Caliper Attachment Radius Measurement Tool & Test

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Caliper Attachment Radius Measurement Tool & Test

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X1 Carbon
P1S
P1P
X1
X1E
A1

0.2mm layer, 3 walls, 25% infill
0.2mm layer, 3 walls, 25% infill
Designer
3.5 h
2 plates
5.0(1)

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Description

These are attachments for a 6" Mitutoyo digital caliper for measuring radii. Any size radius is supported, and the two different formulas are printed on the larger attachment, as well on the reference target block.

FEATURES

  • Caliper slides in and snaps into place, no magnets needed.
  • No supports required to print.
  • Either attachment can measure any radius length, including very large radii.
  • Calibration targets included featuring both small and large radii.
  • Print profile includes an XY scale to compensate for PETG shrinkage (PETG suggested for dimensional stability).
  • The models are all 12mm thick, and the black printing is just one or two layers above the top layer, so there is only one single filament change for the print color.

THE MATH

Both the large and the small attachment are designed to allow for measuring any arbitrary-sized radius, using one of the following basic formulas. Accuracy gradually decreases for radii where a 90° arc segment has a chord larger than the max chord of the tool.

 

Variables:

r = radius

m = measured distance on the caliper

c = max chord of the tool at the tips of the attachment

l = ½ of the maximum chord  (c * 0.5)

s = sagitta, aka height of the arc (l - m)

 

For Small Radii

For a 90° arc segment that has a chord of less than 100mm (small attachment) or 200mm (large attachment), the arc fits inside the tool, so the simple formula can be used:

 

r = m * 2.4142 (rounded value)

 

Example: measure the 25mm radius, and measure a value ~10.36mm, then multiply by 2.4142 to get 25mm.

 

25 = 10.36 * 2.4142

 

For Large Radii

For large radii that will not fit inside the tool, the radius can still be determined using one of the following formulas:

 

r = (s² + l²) / (2*s)

 

or

 

r = c² / (8*s) + s / 2

 

EXAMPLES

We'll use the first formula in these examples.

 

For the small attachment, the chord is 100, so half the chord (l) is 50. For the large attachment, the chord at the tips is 200, so half is 100. 

 

50² = 2500 and 100² = 10000

 

So for the small attachment:

 

s = 50mm - m

r = (s² + 2500mm) / (2*s)

 

For the large attachment:

 

s = 100mm - m

r = (s² + 10000mm) / (2*s)

 

 

In Practice:

 

If you have a measurement of 40mm, then with the small attachment, the s = 10, so:

 

r = (10²  + 50² ) / (2 * 10)

r = (100 + 2500) / (20)

r = 2600 / 20

r = 130mm

 

 

If you have a measurement of 80mm with the large attachment, the s = 20, so:

 

r = (20²  + 100² ) / (2 * 20)

r = (400 + 10000) / (40)

r = 10400 / 40

r = 260mm

 

 

Comment & Rating (3)

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Great idea, love it, but been using radius gages for over 30 years, so I'll just enjoy your publication.
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It looks fabulous
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License

This user content is licensed under a Standard Digital File License.

You shall not share, sub-license, sell, rent, host, transfer, or distribute in any way the digital or 3D printed versions of this object, nor any other derivative work of this object in its digital or physical format (including - but not limited to - remixes of this object, and hosting on other digital platforms). The objects may not be used without permission in any way whatsoever in which you charge money, or collect fees.