Post on 29-Mar-2020
transcript
3RRR
Kinematic Analysis of The 3RRR Parallel
Robot
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Abstract
Parallel robot is a usual important application in the industry. The advantage of
parallel robot is high hardness and parallel robot can absorb heavy load and it can
control accurately in some positions. We usual see parallel robot are 5RRR of 2
freedom, 3RRR of 3freedom, and unsymmetrical 2RRR1RRR.
The paper mainly describes kinematic analysis of the 3RRR parallel robot. The
structure of 3RRR parallel robot has an equilateral triangle and six poles. We put The
structure on the X-Y coordinate in order to analysis kinematics. The kinematic
analysis has two major parts: First part is the inverse kinematics; The second part is
the forward kinematics. First part inverse kinematics: Input coordinate of center of
equilateral triangle and rotative angles of equilateral triangle on the X-Y coordinate
work out rotative angles of poles, and simulates the inverse kinematics of the structure.
The second part forward kinematics: Input rotative angles of poles work out
coordinate of center of equilateral triangle and rotative angle of equilateral triangle,
and simulates the forward kinematics of the structure. These two parts of kinematic
analysis are to simulate by MATLAB software.
v
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7 8 9
4
1 2 3 4 5 6
1 2 3
1
ISO/TC184/SC2/WG1(1984 )
2
Manipulator
3
4
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
1 0 0 0
c 1 0 0
b 0 1 0
a 0 0 1
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
1 0 0 0
c 1 0 0
b 0 1 0
a 0 0 1
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
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0
z
y
x
5
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
1 0 0 0
0 cos sin 0
0 sin- cos 0
0 0 0 1
θθ
θθ
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
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1 0 0 0
0 cos 0 sin-
0 0 1 0
0 sin 0 cos
θθ
θθ
6
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
1 0 0 0
0 1 0 0
0 0 cos sin
0 0 sin- cos
θθ
θθ
7
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
1 0 0 0
c cos sin 0
b sin- cos 0
a 0 0 1
θθ
θθ
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
1 0 0 0
c cos 0 sin-
b 0 1 0
a sin 0 cos
θθ
θθ
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
1 0 0 0
c 1 0 0
b 0 cos sin
a 0 sin- cos
θθ
θθ
8
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10
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1 2 3 4 5
6 1 2 3 4 5 6 7 8 9
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1 2
3 1 2 3 1 2
3 4 4 4 5
5 5 6 6 6 7 7 7
8 8 8 9 9 9
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1°×°×× 210cos30sec5.7
2
1°×°×× 210sin30sec5.7
'8 2
1°−×°×× 30cos30sec5.7
2
1°−×°×× 30sin30sec5.7
'9 3
2°×× 60sin5.7
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9 7 8 9
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
1 0 0 0
0 1 0 0
Y 0 cos sin
X 0 sin- cos
ϕϕ
ϕϕ
7 8 9'
7'
8'
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y
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1 0 0 0
0 1 0 0
Y 0 cos sin
X 0 sin- cos
ϕϕ
ϕϕ
⎥⎥⎥⎥
⎦
⎤
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⎣
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0
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1 0 0 0
0 1 0 0
Y 0 cos sin
X 0 sin- cos
ϕϕ
ϕϕ
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⎦
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0
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y
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y
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1 0 0 0
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Y 0 cos sin
X 0 sin- cos
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⎥⎥⎥⎥
⎦
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b 0 cos sin
a 0 sin- cos
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b 0 cos sin
a 0 sin- cos
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1 2 3 1 2 3 1 2 3
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1 7
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1 2 3
1 2 3
1 2 3 4 5 6
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1 2 3 1 2 3
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05.7)()(
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279
2298
298
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287
2269
269
2258
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2247
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yyxx
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7 7 8 8 9
9 7 7 7 8 8 8 9 9 9
7 7 7 8 8 8 9 9 9
1 2 3
7
7 7 8 8 8 9 9 9
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3987 xxx ++
3987 yyy ++
1 2 3 1 2
3
1−
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xx
yy
−
−
1 2 3 1 2 3
1 2 3 1 2
3 4 5 6
1 2 3
21
1 2 3
22
23