Radius measuring tool

[BillTodd]

Just saw this rather neat idea while browsing:

The precise setting angle of the calliper jaws means the display reads the radius directly :

http://www.sharpfine.com/Calipers/digital-radius-caliper.html

[awemawson]

Neat, but surely there are very few times that you cannot get parallel jaws across a work piece to measure it, and with those long angled ones you can't get into tight spots I would have thought

[BillTodd]

it measures radii so will measure twice the length of tool and  can be used for sectors where diameter measurements are not possible

[SwarfnStuff]

Scratched my head a bit and agree with Bill in that it would be useful to get the Radius of stuff where you have only an arc to work on. Rather a specialized tool but very handy if you do that sort of stuff often.  Trying to get my head around how it would go on very large arcs but guess like any measuring stick it can only measure within the limits of it's length.
Regards,
John B

[BillTodd]

Rather a specialized tool

iwas thinking, that a homebrew pair of blades for the id side of my mitutoyos might be handy :-)

[RussellT]

I'm wondering whether you could just use the existing blades and a conversion table.

Russell

[mattinker]

Following the links, although it requires maths, this might be easier to make!

http://www.sharpfine.com/Indicator/radius-dial-gauge.html

Regards, Matthew

[BillTodd]

All true.

I have written code for a 8 pin microchip PIC that can read the scales (it would just need some kind of display)  and could easily be modified to do the chordal calculation or table look-up, but  the beauty/brilliance of the angle blades is it requires no microprocessor, maths or tables.

[BillTodd]

The geometry :

[RussellT]

That's clever.  I assumed originally that they'd changed the electronics.

Russell

[BillTodd]

Adapter blades:

[dvbydt]

That's clever Bill!
Here's the maths.
This took me a while to remember all the school maths and  there are several ways to proove this geometery.  Esentially, you need to find the angle "y" that will make CD equal to 1/2 of the radius (R).
tan y = CD/XC  also tan y= OE/XE  .................(1)
Since CD = 1/2R and OE and OC =R...................(2)
From (1)
CD/XC = OE/XE
Substituting from (2)
R/2.XC = R/XE
Or XE = 2.XC .............................................(3)
In triangle XOE by Pythagoras -
(XO)^2 = (XE)^2 + (OE)^2
Substituting,
(R+XC)^2 = (XE)^2 + R^2
Using (3)
(R+XC)^2 = (2.XC)^2 + R^2
Multiplying out
R^2 + 2.R.XC + (XC)^2  = 4(XC)^2 +R^2
Simplifying
2.R.XC = 3(XC)^2
Then  2R = 3.XC or XC = 2.R/3
In triangle XOE Sin y = OE/XO  or   R/(XC + R)
Therefore Sin y = R/(( 2.R/3) + R)
Simplifying  sin y = 1/(1 + 2/3)= 3/5  or 0.60 
Therefore y = 36.8698976 Degrees. The angle of the jaws is 2.y = 73.73979
Or if you prefer 73 Deg 44.3877 minutes.
Phew !

Ian

[BillTodd]

Well done Ian. 

Glad someone else can see the cleverness in the thing  (wish i'd have thought of it:))

[JHovel]

That is a brilliant adaptation Bill! I'll give some thought to making a set of 'Radius accessory jaws' for myself.
Just great. I need to figure out how to cut such a precise angle...

[BillTodd]

That is a brilliant adaptation Bill! I'll give some thought to making a set of 'Radius accessory jaws' for myself.
Just great. I need to figure out how to cut such a precise angle...

Forget trying to measure the angle , it's not even expressible as a finite number.

Essentially you'll need a good sine bar and gauge blocks or the means to make and measure a block accurately.

(I.E. You make a slightly tapered block(something I usually find quite easy) and measure where along the taper is the required thickness, this is marked and the sine-bar set on mark.)

I have not yet worked out the sine bar setting but it can be derived from Ian's formula (I think )

[edit] 5" sine bar setting is a nice round 3.0000" or 76.200mm

[Edit 2] just measured my unbranded 123 blocks and they are a surprisingly good 3.0000" (according to my 3" and 4" mics)

[dvbydt]

I don't know if it helps any, but if my maths is right, then if the sin of the half angle is 3/5, we are dealing with a 3,4,5 right angled triangle. Therefore setting up a sine bar to 36.89 degrees is straightforward.

Ian

[dvbydt]

Sorry Bill you got there already!

Ian

[BillTodd]

I don't know if it helps any, but if my maths is right, then if the sin of the half angle is 3/5, we are dealing with a 3,4,5 right angled triangle. Therefore setting up a sine bar to 36.89 degrees is straightforward.

 

Sorry Bill you got there already!

Ian

Reminds me of the constipated mathematician who worked it out with a pencil 

[BillTodd]

Sine bar setting on my Horizontal mill (as an example)

[edit] There is one caveat with this tool: the included angle is <90 so it cannot as designed measure corner radii. 

[sparky961]

Slightly OT but related nonetheless... 1-2-3 blocks, in my experience are very accurate on size and parallelism of like faces. DO NOT under any circumstances assume they are square though!