What the post receives
For each point, CAM provides the tool tip position (X, Y, Z) and a unit tool axis vector (I, J, K) in the part coordinate system. The post must convert this into linear axis positions and two rotary angles.
The kinematic chain
| Machine type | Chain | What rotates |
|---|---|---|
| Table-table (e.g. A/C) | Tool fixed; A tilts table, C rotates on A | The part |
| Head-head (e.g. B/C head) | Part fixed; C rotates head, B tilts spindle | The tool |
| Head-table (e.g. B head, C table) | One rotation each side | Both |
Solving the rotary angles
For an A/C trunnion with the tool along machine Z, the tilt angle comes from how far the vector leans from vertical, and the C angle from the direction the vector points in the XY plane. Conceptually:
A = ± acos(K) (tilt from vertical)
C = atan2(I, -J) (direction in XY; sign convention varies)
Example: vector (0.5, 0, 0.866)
A = acos(0.866) = 30°
C = atan2(0.5, 0) = 90° (one of two solutions)Actual formulas depend on axis directions, the order of rotations and the machine's zero positions. A real post implements the exact convention of the machine.
Two solutions
Most orientations can be reached two ways, for example A+30 / C90 or A-30 / C270. The post chooses based on limits, preferred tilt direction and continuity with the previous point. Switching solutions mid-path causes a large, dangerous rotary move.
The singularity
When the tool is parallel to the C axis (A = 0 on a trunnion), any C angle is valid. Near this point, tiny vector changes can demand huge C rotations. Posts hold C steady at the singularity and interpolate carefully around it.
Linear positions: TCP vs non-TCP
- With TCP, the post outputs the tool tip position in part coordinates plus angles; the controller applies kinematics.
- Without TCP, the post rotates the tip position around the machine's pivot points and adds tool length, so pivot data and tool length must be exact.
Kinematics is where geometry becomes motion. Small errors here become large errors at the tool tip.
5-axis kinematics expertise
See our CNC post processor development service and kinematics configuration in 5-axis posts.