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mklotz
08-06-2007, 06:13 PM
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.

http://i81.photobucket.com/albums/j234/mklotz/tools/protrac1.jpg (http://s81.photobucket.com/user/mklotz/media/tools/protrac1.jpg.html)

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

http://i81.photobucket.com/albums/j234/mklotz/tools/protrac2.jpg (http://s81.photobucket.com/user/mklotz/media/tools/protrac2.jpg.html)

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

http://i81.photobucket.com/albums/j234/mklotz/tools/protrac3.jpg (http://s81.photobucket.com/user/mklotz/media/tools/protrac3.jpg.html)

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
08-06-2007, 06:24 PM
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
08-06-2007, 07:26 PM
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
08-06-2007, 07:49 PM
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
08-06-2007, 08:27 PM
Hmm..

How isn't it a sine bar?

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

BadDog
08-06-2007, 10:32 PM
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
08-06-2007, 10:51 PM
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
08-06-2007, 11:05 PM
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
08-06-2007, 11:13 PM
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
08-06-2007, 11:23 PM
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
08-06-2007, 11:27 PM
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
08-06-2007, 11:49 PM
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 = (b + c − a) / 2bc

BadDog
08-07-2007, 12:15 AM
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. :D

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... :D

Tin Falcon
08-07-2007, 03:46 AM
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
08-07-2007, 12:52 PM
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...

http://i81.photobucket.com/albums/j234/mklotz/sine.jpg

BadDog
08-07-2007, 02:28 PM
Sorry about that, I started just in fun, then it got out of hand. Sad thing is, in my hasty replies, I made so many stupid oversights as to be rather silly. Forgot to include the radius in the formula, forgot to include the pin diameter, didn't notice/include the base pin being offset. Sheesh, sometimes it does not pay to post...

Edit: Or to put it more simply, "Better to remain silent and be thought a fool..." :D

toastydeath
08-07-2007, 02:32 PM
I certainly thought it was all in good fun and vigorous discussion!

I apologize if anyone took it in a different way.

BadDog
08-07-2007, 02:36 PM
Not at all. I knew what Marv meant (as indicated in my post), I was just poking fun too. But the following discussion was very intertesting, even if I did forget to put my brain in gear for a few points. :o

madman
08-07-2007, 07:31 PM
No not really. I just uze my protractor (MZB) with xtra long arm for well extra long work. Or my sine bars and joe blocks. Never trusted verniers much. They wear all over the place the jaws that is ect.

NickH
08-08-2007, 11:41 AM
Edited as I had obviously "lost the plot"

BadDog
08-08-2007, 03:23 PM
"Height" is not measured, distance between the pins is measured. Check out the picture Marv posted, it describes how it works very well.

Evan
08-08-2007, 05:07 PM
Marv,

Check out this page. It describes the double arm drive principle that I used to design and build an astronomical tracking device. It seems to me that the same principle could be used to make a protractor that would be settable by a strictly linear measurement over a good part of the travel. I don't have time to play with this idea now, I have much too much else to do.

http://hometown.aol.com/davetrott/page17.htm

John Garner
08-08-2007, 07:02 PM
Marv --

Great minds really do think alike . . . Moore Special Tool used (uses?) the same concept for their sine plate, which can be used to generate an angle up to 90 degrees without the accuracy degradation exhibited by the conventional-design sine plate.

It's been long enough that I don't remember for sure, but I have a hazy memory that the "separating rolls" on the Moore plate are coaxial when the top and bottom plates are parallel. If so, the thickness of the gage block stack needed to set any given angle would simplify to twice the sine of the half angle times the plate constant less the roll diameter.

John

toastydeath
08-08-2007, 07:26 PM
Oops, didn't mean to reply here. Post removed.

toastydeath
08-08-2007, 07:44 PM
Marv --

Great minds really do think alike . . . Moore Special Tool used (uses?) the same concept for their sine plate, which can be used to generate an angle up to 90 degrees without the accuracy degradation exhibited by the conventional-design sine plate.

It's been long enough that I don't remember for sure, but I have a hazy memory that the "separating rolls" on the Moore plate are coaxial when the top and bottom plates are parallel. If so, the thickness of the gage block stack needed to set any given angle would simplify to twice the sine of the half angle times the plate constant less the roll diameter.

John

Moore still makes the microsine table, which is what you're referring to.

However, last time I saw one for sale, the person wanted $14,000 for it.

Better than the Moore Master Index table, which is $30k and up.

mklotz
08-08-2007, 08:12 PM
Marv --

Great minds really do think alike . . . Moore Special Tool used (uses?) the same concept for their sine plate, which can be used to generate an angle up to 90 degrees without the accuracy degradation exhibited by the conventional-design sine plate.


Ah well, there goes my chance to make a million bucks. In a world where the majority of the people can't read a ruler, a device that requires inverse sine functions to find an angle probably never had a chance anyway.

mklotz
08-09-2007, 02:15 PM
Oldtiffie,

Thanks for the kind words.

I try to make all my programs as user-adaptable as possible. When only a few inputs are required, as in PROTRAC, I have the program query for them directly.

Where large data sets are required, as in CHANGE, the program reads these inputs from a standard ASCII text file modifiable by the reader using any text editor.
This ensures that the user, once having entered the data specific to his situation, can make future reruns of the program without the tedium of reentering his data.

Lots of folks like to go on about measuring to tenths (0.0001") and arc seconds. Such accuracy is gross overkill in most HSM projects and, furthermore, is probably realistically unachievable in the average HSM shop.
For instance, one arc second is about 5 microradians. That translates to a 0.3" error at a distance of one mile.

5E-6 * 5280 ft/mile * 12 in/ft = 0.3 in

"Yeah - I am "metricated" and my rotabs and verniers are calibrated in "deg/min" and not "decimal degree""

Frankly, I would think that the metric countries would use fractional degrees rather than the absurd sexagesimal system inherited from the Babylonians. Ah well, at least you Aussies haven't adopted the French grad. (I may be wrong but I think *only* the French use the grad.)

mklotz
08-09-2007, 09:07 PM
If you examine the equations, you'll see that d and delta have to be known separately in order to solve for either the angle or the separation. Of course, once a protractor is built, the user could hard wire the values of these variables into the code and thus avoid the need to reenter them with each use.

All the calculations are easily done on any scientific calculator. I've never seen a scientific calculator that doesn't have inverse trig functions implemented.

In 30+ years of working on military (both US and foreign) contracts, I have never had occasion to see an angle quoted in grads nor had a need to convert an angle to grads. It was a French idea and seems to have gone the same way that the post-revolutionary "metric" clocks went.

John Garner
08-10-2007, 01:34 PM
Beware the angular unit "grad", which we "murkins think is "1/400 of a circle" or "1/100 of a right angle", because our German brothers think that a grad is "1/360 of a circle" or "1/90 of a right angle" . . . the unit we call "degree".

In an attempt to rectify this dichotomy, the International Federation of Surveyors (FIG, from the French "Federation Internationale des Geometres") about 20-some years ago declared the 1/400 of a circle unit to be officially renamed the GON. The companies making survey equipment went along with the renaming, but the calculator makers haven't.

Then there's the French. I've worked with English-speaking French engineers who use the word "degree" to mean either 1/360 circle or 1 /400 circle . . . the former being a "sexagesimal degree" and the latter a "centesimal degree".

Incidentally, the centesimal degree can be divided into 100 centesimal minutes (abbreviated "c"), each of which can be subdivided into 100 centesimal seconds (abbreviated "cc"). I don't know if there is an "official" way of notating an angle measured in centesimal degrees, centesimal minutes, centisimal seconds, but I've seen them recorded in a number of ways, using slashes, commas, or dots as unit separators. In any case, as long as two digits are recorded for the centesimal minute and centesimal second values the "notational conversion" to decimal division of the centesimal degree is trivial: replace the centesimal degree - centesimal minute separator with a decimal point (or, in European practice, a comma) and delete the centesimal minute - centesimal second separator.

An example to illustrate?

An angle of 123 centesimal degree, 45 centesimal minute, 67 centesimal second may be recorded 123,45c,67cc or 123.45.67 or 123,45,67 or 123/45/67, which is 123.4567 centesimal degree.

John

lynnl
08-10-2007, 01:54 PM
I'm sorry I read that!

lazlo
08-10-2007, 04:25 PM
All the calculations are easily done on any scientific calculator. I've never seen a scientific calculator that doesn't have inverse trig functions implemented.

Neat protractor Marv! Although calculating the linear span of the chord seems like a lot of key punches on a scientific calculator.

I've got one of these (German) micro sine bars high on my projects list:

http://images.mercateo.com/images/products/Hahn+Kolb/gr_37630_5.jpg

Penn Tool Company has a Chicom copy, but it's $149 (!) You can see the obvious difference in quality, even from the stock photos:

http://www.penntoolco.com/images/catalog/4818.gif

lazlo
08-10-2007, 04:27 PM
Moore Special Tool used (uses?) the same concept for their sine plate, which can be used to generate an angle up to 90 degrees without the accuracy degradation exhibited by the conventional-design sine plate.

John,

Here's Moore' Sine Table. How is it better than a conventional Sine plate?

http://mooretool.thomasnet.com/Asset/14a_31050.jpg

Cheers,

Robert

toastydeath
08-10-2007, 07:36 PM
A microsine table doesn't use a stack of gage blocks at 90 degrees to the base.

The two tables listed by lazlo (before the Moore table) are NOT microsine tables - they are traditional sine fixtures. The gage stack is vertical, and the error will increase as the angle increases.

A true microsine table (the Moore, for example) has no fixed angular relationships (which is the root cause of the inaccuracy). As such, there is no increase in sensitivity and associated loss of accuracy as the work table angle approaches 90 degrees.

Setting it is also a little better. It uses a set of micrometer screws (black bar, center of the table, going from the base to the table) for fine adjustment. One either takes a stack of gage blocks, or alternatively, sets the adjustable gage block that comes with the table to the desired height. There are a set of ground pins, in very accurate holes, on either side of the table and base. Thus, you can check the fit on both extremes of the table and make sure there is no twist. The gage block stack is used for "feel" only, and isn't compressed under the load of the work. The screw and the locking clamps on the side of the table take the load.

Unfortunately, a good microsine fixture does cost many thousands of dollars. The Moore is one of the most expensive. When considering purchasing a microsine table, ask yourself, "Would I like a new car, or this fixture?"

lazlo
08-10-2007, 07:55 PM
The two tables listed by lazlo (before the Moore table) are NOT microsine tables - they are traditional sine fixtures.

That's why I called them Sine Bars.



I've got one of these (German) micro sine bars high on my projects list:

mklotz
08-10-2007, 08:07 PM
Neat protractor Marv! Although calculating the linear span of the chord seems like a lot of key punches on a scientific calculator.



That's why they make programmable calculators and also why people write computer programs.

toastydeath
08-11-2007, 01:59 AM
That's why I called them Sine Bars.

My apologies, I read that as "Micro sine bars," as in, microsine bars. Not micro, as in small.

John Garner
08-11-2007, 10:07 PM
Robert --

The major advantage of the Moore-type sine plate is that -- unlike a conventional sine plate -- it can be set to angles approaching 90 degrees without loosing signficiant accuracy.

It's been so many moons since I worked with a Moore plate that some of the details are lost in the dusty wayback of memory. In essence, though, the base and tilting platform of a Moore sine plate form an isosceles triangle with the stack of gage blocks making the third side. The perpendicular bisector of the gage block stack intersects the hinge point at the vertex formed by the equal-length sides, thus forming two equal right triangles, the plate base forming the hypotenuse of one right triangle, the tilting plate forming the other hypotenuse.

Each of these right triangles has a vertex co-located with the plate's base-to-tilting-plate vertex, and because the right triangles are equal their angle at that vertex is one-half of the sine plate's angle. So, to set a given angle on the sine plate takes a stack of gage blocks that is twice as long as the Side Opposite of the right triangle.

Err, well, almost. The geometry of this type of sine plate depends on the spacing of the Roll CENTERS, so the length of gage block stack needs to be reduced by the radii of the two Rolls.

The length of the right triangle's Side Opposite is calculated exactly as the height of gage block stack needed for a conventional sine plate, which is to say "Roll Spacing times Sine of Angle", but THIS Angle is one-half of the set-to angle.

As I dimly recall, the Moore plate has three 5/8 inch diameter rolls: one essentially forms the hinge between the top and bottom plates, one on the tilting plate centered 8 inches from the hinge roll center, and one on the base plate centered 8 inches from the hinge roll center. The algorithm for calculating the required height of the gage block stack is something like this:

2 x 8 inch x Sine (Half of Plate Angle to Be Set) - 5/8 inch

To set the plate to a 90 degree angle would take a gage block stack of

2 x 8 inch x Sine (90 degree / 2) - 5/8 inch

2 x 8 inch x Sine (45 degree) - 5/8 inch

2 x 8 inch x 0.707107 - 5/8 inch

10.6887 inch

To set a plate angle of 89.9 degree, the gage block stack would be 10.6788 inch, 0.0099 inch different.

In contrast, mathematical theory says a conventional sine plate with 10 inch roll spacing would take a 10.0000 inch stack to set a 90 degree angle or 9.999985 inch stack to set the 89.9 degree angle, a difference of 0.000015 inch. Shop practice recognizes this sensitivity of the conventional sine plate and hesitates to use a conventional sine plate to set an angle greater than 45 degrees.

I've probably overlooked something in writing this essay that's important to consider when actually using a Moore sine plate, but it's the best broad-brush description I've been able to drag out of a dusty memory hole. I certainly hope it helps answer your question.

And, if anyone can fill in missing points or correct any errors . . . please do!

John

lazlo
08-12-2007, 12:24 AM
Ouch.
Touche'!

Depends on how much you're willing to type on your calculator in the shop (I don't have a PC in the shop).

Sine bars are 10" or 5" long because you can do the calculation much quicker: you just move the decimal over one place for a 10" sine bar, or move it over one place and divide in half for a 5" sine bar.

Marv's protractor is really neat, but it requires a bunch of keypresses on a calculator to solve the chord. You really need to have Marv's BASIC program for his protractor to be convenient:

http://i81.photobucket.com/albums/j234/mklotz/sine.jpg

lazlo
08-12-2007, 12:35 AM
the base and tilting platform of a Moore sine plate form an isosceles triangle with the stack of gage blocks making the third side.
...
because the right triangles are equal their angle at that vertex is one-half of the sine plate's angle. So, to set a given angle on the sine plate takes a stack of gage blocks that is twice as long as the Side Opposite of the right triangle.

Excellent explanation John -- many thanks!

Sounds like you could convert a conventional Sine plate into a Moore-style sine plate without a lot of work.

I can't remember the last time I needed an angle > 45 though :)

toastydeath
08-12-2007, 12:49 AM
Look up the law of cosines - it's a single step, much much faster way to solve the triangle than by the chord method. Of course, it's only single step on a graphing/scientific calculator.

oldtiffie
08-12-2007, 01:34 AM
Deleted/edited-out

oldtiffie
08-12-2007, 09:27 AM
Edited/deleted-out

mklotz
08-12-2007, 12:37 PM
The error equations for a sine bar are easily derived from the fundamental equation:

sin(theta) = h/L

where:

theta = angle
h = stack height
L = length, i.e., distance between roll centers

Taking the derivative wrt h, we have:

dtheta = dh/[L*cos(theta)]

as the equation that relates an error in the stack height, dh, to the resulting error in the angle, dtheta. Since 1/cos(theta) grows as theta increases, it's obvious that the angle error is much more sensitive to stack errors as the angle increases - which only confirms what most of us already know.

Taking the derivative wrt L, we have:

dtheta = - [dL * tan(theta)]/L

for an error in the sine bar length, dL.

Since the tangent increases with angle, the angle error due to length error also grows as the angle increases.

If one uses the SINEBAR program from my page to compute the stack height (and Jo blocks needed to achieve that height), the numerical value of these errors will be printed out, e.g.:

SINEBAR CALCULATIONS

Distance between sine bar rolls [5] ? Angle input mode [D]ecimal degrees, (X) deg/min/sec ?
angle in decimal degrees [30.125 deg] ?
Distance between rolls = 5.000000
Angle = 30.125000 deg
Stack height = 2.509441
Stack height measured in same units as roll separation.
A .001 error in the roll distance will cause an angle error of 0.006649 deg
A .001 error in the stack height will cause an angle error of 0.013249 deg

Blocks from standard 81 gage block set needed to form stack = 2.5094 in:

block = 0.1004 remainder = 2.4090
block = 0.1090 remainder = 2.3000
block = 0.3000 remainder = 2.0000
block = 2.0000 remainder = 0.0000

lazlo
08-12-2007, 01:13 PM
The error equations for a sine bar are easily derived from the fundamental equation:

Agree Marv -- Tiffie was quoting the sine error from his shop text, which assumed a sine bar error of 0.02 mm (8 tenths) and a gage block stack error of 8 tenths. That's a pretty crappy setup if your sine bar isn't straight/parallel to within 8 tenths.

...and even shop grade gage blocks are accurate to within +4, -2 hundred thousands.

By the way, the second page of Tiffie's text shows a couple of very clever sine bar setups. I've been using a sine bar just as a precision angle gage, with
the work sitting on top of it, but those pictures show a whole new way to construct sine bar setups (to me, anyway)...

mklotz
08-12-2007, 01:38 PM
By the way, the second page of Tiffie's text shows a couple of very clever sine bar setups. I've been using a sine bar just as a precision angle gage, with
the work sitting on top of it, but those pictures show a whole new way to construct sine bar setups (to me, anyway)...

Yes. In particular, his Figure 33 demonstrates why it's seldom necessary to set a sine bar for an angle greater than 45 degrees. I know that I've never used one at >45. There's always some way around that.

toastydeath
08-12-2007, 01:45 PM
Setting the sine bar over 45 degrees is usually done for compound angle fixturing, such as setting a rotary table on top of it to bore or grind holes in a perimeter, at an angle. In that application, small errors can make a difference in the first thing to be attached to the table itself, as now you've starting to stack objects and accumulating error.

It's also done in some inspection applications, where you want to get the specific angle between some feature and another without interpolating it from other features (and thereby increasing the error of the measurement).

And unfortunately, there can be more error in the method detailed in fig. 33 than is suggested by that text, by nature of a somewhat awkward setup.

LES A W HARRIS
08-12-2007, 09:28 PM
Marv, Nice job, thanks for sharing.

Tweeked a bit, rolls at 5.000" C.D. & zero gap at zero angle.
http://i37.photobucket.com/albums/e97/CURVIC9/07%20SHOPSTUFF/protractorassy02.jpg

lazlo
08-12-2007, 10:11 PM
Marv, Nice job, thanks for sharing.

Tweeked a bit, rolls at 5.000" C.D. & zero gap at zero angle.

That's very clever Les. So Theta simplifies down to:

Θ = 2 Sin-1[d+D/10]

Now that's something you can do in the shop without a bunch of keypresses! :)

oldtiffie
08-12-2007, 10:21 PM
Edited/deleted-out

LES A W HARRIS
08-13-2007, 01:40 AM
That's very clever Les. So Theta simplifies down to:

Θ = 2 Sin-1[d+D/10]

Now that's something you can do in the shop without a bunch of keypresses! :)


Minus the Base Angle Constant!


http://i37.photobucket.com/albums/e97/CURVIC9/07%20SHOPSTUFF/protractorassy03.jpg



2*INVSIN ((.5000"+3.3858")/10) - 5.731968deg
40.00038deg
Closer than my eyeball!

Drawn at 40:00:00

dp
08-13-2007, 02:55 AM
I think some math can be eliminated by measuring a pin and zeroing your caliper at that dimension offset, no?

LES A W HARRIS
08-13-2007, 12:18 PM
I think some math can be eliminated by measuring a pin and zeroing your caliper at that dimension offset, no?

The original layout used an inside measure, and therefor, one adds the pin dia to get the center to center dimension (the chord dimension). I presume one could zero at pin dia and measure across the outside of the pins giving the center to center distance, (chord).

oldtiffie
08-14-2007, 10:21 AM
Edited/deleted-out

miker
08-17-2007, 08:00 PM
Thanks for posting this Marv.

Now I HAVE to learn TRIG!!!!!

Thanks a LOT!!! :)

Rgds

John Corden
05-14-2012, 05:57 PM
Gentlemen,

I came across this thread while searching for details of a sine protractor I acquired - see photos below.

http://i1094.photobucket.com/albums/i456/JCphotob/DSCN2912.jpg

http://i1094.photobucket.com/albums/i456/JCphotob/DSCN2911.jpg

http://i1094.photobucket.com/albums/i456/JCphotob/DSCN2913-1.jpg


There are no instructions or details with the device. However, by measuring the height below the arm for various angles, and doing some trig, it would appear that :

the arm length is 100 mm
the height to make the arm parallel to the base is 5 mm.

So from these figures I can use it as a (very nice) sine bar.

Oddly enough, the height of the machined surface (on which to stack the gauge blocks) is 27.69mm - a strange dimension.

My question is: what was it used for, and have I missed something obvious?

I assume that I calculate the height of the stack required for a given angle, then add 5mm?

Any thoughts or more information would be greatly appreciated.

Thanks,
John

Bob Fisher
05-14-2012, 08:56 PM
Should call it an isoceles protractor. It solves as two right angles one half the target angle. Bob.