
Geometries with orientation support
Chapter 4
Rockwell Automation Publication MOTION-UM002F-EN-P - February 2018
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Cartesian target positions in to joint space and vice versa. In order for the
transformations to work correctly, it is required to establish the origins for all the
axes in the joint space with respect to the robot base Cartesian frame.
Top View
Side View
Establish the Base frame
The reference XYZ frame (Base frame) for the Delta geometry is located near the
center of the base plate. Joint 1(J1), Joint 2 (J2), and Joint 3 (J3) are actuated
joints and placed 120 apart, shown as α1, α2, and α3.
When configuring a Delta J1J2J3J6 coordinate system in the Logix Designer
application, with the joints homed as 0 in the XY plane, then the L1 link is
aligned along the X positive axis as shown in the Top View figure. The Side View
figure shows that the X axis will pass through the center of J1’s motor to the center
of Link L1 and L2 joint.
Moving in the counter clockwise direction from J1 to J2 and J3, the Y axis is
orthogonal to the X axis. Based on the right hand rule, Z positive axis is the axis
pointing up in side view (out of the paper in the top view).
•
+J1 rotation is measured clockwise around the -Y axis at the Base frame (+Y
axis is pointing inside in Side View).
•
As each top link (L1) moves downward, its corresponding joint axis (J1, J2,
or J3) is rotating in the positive direction.
Establish the End of Arm frame
End of Arm (EOA) in XYZ reference frame is set at the end of the End Plate. This
frame is rotated by Rx =180 with reference to the Base frame. As a result, the X
axis is in the same direction as Base frame X axis but the Z axis direction is
pointing down, towards the direction of the Tool approach vector.