Two endpoints do not define which path length is being reported. An arc and its chord have different distances.
Name the path quantity
An arc-length dimension measures distance along the selected curved arc. It is different from the straight chord connecting the same endpoints. The selected portion also matters because a circle can provide a shorter or longer arc between two points. Primary reference: Autodesk: dimensions along full or partial arcs.
Keep the path and endpoints with the number. A curve's radius alone does not supply its travelled length without the relevant angle or arc portion. Likewise, a straight endpoint separation does not automatically represent motion constrained to the curved path.
Calculate an invented quarter-circle
For a fictional circle of radius 10 mm, a 90-degree minor arc has length 10 times pi/2, approximately 15.708 mm. Its chord is 2 times 10 times sin(45 degrees), approximately 14.142 mm. The endpoints are the same, while the routes between them differ.
The illustration assumes an ideal circle and a stated minor arc. It gives no conveyor trajectory, cable allowance or manufactured-path tolerance. Selecting the 270-degree major arc would create another travelled length; it should not be hidden behind an unspecified phrase such as distance between the ends.
Retain the route in the drawing question
When a drawing concerns a curved track, wrap or local profile, specify whether the required value follows the arc or joins its endpoints. Identify the included arc portion and nominal geometry. Use the correct dimension type rather than substituting the easier page measurement.
Compare the required path with the actual interface model and any separately defined allowances. The nominal arc calculation can establish its geometry, but it does not predict physical flexure or clearance. A receiver should be able to reconstruct the intended route from the released information without guessing which of several possible distances the note means.
Customer Questions
Is arc length generally the chord length?
No. One follows the curve and the other is straight.
What is the fictional quarter-circle arc length?
Approximately 15.708 mm for radius 10 mm.
Does the included arc portion matter?
Yes. The major and minor arcs can connect the same endpoints.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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