Sine bar protractor

[lazlo]

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:



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

[lazlo]

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?



Cheers,

Robert

[toastydeath]

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]

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]

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]

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]

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]

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:

[lazlo]

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]

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]

Oh yeah?

Deleted/edited-out

[oldtiffie]

Getting rid of a few old Shibboleths

Edited/deleted-out

[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

[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]

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.