FANUC G68.2 P1: why Q123 and Q321 produce different planes with the same IJK angles
Within the 0i-F G68.2 P1 RPY format, original Q123 and Q321 vector calculations demonstrate noncommutative spatial rotations. The article shows how to check a postprocessor’s matrices, feature normal and in-plane directions.
Contents
A tilted-plane program can contain the correct I, J and K values yet produce a different orientation after a postprocessor change. Rotation order may be responsible. Spatial rotations generally do not commute; the individual angle values are insufficient to define a coordinate system uniquely.
Limit the discussion to the RPY format
According to the FANUC 0i-F machining-center operator's manual B-64604EN-2/01, §5.7.1.3, pages 120–122 (pagination of this public copy), G68.2 P1 uses roll-pitch-yaw: I, J and K are angles about the workpiece coordinate system's X, Y and Z axes, while Q specifies their order. Q123 means X→Y→Z and Q321 means Z→Y→X; omitted Q is interpreted as 123. Other angle definitions used without P1 cannot be substituted, and this does not mean every 0i-F has the tilted-plane function.
Tracking one axis is enough to reveal a difference
Original right-handed coordinate calculation: the feature origin is (0,0,0), with I=90°, J=0° and K=90°. Rotate the original Z unit vector u=(0,0,1) about the listed fixed workpiece axes in order:
| Order | Intermediate change | Final feature Z axis |
|---|---|---|
| Q123 | After X: (0,−1,0); unchanged by Y; then rotate about Z | (1,0,0) |
| Q321 | After Z: still (0,0,1); unchanged by Y; then rotate about X | (0,−1,0) |
The same angles produce normals differing by 90°. A feature-coordinate point (0,0,20) mm becomes (20,0,0) or (0,−20,0) in workpiece coordinates, separated by 20√2≈28.284 mm. This is not decimal rounding of the same tilted plane.
How matrix multiplication corresponds to program order
When directions are column vectors, the first rotation is the rightmost factor. Q123 above corresponds to Rz(90°)Ry(0°)Rx(90°), and Q321 to Rx(90°)Ry(0°)Rz(90°). Entering the three IJK numbers into a software Euler-angle field can still yield another result if it uses moving axes or a different multiplication convention.
To check a postprocessor, transform all three feature-coordinate unit axes into workpiece coordinates, then compare their directions and right-handed relationship. Matching angle text does not prove equivalent representations; matching only the normal does not fully determine the in-plane X and Y directions either.
A coordinate definition is not a machine rotary move
This example checks only the geometric definition of the feature coordinate system. It predicts no actual A, B or C solution, rotary path or clearance. Once the coordinate definition is confirmed, actual orientation still needs verification through the specific machine's kinematics and orientation process. No directly executable positioning program is supplied. Function background is in the OPTION section.