Basic
Supply the X-Axis origin, a point in the +X direction, and a second point in the +Y direction. Then supply the origin.
Base Plane
Define a Base Plane, then use any mixture of line-line intersections (circle centers, sphere center points, or plane intersections) to construct the alignment. The construction geometry you select projects onto the Base Plane. The projection direction is always normal to the Base Plane from the digitized location.
Define a Base Plane, then define the X- and Y-Axes. Then define the Origin. Then offset in XYZ space from any one of the above construction points.
Leap Frog
Record three reference positions within reach of both setups. Reposition the digitizer or the workpiece, then reference the same three positions from the new setup position. As such, this is very similar to the BasePlane or Basic Alignment but executed twice.
Supply three reference locations BEFORE you move the digitizer or the workpiece.
Reposition the arm or the workpiece. Do not turn off power to the digitizer or close the digitizer program in the middle of a leap-frog since the intermediate data and your original alignment position will be lost.
Digitize the same three reference locations in the same order as initially digitized, after which the coordinate transformation occurs.