Why trunnion offset compensation matters
A part mounted off-center on a trunnion table does not stay in the same X and Z position once the table tilts, since it is physically swinging through an arc around the trunnion's center of rotation. Programs that assume the part offset stays fixed through a tilt move will cut in the wrong place unless that swing is accounted for.
How the numbers are calculated
This is a standard rotation about the Y axis applied to the part offset from the trunnion center. New X offset equals the original X times the cosine of the tilt angle plus the original Z times the sine of the tilt angle, and new Z offset equals the original X times the sine of the tilt angle minus the original Z times the cosine of the tilt angle.
Practical tips
Measure the part offset from the true mechanical center of the trunnion's rotation, not from an approximate table center, since even a small error there gets amplified once the table tilts to larger angles. Most modern controls with proper tilted-plane or TCP support handle this automatically, but understanding the underlying math is essential when troubleshooting a position error on an older machine or a manually programmed tilt move.