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Radius measuring tool

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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  :thumbup: (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:

--- Quote from: JHovel on November 09, 2015, 06:13:33 AM ---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...

--- End quote ---

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 :scratch:)

[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)

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