# Can we build a tool that measure curvature on an arc?

I know some biologist that are taking curvature measurements on photos with softwares to understand the variation on beak morphology.

I'm wondering if there is a way to build a mechanical tool (or if one exist already) to measure the curvature of a circle's (or ellipse) arc. The arc is not always of the same length, so it would need to be adjustable.

There is a constrain (see the grey line):

I can't fit a big calliper on the bird's head.

I want to know:

1. the radius of the circle that correspond to the beak curvature
2. how "steep" is that curvature (probably a lack of vocabulary on my side but see the image down to see what I mean by "steep")

You can see this image as the different birds in the image above. Bird #4 would have a flatter beak than bird #1.

I need to be able to calculate the "steepness" even if the x, y or z are not of the same length.

The idea of bringing a mechanical tool is to calculate rapidly and conveniently a number and add it directly to a dataset. It's much faster than to look at photos and analyse with a software. So if there is a mechanical tool designed for this, it would be super useful.

Again, the image is just a visualization of the problem. I would like to measure the beak of different birds on the field.

• To what class of curves are you constraining this question? E.g., are you asking about tools for determining the major and minor radii of an ellipse based on a sample segment? Jul 18, 2016 at 21:26
• Software is a tool. Did you mean a mechanical tool? Jul 19, 2016 at 3:05
• There are also Digital Radius Gauges which can measure small arcs (~10mm) cutwel.co.uk/measuring-tools/small-tool-instruments/… Jul 19, 2016 at 10:15
• It's not clear to me what class of curves a bird's head can be assumed to follow, so your question is still unclear: Is it an arbitrary curve? Or are you interested in the "best fit" circular segment? Jul 19, 2016 at 14:54
• @CarlWitthoft there are heaps of valid reasons people might want measuring tools that don't depend on software. For example if you need to do the measurements in the field where there is no power available for long periods of time or if you need to produce a large number of gauges so volunteers can help collect data. In most simple cases, it's also much easier to validate a non-software solution. Jul 20, 2016 at 13:21

For a circle, yes. Such a tool exists: Digital Radius Caliper

There are also Digital Radius Gauges, which may be useful for smaller curves.

For a general curve, you can't measure the curvature exactly since it varies continuously along the curve. You could perhaps assume a region is approximately circular and measure that. But depending on the size of the tool and the rate of curvature change this could be wildly inaccurate.