Quote of the Day

It is a universal truth that the loss of liberty at home is to be charged to the provisions against danger, real or pretended, from abroad.

— James Madison

## Introduction

I am continuing to work through some basic metrology examples – today’s example uses roller gages to measure the angle of a drilled hole (Figure 1). The technique discussed here uses two roller gages and a plug. The plug must fit the hole snugly (i.e. no backlash) as it will provide the surface that we will be measuring. Using this approach assumes that you need a very accurate measurement of a hole’s angle as rough measurements can be made using a protractor.

## Background

This example is based on the material found on this web page. I will derive the angle relationship presented there (Equation 1) and present a worked example that is confirmed using a scale drawing (Figure 1).

Eq. 1 |

where

*L*is the distance from reference to outside edge of roller gage._{1}*L*distance from reference to outside edge of roller gage._{2}*D*diameter of the first roller gage._{1}*D*diameter of the second roller gage._{2}*θ*is the angle of the drill hole relative to the surface that is drilled.

These variables are all indicated in Figure 2.

## Analysis

### Derivation

Figure 3 shows how to derive Equation 1. The basic derivation process is simple:

- The center of each roller gage is on a line that is makes an angle of
*θ*/2 with the plug. - The slope of line connecting the roller gage centers has the value tan(
*θ*/2). - The line’s slope is computed using the rise () and run (
*L*–_{1}*L*) values shown in Figure 2._{2}

### Example

Figure 4 shows works through the angle calculation example of Figure 1.

## Conclusion

I have some designs I plan to build that have angled holes. This procedure will give me a way to accurately measure the angle of these holes.

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