Chapter 4
Geometries with orientation support
120
Rockwell Automation Publication MOTION-UM002F-EN-P - February 2018
The three 3 by 1 vectors
n o a
form a 3 by 3 Rotation matrix which defines the
rotated frame with respect to the base frame of the robot. The vectors
n o a
are
unit vectors with respect to the base coordinate system. The columns of the
rotation matrix
n o a
represent the direction cosines of the rotated orientation
frame with respect to the base coordinate system.
Translation Specification of Point -
n,o,a,t
The translation and rotation specifications are combined to form a 4 by 4
transform matrix with elements from translation and orientation specification as
shown below which completely specify the position and orientation of a point.