KEVOS® MAKEOS · Manufacturing
CNC Arc Linearisation Chord Error
What chord error do these line segments leave on an arc, or what segment length meets a tolerance?
Chordal deviation of straight line segments approximating an arc or contour, the longest segment for a given tolerance, and the number of segments for the arc.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Calculate | choice | Find the segment length for a tolerance, or the error for a segment length. |
| Arc radius | mm | Radius of the arc or local radius of curvature of the contour. |
| Chord tolerance | mm | Allowed deviation between chord and arc. |
| Segment length | mm | Length of each straight segment (error mode). |
| Arc angle | ° | Angle of the arc, for the number of segments. |
Method and formulas
- Error e = R (1 − cos(θ/2)), where θ is the angle subtended by one segment.
- Segment length L = 2√(2Re − e²).
- Segments = arc angle ÷ θ, rounded up.
- Example: R 50 mm with a 0.005 mm tolerance allows 1.4142 mm segments, 56 for 90°.
Limitations
- Error on one side of the profile only (chords lie inside a convex arc); CAM systems may split the tolerance inside and outside.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set CAM output tolerance
- Check whether a posted program meets the profile tolerance
- Estimate block count for a contour
Who it is for
- Machinists
- CNC programmers
- Manufacturing engineers
What you get
- Segment length and angle
- Chord error
- Segments for the arc
Interpreting the result
- Very small tolerances create huge programs; use arc output (G02/G03) or spline interpolation where the control allows.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1279–1300, 77–80. Topic reference; no source tables or recommended settings are reproduced.
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