Friday, February 15, 2013

Fractional Inch Vernier Caliper

[SUNDAY, AUGUST 14, 2011: I've added a brief note on how a fractional vernier is read. Scroll way down.]

I bought the pictured caliper at Lee Valley in 2006 for $21.50, and it's a wonder I haven't worn it out; I use it very frequently. (The caliper is still available -- the catalogue number is 88N70.01.)

Note that the inch scale is fractional, not decimal. That's what makes the thing so useful to me. A precision caliper that reads directly in fractions of an inch along with millimetres is a real blessing in the workshop. (And I don't mean to appear backward or unschooled here. I'm quite conversant with metric and decimal inch measure as well, and I make use of them both as it suits me to.)

It actually baffles me a bit that precision fractional inch vernier calipers have always been a somewhat obscure item, considering the ubiquity of fractional inch measure that still adheres throughout Canada and the USA.

Anyway, I wanted to introduce the tool and recommend it. If you're a boomer of a certain age for whom fractional inch measure is second nature, I think you may find it useful; I certainly have. And if you're beginning to think I'm some kind of shill for Lee Valley, read on. I'll tell you of the problem I encountered with this caliper, and how I solved it.

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If you look closely at the caliper's inch cursor in the photograph, you'll notice that the screw recesses have a rather blank appearance, unlike those in the metric cursor, which obviously contain tiny screw heads. There's a reason for that; the inch cursor has no screws holding it in place.

When I got the caliper home and started using it, I noticed that the inch cursor was imperfectly zeroed. Rather than go through the aggravation of returning it to the store, I set about looking into what could be done to zero it.

I loosened the cursor and tried to zero it and retighten it -- no way. If anything, I'd made it worse. What no doubt happened at the factory was that the assembler encountered a marginal cursor fit, levered the thing into place as best he could with whatever means he had at his disposal, said, "Close enough for this outfit." and boxed the caliper. I doubt he'd have been thanked for doing otherwise.

Since I could see no way to zero the cursor and install the screws, I tried a different approach. I thoroughly degreased the cursor mounting area with lacquer thinner, got the cursor in place and zeroed, clamped it there and then filled the screw holes with epoxy. It worked remarkably well. The feel of the slide on the beam is flawless, and it's held together for four years now.

So there we are. When a twenty-buck 'precision' tool comes up a bit short on precision, there may be a way to deal with it. There certainly was in this case.

By the way, there's more to fractional inch measure with this caliper than meets the eye. See this post for a look at a practical application of some really tiny fractions of an inch.

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Addendum -- Reading a Fractional Vernier

It dawned on me recently that some may have found this post while looking for instruction on how to read a fractional vernier. I'm not a mathematician, and I'm not going to attempt a rigourous explanation, but following is how I understand it. It works for me.

If you enlarge the above photograph, you can clearly see that the caliper is reading zero -- the cursor's zero is directly aligned with the beam's zero. Now, look at where that puts the cursor's '8' -- directly aligned with the beam's '15/16'. So, we can think of the cursor as representing a 'short inch' that's 1/16" shy of a full inch.

That 'short inch' on the cursor is divided into eight equal parts ('short eighths'). Each of those 'short eighths' is 1/128" shy of a full eighth. (True. You're more than welcome to work it out and prove it.) So, moving the cursor rightward until the cursor's first 'short eighth' aligns with the beam's first full eighth represents a cursor displacement of 1/128". As each successive 'short eighth' aligns with each successive full eighth, another 1/128" of cursor displacement occurs until we arrive at a direct reading of 1/16".

Here's the sequence of eight 'short eighth'/full eighth alignments that occur within 1/16" of cursor motion to the right:









Think of it this way; what the cursor's divisions do for you is they give you a means of accurately interpolating eighths of sixteenths. One-eighth of one-sixteenth is 1/128th.

And that's the best I can do. I'd be delighted to read a better explanation if anyone has one.

And by the way, the vernier scale was invented by Pierre Vernier. He published the invention at Brussels in 1631. How's that for leaving a legacy?

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Addendum No. 2 -- A Fractional Vernier Variant

As with everything, there's a variation on the preceding. Pictured below are a couple of examples of half-inch/'short half-inch' verniers.

The nominal resolution is the same at 1/128", but the eight-division vernier on the cursor is only 7/16" long. On these verniers, one is looking for successive 1/16" alignments, rather than successive 1/8" alignments. Apart from that, the operating principle is no different.

Obviously, though, the inch/'short inch' vernier has inherently better visual resolution owing to its increments being more spread out.

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