WOLFRAM|DEMONSTRATIONS PROJECT

Kinematics of SCARA Robot in 2D

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time
0.1
SCARA robot kinematics
endpoint displacement
endpoint velocity
joint displacement
joint velocity
joint acceleration
The SCARA robot (Selective Compliance Assembly Robot Arm) has four degrees of freedom: three rotations and one translation.
This Demonstration shows the inverse-kinematic simulation of a SCARA robot in 2D. The forward equation of the SCARA robot comes from the D-H coordinate method, based on the matrix
cos(
θ
1
+
θ
2
-
θ
4
)
sin(
θ
1
+
θ
2
-
θ
4
)
0
L
1
cos
θ
1
+
L
2
cos(
θ
1
+
θ
2
)
sin(
θ
1
+
θ
2
-
θ
4
)
-cos(
θ
1
+
θ
2
-
θ
4
)
0
L
1
sin
θ
1
+
L
2
sin(
θ
1
+
θ
2
)
0
0
-1
-
d
3
0
0
0
1
.
The inverse equation of the SCARA robot uses the inverse transform method.

cos
θ
2
=
2
p
x
+
2
p
y
-
2
L
1
−
2
L
2
2
L
1
L
2
sin
θ
2
=±
1-
2
cos
θ
2
θ
2
=arctan2(sin
θ
2
,cos
θ
2
)

sin
θ
1
=-
sin
θ
2
L
2
p
x
-
L
1
p
y
-cos
θ
2
L
2
p
y
2
p
x
+
2
p
y
cos
θ
1
=-
-
L
1
p
x
-cos
θ
2
L
2
p
x
-sin
θ
2
L
2
p
y
2
p
x
+
2
p
y
θ
1
=arctan2(sin
θ
1
,cos
θ
1
)

sin
θ
4
=cos(
θ
1
+
θ
2
)
n
x
+
n
y
sin(
θ
1
+
θ
2
)
cos
θ
4
=-cos(
θ
1
+
θ
2
)
n
y
+
n
x
sin(
θ
1
+
θ
2
)
θ
4
=arctan2(sin
θ
4
,cos
θ
4
)
d
3
=-
p
z
.
To simulate the inverse kinematics of the SCARA robot, the endpoint of the robot traces a straight line from
(20,45,-4)
to
(40,15,-8)
in five minutes with the velocity shown in the Demonstration.