Sine bar protractor

[Bob Fisher]

Should call it an isoceles protractor. It solves as two right angles one half the target angle. Bob.

[John Corden]

Gentlemen,

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








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

[miker]

Keeper

Thanks for posting this Marv.

Now I HAVE to learn TRIG!!!!!

Thanks a LOT!!!

Rgds

[oldtiffie]

Edited/deleted-out

[LES A W HARRIS]

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).

[dp]

I think some math can be eliminated by measuring a pin and zeroing your caliper at that dimension offset, no?

[LES A W HARRIS]

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!






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

Drawn at 40:00:00

[oldtiffie]

Correction

Edited/deleted-out

[lazlo]

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!

[LES A W HARRIS]

Marv, Nice job, thanks for sharing.

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

[toastydeath]

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.

[mklotz]

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.

[lazlo]

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]

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

[oldtiffie]

Getting rid of a few old Shibboleths

Edited/deleted-out