FANUC spiral and conical interpolation: why L3 can mean only two turns plus 90°
Original 30i-A definitions explain partial-turn counting in variable-radius spiral and conical interpolation. An original 2.25-turn example with L3 checks radius and height without interpreting the integer L as a count of complete revolutions.
Contents
In variable-radius interpolation, endpoint direction, radius change per revolution and turn count must be interpreted together. Treating L3 as three complete turns can produce wrong endpoint radius and conical height simultaneously.
The subject here is variable-radius Spiral
The FANUC 30i/31i/32i-A descriptions manual B-63942EN/02, §3.18, pages 115–117 (public mirror of the original manual) defines Q as radius increase or decrease per revolution. L is a positive integer including a final partial turn, rounded upward. Q takes precedence if L and Q conflict. Conical interpolation adds axial change outside the selected circular plane; in XY, I and J define the center and K the height change per revolution. Option availability depends on the specific model and machine configuration.
Original example: two complete turns, then a quarter turn
Let the XY-plane center be (0,0), starting at (24,0) and moving counterclockwise with Q=−4 mm/revolution. Z starts at 0 and height change per revolution is K=−8 mm. The target total angle is 810°, or 2.25 turns. L must therefore be expressed as 3, but the geometric turn count remains 2.25.
With n denoting the continuous number of revolutions traversed, the principle gives r=24−4n and z=−8n; n is not an integer counter. Checkpoints are:
| Continuous turn count n | Radius r | Height z |
|---|---|---|
| 0 | 24 mm | 0 |
| 0.25 | 23 mm | −2 mm |
| 1 | 20 mm | −8 mm |
| 2 | 16 mm | −16 mm |
| 2.25 | 15 mm | −18 mm |
The final direction is +Y, giving endpoint (0,15,−18) mm. Incorrectly calculating 3 full turns gives radius 12 mm, height −24 mm and a direction back along +X. This is not another notation for the same path.
Use the endpoint to check pitch in reverse
Dividing endpoint radius change −9 mm by 2.25 turns gives Q=−4; dividing height change −18 mm by 2.25 turns gives K=−8. Agreement between forward and reverse calculations establishes compatibility of this example's geometric constraints. Q describes continuous radial change, not a sudden 4 mm inward jump at each revolution's end.
The B-63944EN/03 user's manual, §4.7, pages 70–71 also specifies the PS5123 check for disagreement between programmed and calculated endpoints. Investigate center, direction, partial turns and pitch before considering any endpoint-difference tolerance; widening that tolerance should not conceal inconsistent geometry.
How this differs from a constant-radius helix
Both radius and height change in this example; an ordinary constant-radius Helical model has no radial-change term of this kind. Multiplying the circumference of a constant-radius helix by 2.25 therefore does not estimate this path's length. This is a geometric review example, without entry/exit moves, speed or compensation modes, and is not directly executable code. Other advanced interpolation topics are in the OPTION section.