Geometries with orientation support
Rockwell Automation Publication MOTION-UM002F-EN-P - February 2018 123
the base frame. The transforms align XYZ base frame to n o a with one to 3
successive rotations. The transforms below only represent one rotation.
Using this rotation matrix one can rotate Ɵ to any value in the range of +/-180
to obtain the rotation matrix around desired base axis.
Translation + Rotation Transform
The translation plus rotation transform is more complex. With 3D space the
example would be more complex but can be worked using matrix multiplication
and trigonometric mathematics.
The 4 by 4 matrix form of point specification is sometimes difficult to handle for
user defined points but as shown in the calculations above easy to map points
from one coordinate frame to another coordinate frame. E.g. End of Arm Frame
to TCP frame.
When the points need to be taught it becomes difficult to teach approach and
orientation vector to specify the orientation. A representation that requires only
three numbers to completely specify the orientation is more desirable. It also
facilitates jogging the robot around a robot base coordinate axis. E.g. Z axis.
There are several representations that require three numbers to specify the
rotations. As these are rotations around an axes they are specified in degrees. The
two common rotations are XYZ Fixed Angle convention and ZY’X" Euler angle
conventions described below.
Fixed Angle - X-Y-Z
One method of describing the orientation of a frame {B} is as follows:
Orientation specification
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