Sine bar protractor

[mklotz]

Reading a conventional protractor to any decent accuracy always tries my patience. So, I built a sine bar protractor. As can be seen, in addition to the measuring arms, it has two rolls, similar to those on a sine bar.



An offset half-lap hinge allows both arms to close flat against each other.



In use the device is set (or read) with calipers reading the separation between the two rolls.



The mathematics for converting between angle and caliper reading are a bit complicated, so I wrote a program to do the dirty work. It's available in the PROTRAC.ZIP archive on my page.

[Carld]

Very nice. Yep, it would be difficult to compute since a sine bar is set using the verticle height and your bar uses a variable angle and gap to compute the correct angle.

I don't use a sine bar much but it is troublesome sometimes. I can see where you could stick that in an angle gap and set it to the angle there and then measure the gap between the pins and compute the angle. That tool has posibilities.

[toastydeath]

You've actually created a device a good deal more accurate than a sine bar (if it was made to the right degree of precision). Sine bars rapidly become sensitive to small changes in height the greater the angle, and rapidly lose accuracy. The thing you've got, sometimes called a microsine bar/table, eliminates the fundamental geometry problems encountered with a sine table.

The difficulty in calculating the angle is paid off manyfold in the accuracy of the angle it can be set to.

[BadDog]

Yeah, errors can be rather large for large angles (generally over 45*). And not to split hairs, but technically not a "sine" bar anyway...

Nice as always!

[toastydeath]

Hmm..

How isn't it a sine bar?

http://en.wikipedia.org/wiki/Law_of_sines

[BadDog]

The term "sine" bar has to do with the trigonometric function whereby you can determine the angle based on the height of the blocks where the orientation forms a right triangle. In standard form:

sine(a) = opposite / hypotenuse.

But this is true only of a right triangle. When using sine bar, you know the hypotenuse, that's the length of the sine bar. You know the angle you want. So you solve for "opposite" and have your gage block stack.

The key measurement (the calipers) for the described device does not utilize the "sine" function because the orientation does not form a right triangle. Instead, it requires a more complex calculation represented by Marv's program he mentioned. It's generally simplified by expressing as 2 equal right triangles, so perhaps this would be a "double sine of half the angle bar"?

[Tim Clarke]

I like it. You guys who have served your apprentieships, or are knowledeble in math can juge the merit much better than I. However it looks like it's so simple that I wonder why I never thought of it. Seems like setting it with a height guage would be the way to go.

TC

[toastydeath]

I guess what I was saying is that sin(a) = o/h isn't the law of sines, from which I assumed sine tables took their name.

But I'm not into the history of the device so much, so I'm certainly not an authority on the taxonomy of it.

[BadDog]

Oh, I'm certainly not either. I just always "assumed" (heh) that it was called a "sine bar" because of the simple basic trig function/equation employed in it's use. You can surely get there from the law of sines, but I never considered that the name was derived from the law of sines. <shrug> But as I said initially, it's "splitting hairs" anyway as we all know what he meant...

Edit
Tim: Setting with a height gage is possible, and takes you back to simple right triangle trig, but you loose your reference point, which complicates things again.

Also just noticed that the bottom pin is not located on line with the pivot, so it's more complicated than 2sin(a/2), or "twice the sine of half the angle".

[dp]

Hmm..

How isn't it a sine bar?

http://en.wikipedia.org/wiki/Law_of_sines

A sine bar (as I understand them) requires that one angle must always be 90 degrees. This tool has no imposed angle of 90 degrees. A ray between the pin centers forms a chord of a circle with a radius of the pin/hinge length, and where the hinge is the center, but because the pins are not infinitely small in diameter the math to determine the angle is more complex as Marv has stated.

If you measure the distance between the points opposite on the pins, you actually describe a ray that extends symmetrically beyond the circumference of a circle by one half pin diameter, and which forms a chord of a circle between the intercept points of the circumference and the pin center. Measuring the adjacent points of the pins as shown in the photos describes a ray that is shorter than the chord of the circle by the diameter of one pin.

[BadDog]

Yeah, looking at it more I'm realizing I missed several key points in my initial take on the complexity of calculation. Been a lot of years since I used anything but the basic trig right triangle stuff...

[toastydeath]

The same equations are used to solve both right and scalene triangles, except in right triangles, you can use the simplified versions of the law of sines and law of cosines to do the work.

Which is why I keep coming back to this - it's a sine table, it just uses the unsimplified versions of the same equations to solve. Namely, the law of cosines can be used to directly give you the angle of the microsine fixture once you measure the distance between pin centers (which is implied in the use of the fixture):

cos A = (b² + c² − a²) / 2bc

[BadDog]

Ok, so maybe my assumption that the name was based on the simple formula used (i.e. sin(A)=o/h) was naive. I recall going through all the derivations and proofs in Trig and Linear (even some Cal?, can't recall exactly what was in which classes from 25 years ago), but it never occurred to me that the name was based on the general law of sines rather than the simplified formula applied for it's use. That certainly provides for a broader answer to "what exactly is a sine bar?" Not sure that is a good thing though. In my myopic view, at least I know what someone is talking about when they say, "how do I use a sine bar", and I can give them a short answer they can easily apply.

Oh, and one adjustment to that equation as applied. Of course the user would need to account for pin radius (add 1 dia. to measurement to get a required angle) in your equation. I'll stick with my sketches and converting to right triangles, I can keep that in my head. Otherwise I have to pull out a book...

Ahhh, I love this forum/hobby...

[Tin Falcon]

I like it. You guys who have served your apprentieships, or are knowledeble in math can juge the merit much better than I. However it looks like it's so simple that I wonder why I never thought of it. Seems like setting it with a height guage would be the way to go.

TC

Using a height gage ould create the right triangle then you could use the sine funtion.
Tin

[mklotz]

I seem to have created a monster by referring to this thing as a "sine bar protractor". I wanted a simple name that would be familiar to readers and suggest how the device worked.

In reality, the only similarity to a sine bar is the fact that it uses rolls and a linear measurement to obtain an angle. It does not rely on the right triangle relationship utilized by a sine bar but rather infers the subtended angle from the (linear) measurement of the chord. Technically, this involves the use of the sine *function*, but in a way different from its use in a typical sine bar setup.

Perhaps things will be clearer if one examines the jpg that is included in the PROTRAC.ZIP archive...