FUNCTION_BLOCK Kin_4AxesPalletizer IMPLEMENTS ISMKinematicWithConfigurations,
Transformation FB for a 4 axes palletizer.
The 4-axis palletizer is a common robot type, employed mostly for palletizing tasks. It has 4 controlled rotary axes (drawn in red in the figure aside) and a fifth rotary mechanical axis (drawn in grey). The fifth axis mechanically keeps the gripper horizontally aligned.
The coordinate system at the bottom of the robot is the machine coordinate system. The Z axis points vertically upwards, the X axis points "forward", i.e. that direction the robot arm points to if it is in zero position. The coordinate system origin is the intersection point of the joint axis 1 and the bottom side of the robot. The picture aside shows the rotation direction of the 4 axes. The black arrows run along the joint axis. The direction of rotation is defined according to the "right-hand rule": If the thumb of the right hand is along with the arrow, then the positive direction of rotation is along with the slightly curved fingers of the hand. For example, seen from the top, the positive direction of rotation of axis 0 is counterclockwise, axis 1 and axis 2 tilt forward.
The picture aside shows the kinematics in zero position of all axes: The names of the parameters are according to the Denavit-Hartenberg convention.
Robots with the following Denavit-Hartenberg configuration are supported (the values of d_i and a_i are supplied in the configuration):
joint number |
joint offset |
link offset d_i |
link length a_i |
link twist |
0 |
0° |
d1 |
a1 |
-90° |
1 |
-90° |
0 |
a2 |
0° |
2 |
90° |
0 |
a3 |
0° |
3 |
0° |
0 |
a4 |
90° |
4 |
0° |
d5 |
0 |
180° |
In contrast to our convention, the Z axis of the tool coordinate system points in the direction of the tool, that is, away from the robot.
The single axes values have the following interpretation:
a0 |
position of the first rotary axis around Z in degrees |
a1 |
position of the second rotary axis in degrees |
a2 |
position of the third rotary axis in degrees |
a3 |
position of the fourth rotary axis in negative direction of Z axis in degrees |
The axes have the following maximum ranges:
Axis 0: ]-180°; 180°[
Axis 1: [-90°; 90°]
Axis 2: [-180°; 90[
Axis 3: not limited, the range can be larger than 360°
Note
This position kinematics does not support orientation mode "Axis" for CP movements.
Attributes:
sm_kin_libdoc
InOut:
Scope |
Name |
Type |
Comment |
Input |
d1 |
LREAL |
Denavit-Hartenberg Parameter d1, >= 0 |
a1 |
LREAL |
Denavit-Hartenberg Parameter a1, >= 0 |
|
a2 |
LREAL |
Denavit-Hartenberg Parameter a2, > 0 |
|
a3 |
LREAL |
Denavit-Hartenberg Parameter a3, > 0 |
|
a4 |
LREAL |
Denavit-Hartenberg Parameter a4, >= 0 |
|
d5 |
LREAL |
Denavit-Hartenberg Parameter d5, < 0 |