FANUC G16 polar coordinates: why changing the angle at a fixed radius can still produce a straight move
The 0i-D polar endpoint definition and an original chord calculation show why G16 does not turn G01 into an arc. A comparison with Cartesian input and rotary-axis conversion in 0i-F lathe G12.1 distinguishes the two polar functions.
Contents
Describing two points on the same circle as having the same radius and different angles does not mean the tool will follow the circle. Endpoint representation and interpolation between endpoints must be considered separately; otherwise a bolt-hole positioning program can be mistaken for a circular cutting program.
G16 changes how endpoint coordinates are expressed
The 0i-D / 0i Mate-D machining-center manual B-64304EN-2/01, §4.1, pages 25–27 (public mirror of the original manual) defines G16 as endpoint input by radius and angle, canceled by G15. In the G17 plane, address X represents radius and Y represents angle. The following is limited to G90, the workpiece origin as the polar origin, millimeter input, and no local coordinates, rotation, scaling or tool compensation.
For the same series, B-64304EN/02, §4.2, page 35 defines G01 as linear interpolation. Entering an endpoint in polar coordinates therefore does not turn the G01 path into an arc around the pole.
A 90° example reveals the difference
Original model: the start has radius 40 mm and angle 0°; the endpoint has radius 40 mm and angle 90°. Their Cartesian coordinates are (40,0) and (0,40), since x=r cosθ and y=r sinθ.
| Geometric object | Calculation | Result |
|---|---|---|
| Straight chord between the endpoints | √(40²+40²) | 56.569 mm |
| Quarter-circle arc of radius 40 | 40π/2 | 62.832 mm |
| Distance from the line midpoint to the pole | √(20²+20²) | 28.284 mm |
Both endpoints lie on the circle of radius 40, yet the middle of the straight path reaches radius 28.284. This is a difference in the path itself, not decimal rounding error. An arc under G16 still requires the corresponding interpolation definition; page 27 of the cited manual also requires the arc radius in this mode to be specified with R.
Why G16 and G12.1 are not interchangeable
As a comparison across series, G12.1 in the 0i-F lathe manual B-64604EN-1/01, §3.1, pages 16–17 accepts Cartesian coordinates in the interpolation plane and converts them into linear- and rotary-axis motion. Its role differs from G16, which inputs endpoints as radius and angle. This article does not infer that the two can be used interchangeably on the same machine.
Which level to check in a circular-path program
First convert adjacent endpoints into XY coordinates, then check the block's interpolation method, and finally the actual axis combination and function configuration. Correct endpoints matter when calculating distributed hole positions; they are far from sufficient for cutting along a circle. For G12.1 speed behavior near the rotary center, see the polar interpolation article.