MadSci Network: Engineering

Re: What's needed to construct a vernier caliper?

Date: Thu Jan 18 12:39:13 2001
Posted By: Justin Roux, Engineering and Physiological Scientist.
Area of science: Engineering
ID: 976459660.Eg

Hello Bob,

please forgive the long wait for an answer but sit back and enjoy while I revel in the answer to this question that owes itself far more to mathematics than to engineering.

First, a story.

There was once a gold merchant who had a fleet of ten camel drivers. Every week he would give ten 1Kg (Metric system ha ha ha) bars of gold to each camel driver and send them to market to sell the gold. One camel driver, however, was a dishonest fellow; once out of sight he would shave exactly 1/10th from each bar in such a way as it was invisible to the eye and keep the shavings for himself. At the weigh in, the 100 bars from all the camel drivers would weigh only 99Kg. The bars were weighed individually and the light bars were discovered, but not the culprit. The gold merchant consulted a wise man who told him that he could catch the thief with a single use of the scales.. How? Simple. You line up all of the camel drivers when they arrive at market and take one bar from the first man, two from the second, three from the third, and so on until you have 55 bars. The scales should show 55 Kg. You find out how many 1/10s you fall short by, let's say 6, and that will point to camel driver number six, because you took six bars from him and only he could have offset the weight by that amount.

Now for the Vernier scale.

Take two sliding scales marked in units with 1/10th divisions but make the divisions on one scale 10% bigger than those on the other. This is the Vernier scale invented by Pierre Vernier at the start of the 17th century. To picture this have a look at figure A from the wonderful Reader's Digest Encyclopaedic Dictionary.

Do you see what I mean? The fixed scale is the larger one, the sliding scale is the smaller one. Now slide the smaller scale along the larger one until it's origin falls some way between two divisions on the fixed scale. Let's imagine that it falls halfway between two divisions as shown in figure B. If the two scales were exactly the same size, then every marker up the scale would now be half of a division out of line; but they're not. Because the smaller scale has divisions that are 10% smaller, the next marker on the sliding scale will only be 0.4 out of synchronicity. The next will be 0.3, the next 0.2, the next 0.1, until you get to the fifth marker, which will line up with a marker on the fixed scale. If each marker on the sliding scale has 'shaved off' 0.1 of the offset, an offset of 0.5 could only be corrected by the fifth marker on the sliding scale. This exposes the offset for the value that it is.

To make a Vernier scale, you need two pieces of flat-edged material, a fine pencil, and a good ruler. That is all.

I hope I've made it clear, go to your workshop and have a good look at a your Vernier calipers.... unless some dishonest camel driver has stolen them!


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