Precision angles without a sine bar

[mklotz]

Precision angles generally makes one think of sine bars and Jo blocks.  That's certainly one way to go but Jo blocks can be expensive for the impoverished novice.

Fortunately, there's another way to go that involves only turning a cylinder to an accurate diameter-something most folks learn to do early in their career.

Let's say we have two cylinders; a smaller with diameter 'd1' and a larger with diameter 'd2'.  If we lay these two cylinders on a flat surface so they touch each other and then lay a flat plate on top of the two cylinders, that plate will form some angle, 'A' with the flat surface.

Now, with a bit of trig that's probably too much for most of this audience, one can solve for that angle as a function of the cylinder diameters.  Then, by inverting that equation, one can obtain an equation that yields the diameter of the smaller cylinder (d1) in terms of d2 and the angle (A).

Using the notation:

sa = sin(A/2)

this equation is:

d1/d2 = (1-sa)/(1+sa)

Select a size of stock you have (d2) and solve the above for d1.  Carefully turn a chunk of the d2 stock down to size d1.  Lay the two chunks next to each other and lay the flat side of your workpiece across the two and it should form an angle A with the base on which the cylinders rest.

[b.lindsey]

Nice simple solution Marv, and for most of our tasks more than adequate!!  Thanks.

Bill

[Kim]

Math is so cool!
Thanks for sharing this Marv.  Now I need to find something to use it on!
Kim

[PStechPaul]

If you have a sine bar but don't have gauge blocks (or don't want to mess with them), you can set a pretty accurate angle by using adjustable parallels and a micrometer or calipers. Also, for most angles, you can just make your own gauge block and mark it with the corresponding angle so you don't have to do all that math more than once.

[jschoenly]

If you need a custom Angle Block, you can clamp a plate in yous vise and trig out the location of 2 holes at the desired angle.  Drill the 2 hole locations with dials, DRO, as you wish.  Then place the plate in the vise with 2 dowel pins through the holes (no press needed, technically, size doesn't matter much) resting on the vise jaw or parallels and mill the top for the length needed.  Poof, custom angle blocks.  Many ways to get it done.  Fun stuff!

[Arbalest]

If you have a sine bar but don't have gauge blocks (or don't want to mess with them), you can set a pretty accurate angle by using adjustable parallels and a micrometer or calipers. Also, for most angles, you can just make your own gauge block and mark it with the corresponding angle so you don't have to do all that math more than once.

Agreed. Turning a gauge block on the Lathe to the size needed doesn't take long and is more than accurate enough for my needs.

This is how I make angle plates though if needed.

http://www.modelenginemaker.com/index.php?action=dlattach;topic=1476.0;attach=3718

[mcostello]

Marv, You are SO right about Math being too much for this audience of one!

[mklotz]

If you have a sine bar but don't have gauge blocks (or don't want to mess with them), you can set a pretty accurate angle by using adjustable parallels and a micrometer or calipers. Also, for most angles, you can just make your own gauge block and mark it with the corresponding angle so you don't have to do all that math more than once.

With a little bit of differential calculus, it's easy to develop an equation for the angle error due to the error in setting the height.  That feature is built into my SINEBAR program.

All that math?  There are very few equations simpler than the one that characterizes the sinebar.

This is how I make angle plates though if needed.

I've always been curious about machinists' seeming fascination with gigantic tables of numbers.  Given that scientific calculators can be had for less than $10, why would you make up a table of a constant times the tangent of an angle?  Also, what does the user do if his particular angle isn't in the table?  If he can't do a simple calculation on a calculator, he surely can't do non-linear interpolation in a table.

[Arbalest]

It's not difficult Marv, the best Calculator I've ever had is the one on my iPad but I don't keep it in the shed. If I need an angle not listed the formulas on the second sheet, you did look at the second sheet Marv didn't you?!     

[Allen Smithee]

You mean the sheet with the incorrect equation?

 

The equation *should* read:

Y = X * Tan(A)

 

It also gives an excellent example of why there is a convention that lengths and angles should be represented by different symbols (either using greek alphabet or even just upper/lower case letters) to improve clarity and avoid confusion...

Of course for low-precision and small angles the handy rule of thumb is "17 thou per inch per degree", which is extremely useful when working out how much packing to put where to level something.

AS

[mklotz]

It's not difficult Marv, the best Calculator I've ever had is the one on my iPad but I don't keep it in the shed. If I need an angle not listed the formulas on the second sheet, you did look at the second sheet Marv didn't you?!

Yes, I looked at the second sheet.  When I saw the equation, I stopped reading.

BTW, scientific calcs are way cheap enough to keep one in the shop.  In fact, keep one at each machine as well as on the bench.  The ipad isn't going to be more accurate.

[steamer]

OK Guys.....Marv posted a great tool.   To which I am very thankful.

Marv is an awesome guy...and a valued member here.

I think I did a spreadsheet on that some time back Marv...but I haven't gone there...I know how you feel about spreadsheets.....

IN ANY EVENT.

Let's keep it cool...and helpful, and respectful....please.......Hmmmm?

Dave.......with a raised eyebrow......no emoticon required...

[Arbalest]

I guess only the spreadsheets that you've generated are of value Marv. 

For those that find them useful however here's another one in imperial for our American cousins.

https://docs.google.com/file/d/0Bykt5WZ092aWZVdCcW5ya2xUc0k/edit?pli=1

[mklotz]

I guess only the spreadsheets that you've generated are of value Marv. 

For those that find them useful however here's another one in imperial for our American cousins.

https://docs.google.com/file/d/0Bykt5WZ092aWZVdCcW5ya2xUc0k/edit?pli=1

Sigh.

[Arbalest]

Sorry forgot the source link.

https://sites.google.com/site/lagadoacademy/machining---lathes-mills-etc/angle-plate