Chapter 4
Geometries with orientation support
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Rockwell Automation Publication MOTION-UM002F-EN-P - February 2018
Tips:
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For transformations to work correctly, be sure to establish the reference frame for the joint coordinate system first. For the
Delta J1J2J3J6 and Delta J1J2J3J4J5 robots, the normal reference positions for J1, J2 and J3 axes are homed to 0 when
the J1, J2 and J3 links are horizontal. The J6 axis is homed to 0 when it is parallel to J1 link.
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The J6 rotation is opposite to Rz rotation with respect to the robot base frame.
Once the robot reference frame is established, move the robot to a position in joint
space, if needed, before enabling the MCTO instruction. After enabling the
MCTO instruction, a bidirectional transform link is established so that, if the
Cartesian coordinate is commanded to move to Cartesian coordinate target, the
robot moves to Cartesian target coordinates along a linear path. Similarly, if the
robot joint coordinate system is commanded to move to joint coordinate target,
the robot moves to target joint coordinates along a non-Cartesian path. As the
MCTO instruction is enabled, the system maintains the coordinate system related
data (that is Cartesian position) for Cartesian and robot coordinate systems.
Turns counter
As shown in the previous diagram, positive orientation rotation for Rz is
counterclockwise around the Z axis of the robot base frame. However, the positive
rotation for J6 axis is clockwise around the Z axis of the robot base frame which is
opposite to Rz axis rotation.
With the 3D Delta robot system since there is no rotation possible around X and
Y axis of base frame, the only rotation possible is around Z axis. As a result, the
Cartesian coordinate system can be described with the following translation and
orientation specifications:
X, Y, Z: [-inf,+inf]
Rx: [180.0]
Ry: [0.0]
Rz: [-179.999, +180.0]
The Rz target position is the rotation around base Z axis and so any rotation can
be specified with a range of +/- 180 with one exception of -180 . As 180 and
-180 is the same point, the system does not allow specification of -180 as Rz
target point.
However, this specification will not be complete as J6 axis can rotate more than
one turn. The system handles this functionality by adding an additional turns
counter specification for each target point specification.
Co-relating Rz axis with J6 axis and turns counter
This diagram explains how Rz and turns counter varies with J6 (assuming that the
work frame offset, the tool frame offset and the zero angle offset on J6 are 0). J6 is
a linear axis and for example can have total travel of 15 revolutions with for
example a range from -7.5*360 = -2700 to +7.5*360 = +2700 . As a result,
physically the J6 can have multiple turns and have an attribute of turns counter
which keeps track of number of the turns associated with the current position of