BIZOMAT MAKEOS · Quality
Arc Radius from Measurement over Rolls
What radius does this concave or convex gauge or part have, from a measurement over two rolls?
Radius of a large concave or convex arc from the distance over two equal rolls and the height of the arc above the surface plate, by the handbook construction.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Arc | choice | Concave gauge resting on the rolls, or convex arc resting on them. |
| Roll diameter | mm | Measured diameter of the two equal rolls. |
| Measurement over the rolls | mm | Outside distance over both rolls. |
| Height of the arc above the plate | mm | Height from the surface plate to the arc (top of a concave arc, lowest point of a convex arc). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Arc
- What it is
- Whether the arc being measured is concave (a hollow that bridges over the two rolls) or convex (a curved part that rests on top of the rolls). It sets which height you measure.
- Units and format
- Choose one of 2 options from the list: Concave (arc bridges the rolls; H = height of the arc’s top); Convex (arc rests on the rolls; H = height of the arc’s lowest point).
- Example
- The form opens with “Concave (arc bridges the rolls; H = height of the arc’s top)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Concave: measure to the top of the arc. Convex: measure to the arc’s lowest point between the rolls.
What this means: Roll diameter
- What it is
- The measured diameter of each of the two equal rolls or pins set on the surface plate under the arc.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure the rolls themselves with a micrometer; both must be the same size.
What this means: Measurement over the rolls
- What it is
- The outside distance across both rolls, measured over their far sides with the arc in place on them.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- This is over the outsides of the rolls, not between their centres.
What this means: Height of the arc above the plate
- What it is
- The height from the surface plate up to the arc: to the top of a concave arc, or to the lowest point of a convex arc between the rolls.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For a concave arc it must be more than the roll diameter; for a convex arc, less.
Method and formulas
- Half the roll centre distance cb = (L − D) ÷ 2.
- Concave: ce = H − D; ab = (cb² + ce²) ÷ 2ce; R = ab + D/2.
- Convex: ce = D − H; ab = (cb² + ce²) ÷ 2ce; R = ab − D/2.
- Example: 20 mm rolls 120 mm over, arc 40 mm high: R = 82.5 mm.
Limitations
- Rolls must touch the arc on its true radius, away from its ends.
- Small heights make the result sensitive to measurement error.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check radius templates and gauges
- Measure large radii without a CMM
- Inspect curved parts on a surface plate
Who it is for
- Quality inspectors
- Toolmakers
- Metrology technicians
What you get
- Radius of the arc
- Roll centre distance
Interpreting the result
- Use the largest roll spacing the arc allows for better accuracy.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 687–688. Topic reference; no source tables or recommended settings are reproduced.
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