Description
Ideal circular neutral-axis bend geometry with a supplied inside radius.
Dental model and device records use coordinate frames, image scale, dimensions, force references, and observation schedules. A projection, gap, ratio, or metadata order checks a particular supplied representation. These local calculations do not establish a treatment plan or the clinical suitability of a device.
Ideal circular neutral-axis bend geometry with a supplied inside radius.
When to use this tool
Use Orthodontic Wire Bench Bend Radius Term when you need this particular model geometry, device budget, observation share, or record comparison.
How to use the tool and how it works
- Enter wireDiameter, insideRadius, bendRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read neutralRadius, neutralArcLength, outerFiberStrain. Use the output convention below.
For positive wireDiameter and nonnegative insideRadius return neutralRadius=insideRadius+wireDiameter/2, neutralArcLength=neutralRadius*abs(bendRadians), and outerFiberStrain=wireDiameter/(2*insideRadius+wireDiameter).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| wireDiameter | Wire Diameter | Required. Finite number; strictly above 0. |
| insideRadius | Inside Radius | Required. Finite number; minimum 0. |
| bendRadians | Bend Radians | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| neutralRadius | Neutral Radius | Required. Finite number. |
| neutralArcLength | Neutral Arc Length | Required. Finite number. |
| outerFiberStrain | Outer Fiber Strain | Required. Finite number. |
{
"input": {
"wireDiameter": 2,
"insideRadius": 9,
"bendRadians": 1.5707963267948966
},
"output": {
"neutralRadius": 10,
"neutralArcLength": 15.707963267948966,
"outerFiberStrain": 0.1
}
}Limitations and assumptions
- Lengths need one unit and angle is radians. The ideal circular-bend geometry can give strain one at zero inside radius; no elastic/plastic behavior, springback, material limits, or safe wire-forming procedure is validated.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a validated measurement or device model and appropriate source records for the full task. Check coordinate systems, calibration, geometric assumptions, and observation denominators before interpreting the term.
References
Similar or alternative tools
- Orthodontic Device Package Count Balance
For nonnegative integer packages, loose, issued, returned, and damaged and positive integer perPackage require packages*perPackage+loose-issued+returned>=damaged.
- Orthodontic Photo Reference Plane Gap
Pinhole out-of-plane photo scale error relative to an explicit reference plane.