The Abbe Principle in design
We all know what a vernier calliper or a screw gauge looks like. And if you’ve ever used them, you would have observed that a screw gauge tends to give more precise readings, than a vernier calliper.
But that’s not all.
If suppose a vernier calliper and a screw gauge were specially designed such that both of them were equally precise, we would still note a difference in their readings. But we know that the measurements from both are equally precise — then where does the difference creep in from?
You see, for measurements, just precision is not enough, there’s another very important factor without which this precision would hardly matter — Accuracy.
Through this piece we’ll be learning the Abbe Principle.
Well, as you know by now, a screw gauge is more precise and accurate than a vernier calliper. You might be wondering, what the difference between accuracy and precision is anyway.
Simply put, precision denotes the closeness of two arbitrary measurement values to each other. Accuracy on the other hand, refers to the closeness of your measurement reading to a known value, or the correct value.
Now, this Abbe principle is what will provide the answer to why a vernier calliper and a screw gauge of the same precision, still comes with different accuracies. The principle is basically a set of rules for linear measurements laid down by a German physicist, Ernst Abbe in around 1890.
The overall claim of the Abbe principle is that you’ll get the best measurements when you take the readings as close to the action as possible. For example, if you were to find the temperature of a pot of boiling water, it would obviously give you more accurate readings when you dipped a thermometer in the water, than if you laid down the thermometer beside the pot.
Using this same theory, if you can remember how a vernier calliper and screw gauge looks like, you’ll understand the Abbe principle in effect. You see, when measuring with the vernier calliper, the pincers that hold the object are not in line with the measuring scale. A screw gauge does the measuring within the line of action itself — the measuring scale and the object being measured are on the same imaginary line — and this is why a screw gauge is always going to be more accurate than a vernier calliper, no matter how precise its competitor may be.
So, measuring with the screw gauge is the best-case scenario. But, measuring with the Vernier calliper, introduces a minimal second order error, called the Abbe Offset.
This offset is negligible just because although the action and measurement does not take place in the same line, the lines of measurement and action are parallel to each other.
However, when this parallelism is no longer respected, angular first order errors are introduced — and these are quite significant. This is because, the angular error keeps increasing manifold, the farther you move the object from the scale.
For example, if you had a spinning top, and you bent the axis slightly, the top would start to wobble when you try to spin it. And this wobble will only increase, the more you bend the axis.
This, is the Abbe error.
In designing mechanisms like actuators and bearings, the Abbe principle is literally a life-saving tool. If and when making mechanical systems and structures, no matter how small or large it may be, this principle will make sure, that you are being accurate and precise, for best results.
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