sin(x3))*c5(x4)+sin(x1)*s
in(x4})*sin(x5)+(-cs(x1)cos(×2)ksinx3)-cos(x1)*sin(x2)c5(x3))c
s(x5)
(ccs(xl)*cos(x2)*cos(x3)-ccis(xl)*sin(x2)*sin(x3))*a3+(-cCis(xl)*cos(x2
)ts1r(x3)-c(x1)*a1n(x2)tco8(X3))*4+C8(81)*cs(2)a2+C8(x1)*a1
(((sin(x1)*c0s(x2)*Os(x3)-sinx1)*sin(x2)*sin(x3})*c合s(x4)-cs(x1
gir(x4))*cos(x5)+(-sin(x1)*Co8(x2)*sin(x3-sin(x1)*gin(x2)*C8(x3))
*sin(xs))*cos(x61-((sin(x1)*cos(x2)*c09(x3)-sir(x1)*sin(x2)*sin(x3)i*
sin(x4)+cos(x1)*C03(x4))*sin(x6)r
((sir.(X1)c。s(x2)*cs(x3)-sin(x1)s⊥n(x2)*sir.(3))cs(X4)-C。8(K1)木
sin(x4))*Cos(x5)+(-sin(xl)*cos(x2)*sin(x3)-sin(x1)*sin(x2)*COs(x3))vs
in(x5))*sin(x6)-((sin(x1)*cos(x2)*cos(x3)-sin(xl)*sin(x2*sin(3))*si
n(x4)+cos(xl)*cos(x4))*cos(x6
((in(×1)*c:s(x2)*cs(x3)-1n(x1)*1n(x2)*sin(x3))*Cs(×4)-0a(x1)a
in(x4))*sin(x5)+(sin(x1)*cos(x2)*sin(x3)-sin(xl)*sin(x2)*cos(x3))*co
s(x5)
(sin(x1)+cos(x2)+cos(x3)-sin(x1)+sin(x2)*sin(x3))*a3+(-sin(x1)+cos(x2
)ssin:(x3)-sin(x1)*sin(x2)co(x3})*d4+s-n(x1)cOs(x2)*a2+sin(x1)a1
((-sin(x2)*cos(x3)-cos(x2)*sin(x3))*cos(x1)*co3(x5)+(sin(x2)*sin(x3)
cos(x2)*cos(x3))*sin(x5))*cos(x2)-(-sin(x2)*cos(x3)-cos(x2)*sin(x3))*
sin(x4)*sin(x6)
((-sir(K2)*cos(x3)-203(x2)sin(x3))*Coa(x41*co8(x5)+(sin(x2)*ain{x3)
cCs(x2)*cos(x3),*sin(x5))*sin(x6)-k-sin(x2)*cos(x3)-cos(x2)*sin(x3))
*sin(x4)*Cos(x6),
(-sin(x2)*cos(x3)-Cos(x2)*sin(3))*cos(x4)*sir(x5)+(sin(x2)*sin(x3)
COS(x2)*cOs(x3))*COS(x5)
(-Gir(x2)*cos(x3)-co5(x2)*s-n(x3))*a3+(sin(x2)*sinix3)-CO5(x2)*Cos(x3
))*d4-1n(x2)*a2
0
0
1
[(((c。s(x1)*c。s(x2)*c。3(K3)-cs;x1)*in(x2)*sin(x3))xe5ix4)+sin(x1
)*sir(x4))*cos(x5)+(-cos(x1)*cos(x2)*sin(x31-Cos(xl)*sin(x2)*Cos(x3)
s⊥n(X5))*cs(x6)-((c08(x1)c08(X2)+COs(x3)-C0a(81)*n(x2)↑s⊥n(x3))
sin(x4) sin(x1*c08(x4))*sin(x6:
((Co(×1)*cos(x2)*s(x3)-Cos(x1)*s⊥n(x2)*sin:(x3))Cs(x4)+sin(x1)
sin(x4))cos(x5)+(-Cs(X1)*已O(x2)*Sin(x3)-CCs(x1)*s⊥n(x2)*Cs(X3))xs
in(x5))*sin(x6)-((c5(x1)大cs(x2)+c5sx3)-C0s(x1)*sin(x2)*sin(x3))+si
n(x4)3in(x1)Cos(x4))Cos(x61
((cos(x1)*cos(x2)*cos(83)-cos(x1)*sin(x2)*sin(X3))*Cos(x4)+sin(x1)*s
in(x4))*sin(x5)+(-C5(x1)*ccs(x2)*sin(x3)-cDs(x1)*sin(x2)*cs(X3))*e口
s(x5),
(cs《×1)*cDs(x2)*c(X3)-C0(x11*ain(x2)*sin(x3))*a3+(-C0s(×1)*cs(x2
)*sir(x3)-C(x1)wgin(x2)CO8(x3))*d4+COs(x1)*Cg(x2)*a2+CDg(x1)*a1
[4((sin(x1)*co9(x2)*cos(x3)-sinx1)*gin(x2)*sin(x3))*CS(x4)-Cos(x1
)*sir(x4))*c05(x5)+(-sin(x1)*cos(x2)*sin(x31-sin(x1)*sin(x2)*COs(x3)
sin(x5))*cs(X6)-((51n(x1)C(x2)cs(X3)-8ir.(属1)*ain(K2)sin(x3))木
sin(x4)+cos(x1*cc3(x4))*sin(x6)r
((si:.(x1)*cos(x2)*cos(x3)-sin(x1)+s⊥n(x2)*sir.(x3))*cs(x4)-cs(x1)
sin(x4))+cs(x5)+(-s⊥n(x1)*co9(x2)*gin(x3)-sin(x1)+s⊥n(x2)sc。s(83))
in(x5))*sin(x6)-((sin(x1)*cos(x2)*cosix3)-sin(x1)*sin(x2)*sin(3))*si
n(x4)+Cos(x1)*Cos(x4))*COs(x6!
((sin(x1)*cos(x2)*cos(x3)-sin(xl)*sin(x2,*sin(x3))*Cos(x4)-C0s(x1)*s
in(x4))*sin(x5)+(-sin(xl)cos(x2)*sin x3)-sin(x1)*sin(x2)*Co5(x3))*co
s(x5)
(sin《x1)*cos(x2)*c5(K3)-sin(x1}*in(x2)*sin(x3))*a3+(-sin(x1)*cos(x2
)s1r.(x3)-s1n(x1)*sin(x2)cos(x3))*4+s=n(x1)*cos(x2)*a2+s⊥n(x1)*a1
((-sin(x2)*cos(x3)-Cos(x2)*sin(:3))*cos(x4)*C03(5)+(sin(x2)*sin(x3)
Co(x2)*cos(x3))*ain(x5))+coa(x)-(-3in(x2)*C0a(3)-C3(x2)*sin(x3))
×4)*sin(x6
((-Eir.(E2)*cos(K3)-c08(x2)wgin(3))*cos(K4cos(x5)+(s⊥n(x2)*ginK3)
cCs(x2)*Cos(x3))*sin(x5))*sin(x6--sin (x21*cos(x3)-cos(x2)*sin(x3)
sin《x4)*cos(x6)
-(-in(x2)cos(x3)-c。s(x2)*sin(x3))*c⊙s(x4)*:.(x5)+{sin(x2)*sin(x3)-
Cs(X2)*二s(x3))c。s(x5),
(-sir(x2)*cos(x3)-c05(x2)*s-n(x3))*a3+(sin(x2)*sinix3)-cos(x2)*cos(x3
))d4in(x2)+a2
0
0
1
将表1的数据带入A中,可得初始的A
0.00001.30300.000C0.0000
0,00000.00001,0000450,0000
1.0000
0.0000363.0000
1.0000
三.机器人误差计算
机器人的位姿描述
Tu T1? 713 TI
f21 f2? /23 t
A.1=
I31t32133t:
000
末端相对于固定坐标系的位置广义坐标为:
x,7
]=[1,12;,4
用欧拉角描述姿态产义坐标,可根据下式求得机器人木端相对丁定丛标系的广
义坐标:
g
v2=y1+180
23
B=arcte 1 Sny-22 cosy
F12 sIn, sIny
p= actg
(LI cosy +42 sinw)
用框架角描述姿态产义坐标,可根据下式求得机器人末端相对于定丛标系的广
义坐标
a=arcing
r、的÷a,+180°
ctg
(t3 sin a-433 cos a)
(t, sin a +fu sin a)
y=arcing
(t22 cos a+fy, sin a)
其中从!的结果得
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