Forward kinematics robotics m tech.
-
Upload
nshm-knowledge-campus -
Category
Documents
-
view
341 -
download
6
Transcript of Forward kinematics robotics m tech.
CS 4733, Class Notes: Forward Kinematics II
1 Stanford Manipulator - First Three Joints
Figure 1: Stanford Robotic Arm. The frame diagram shows the first three joints, which are in a R-R-P configuration (Revolute-Revolute-Prismatic.
0 S2 0 1 0 0 00 -C2 0 0 1 0 01 0 d2 0 0 1 d3
0 0 1 0 0 0 1
C1 C2 -S1 C1 S2 -S1 d2 C1 C2 -S1 C1S2 C1 S2 d3 - S1 d2
S1C2 C1 S1 S2 C1 d2 0 S1 C2 C1 S1S2 S1 S2 d3 + C1 d2
-S2 0 C2 d1 -S2 0 C2 C2 d3 + d1
0 0 0 1 0 0 0 1
1 0 0 00 1 0 d2
0 0 1 d1
0 0 0 1
2
T3 =
1
d1 01 0
T2 =
0 C2
0 S2 C1 0 -S1
S1 0 C1
0 -1 00 0 0
0T1 =
T3 =
T2 =0
if θ1 = θ2 = 0, d3 = 0: T3 = 0
(Zero Position)
1
joint θ d a α
nnn1 θ1 d1 0 -902 θ2 d2 0 903 0 d3 0 0456
2 4-DOF Gantry Robot
Figure 2: Gantry Robot Arm. This arm is in a R-P-R-R configuration. θ1 , θ3 , θ4 are the revolute joint angle variables and d2 is the prismatic joint variable. d4 is a constant.
0 00 1 -1 00 0
-S4 0C4 00 10 0
40 S4
1 0
A1 =
0 0
2
0 10 00 01 0
0 C4
A3 =
2
00 d2
1
0 0
-S1 0C1 00 10 0
S3 -C3
0 0
C1
S1
0 0
A0 =1
C3 0S3 00 10 0
3A2 =d4
1
joint θ d a α
1 θ1 0 0 02 0 d2 0 -903 θ3 0 0 904 θ4 d4 0 0
C1 -S1 0 0 1 0 0 0 S1 C1 0 0 0 0 1 00 0 1 0 0 -1 0 d2
0 0 0 1 0 0 0 1
S3 0 C4 -S4 0 0 -C3 0 S4 C4 0 0
0 0 0 0 1 d4
0 1 0 0 0 1
C1 0 -S1 0 C3 C4
S1 0 C1 0 S3 C4
0 -1 0 d2 S4
0 0 0 1 0
C1 C3 C4 - S1S4 -C1 C3 S4 - C4S1 C1 S3
C3 C4 S1 + C1 S4 -C3S1S4 + C1 C4 S1 S3
-S3C4 S3S4 C3
0 0 0
if θ1 = θ3 = θ4 = 90, d2 = D: A0 =
=
S3 d4 -C3 d4
0 1
C3 0 S3 00 10 0
2A0 =
C1 0 -S1 0S1 0 C1 00 -1 0 d2
0 0 0 1
=
A2 =
-C3S4
-S3S4
C4
0
S3 -C3
0 0
C1 S3 d4
S1S3 d4
C3 C4
S3 C4
S4
0
-C3S4
-S3S4
C4
0
4
S3
-C3
0 0
S3 d4 -C3 d4
0 1
4 2 4 A0 = A0 A2 =
=C3 d4 + d2
1
1 0 00 1 00 0 10 0 0
if θ1 = θ3 = θ4 = 0, d2 = 0: A0 =4
0 d4
D1
3
00 d4
1
0 1 0 0
(Zero Position)
-1 00 00 10 0
4