# Manually Cutting a Radius



## rake60 (Jan 22, 2010)

Forming a small radius on a manual machine is easy.
You grind a form tool and plunge it into the work piece to make the curve.
As the radius gets bigger that may not be an option. 
Two of the jobs I hated at work were manually cutting the rope groove in 
wire rope sheaves, and cutting the big clearance radius on the top ID of large 
brass bushings. I worked with guys who could manually free hand cut a 
perfect radius. I never could so I found an easier way. 

First you need a bolt circle calculator. I use Marv's _*BOLTCIRC.ZIP *_.
The program will give you coordinates to the center of a tool.
To keep it simple, say I want to cut a 1/2" radius using a .030" nose radius
tool. Add 1/2 that nose radius to the formula. In the program I'd enter:

Number of holes? = 360 
Radius of bolt circle? = .515
Diameter of holes? = .020 (You can put ANY value in there.)
Angular offset of first hole? Zero is fine.
X offset of bolt circle? Once again Zero is fine.
Y offset of bolt circle? Again Zero works.

You end up with a set of coordinates that look like this.
(It's a long list. Don't bother reading all of it! )

*Bolt circle specification:
Radius of bolt circle = 0.5150
Bolt hole diameter = 0.0200
Spacing between hole edges = -0.0110
Angular offset of first hole = 0.0000 deg
X offset of bolt circle center = 0.0000
Y offset of bolt circle center = 0.0000

HOLE    ANGLE   X-COORD   Y-COORD

  1   0.0000   0.5150   0.0000
  2   1.0000   0.5149   0.0090
  3   2.0000   0.5147   0.0180
  4   3.0000   0.5143   0.0270
  5   4.0000   0.5137   0.0359
  6   5.0000   0.5130   0.0449
  7   6.0000   0.5122   0.0538
  8   7.0000   0.5112   0.0628
  9   8.0000   0.5100   0.0717
 10   9.0000   0.5087   0.0806
 11   10.0000   0.5072   0.0894
 12   11.0000   0.5055   0.0983
 13   12.0000   0.5037   0.1071
 14   13.0000   0.5018   0.1158
 15   14.0000   0.4997   0.1246
 16   15.0000   0.4975   0.1333
 17   16.0000   0.4950   0.1420
 18   17.0000   0.4925   0.1506
 19   18.0000   0.4898   0.1591
 20   19.0000   0.4869   0.1677
 21   20.0000   0.4839   0.1761
 22   21.0000   0.4808   0.1846
 23   22.0000   0.4775   0.1929
 24   23.0000   0.4741   0.2012
 25   24.0000   0.4705   0.2095
 26   25.0000   0.4667   0.2176
 27   26.0000   0.4629   0.2258
 28   27.0000   0.4589   0.2338
 29   28.0000   0.4547   0.2418
 30   29.0000   0.4504   0.2497
 31   30.0000   0.4460   0.2575
 32   31.0000   0.4414   0.2652
 33   32.0000   0.4367   0.2729
 34   33.0000   0.4319   0.2805
 35   34.0000   0.4270   0.2880
 36   35.0000   0.4219   0.2954
 37   36.0000   0.4166   0.3027
 38   37.0000   0.4113   0.3099
 39   38.0000   0.4058   0.3171
 40   39.0000   0.4002   0.3241
 41   40.0000   0.3945   0.3310
 42   41.0000   0.3887   0.3379
 43   42.0000   0.3827   0.3446
 44   43.0000   0.3766   0.3512
 45   44.0000   0.3705   0.3577
 46   45.0000   0.3642   0.3642
 47   46.0000   0.3577   0.3705
 48   47.0000   0.3512   0.3766
 49   48.0000   0.3446   0.3827
 50   49.0000   0.3379   0.3887
 51   50.0000   0.3310   0.3945
 52   51.0000   0.3241   0.4002
 53   52.0000   0.3171   0.4058
 54   53.0000   0.3099   0.4113
 55   54.0000   0.3027   0.4166
 56   55.0000   0.2954   0.4219
 57   56.0000   0.2880   0.4270
 58   57.0000   0.2805   0.4319
 59   58.0000   0.2729   0.4367
 60   59.0000   0.2652   0.4414
 61   60.0000   0.2575   0.4460
 62   61.0000   0.2497   0.4504
 63   62.0000   0.2418   0.4547
 64   63.0000   0.2338   0.4589
 65   64.0000   0.2258   0.4629
 66   65.0000   0.2176   0.4667
 67   66.0000   0.2095   0.4705
 68   67.0000   0.2012   0.4741
 69   68.0000   0.1929   0.4775
 70   69.0000   0.1846   0.4808
 71   70.0000   0.1761   0.4839
 72   71.0000   0.1677   0.4869
 73   72.0000   0.1591   0.4898
 74   73.0000   0.1506   0.4925
 75   74.0000   0.1420   0.4950
 76   75.0000   0.1333   0.4975
 77   76.0000   0.1246   0.4997
 78   77.0000   0.1158   0.5018
 79   78.0000   0.1071   0.5037
 80   79.0000   0.0983   0.5055
 81   80.0000   0.0894   0.5072
 82   81.0000   0.0806   0.5087
 83   82.0000   0.0717   0.5100
 84   83.0000   0.0628   0.5112
 85   84.0000   0.0538   0.5122
 86   85.0000   0.0449   0.5130
 87   86.0000   0.0359   0.5137
 88   87.0000   0.0270   0.5143
 89   88.0000   0.0180   0.5147
 90   89.0000   0.0090   0.5149
 91   90.0000   -0.0000   0.5150
 92   91.0000   -0.0090   0.5149
 93   92.0000   -0.0180   0.5147
 94   93.0000   -0.0270   0.5143
 95   94.0000   -0.0359   0.5137
 96   95.0000   -0.0449   0.5130
 97   96.0000   -0.0538   0.5122
 98   97.0000   -0.0628   0.5112
 99   98.0000   -0.0717   0.5100
 100   99.0000   -0.0806   0.5087
 101  100.0000   -0.0894   0.5072
 102  101.0000   -0.0983   0.5055
 103  102.0000   -0.1071   0.5037
 104  103.0000   -0.1158   0.5018
 105  104.0000   -0.1246   0.4997
 106  105.0000   -0.1333   0.4975
 107  106.0000   -0.1420   0.4950
 108  107.0000   -0.1506   0.4925
 109  108.0000   -0.1591   0.4898
 110  109.0000   -0.1677   0.4869
 111  110.0000   -0.1761   0.4839
 112  111.0000   -0.1846   0.4808
 113  112.0000   -0.1929   0.4775
 114  113.0000   -0.2012   0.4741
 115  114.0000   -0.2095   0.4705
 116  115.0000   -0.2176   0.4667
 117  116.0000   -0.2258   0.4629
 118  117.0000   -0.2338   0.4589
 119  118.0000   -0.2418   0.4547
 120  119.0000   -0.2497   0.4504
 121  120.0000   -0.2575   0.4460
 122  121.0000   -0.2652   0.4414
 123  122.0000   -0.2729   0.4367
 124  123.0000   -0.2805   0.4319
 125  124.0000   -0.2880   0.4270
 126  125.0000   -0.2954   0.4219
 127  126.0000   -0.3027   0.4166
 128  127.0000   -0.3099   0.4113
 129  128.0000   -0.3171   0.4058
 130  129.0000   -0.3241   0.4002
 131  130.0000   -0.3310   0.3945
 132  131.0000   -0.3379   0.3887
 133  132.0000   -0.3446   0.3827
 134  133.0000   -0.3512   0.3766
 135  134.0000   -0.3577   0.3705
 136  135.0000   -0.3642   0.3642
 137  136.0000   -0.3705   0.3577
 138  137.0000   -0.3766   0.3512
 139  138.0000   -0.3827   0.3446
 140  139.0000   -0.3887   0.3379
 141  140.0000   -0.3945   0.3310
 142  141.0000   -0.4002   0.3241
 143  142.0000   -0.4058   0.3171
 144  143.0000   -0.4113   0.3099
 145  144.0000   -0.4166   0.3027
 146  145.0000   -0.4219   0.2954
 147  146.0000   -0.4270   0.2880
 148  147.0000   -0.4319   0.2805
 149  148.0000   -0.4367   0.2729
 150  149.0000   -0.4414   0.2652
 151  150.0000   -0.4460   0.2575
 152  151.0000   -0.4504   0.2497
 153  152.0000   -0.4547   0.2418
 154  153.0000   -0.4589   0.2338
 155  154.0000   -0.4629   0.2258
 156  155.0000   -0.4667   0.2176
 157  156.0000   -0.4705   0.2095
 158  157.0000   -0.4741   0.2012
 159  158.0000   -0.4775   0.1929
 160  159.0000   -0.4808   0.1846
 161  160.0000   -0.4839   0.1761
 162  161.0000   -0.4869   0.1677
 163  162.0000   -0.4898   0.1591
 164  163.0000   -0.4925   0.1506
 165  164.0000   -0.4950   0.1420
 166  165.0000   -0.4975   0.1333
 167  166.0000   -0.4997   0.1246
 168  167.0000   -0.5018   0.1158
 169  168.0000   -0.5037   0.1071
 170  169.0000   -0.5055   0.0983
 171  170.0000   -0.5072   0.0894
 172  171.0000   -0.5087   0.0806
 173  172.0000   -0.5100   0.0717
 174  173.0000   -0.5112   0.0628
 175  174.0000   -0.5122   0.0538
 176  175.0000   -0.5130   0.0449
 177  176.0000   -0.5137   0.0359
 178  177.0000   -0.5143   0.0270
 179  178.0000   -0.5147   0.0180
 180  179.0000   -0.5149   0.0090*

Turn the OD of the stock to the desired radius. In this example that would be 1"
Touch on the end of the stock and set a zero. Then touch on the OD
of the stock and set a zero. For a 90° radius use coordinates 1 - 90.
For a half round use 1 - 180 

You will end up with a perfect radius that has a whole bunch of tiny ridges that 
are easily blended in with emery paper. If that is too many coordinates for you
the number of holes can be reduced. You will still wind up with a perfect radius
but it will take much more polishing to get the ridges out.

This system also works for an internal radius.
Just invert the X and Y coordinates. 

Rick


----------



## mklotz (Jan 22, 2010)

Rick,

Thanks for the endorsement but you're using the wrong program - although what you did is fairly clever.

BOLTCIRC, as the name suggests, is used for laying out coordinates for bolt circles.

I do lots of radii by the incremental method and wrote a program, ROUNDER, for just that purpose. I've appended the text file that accompanies the program below. While the description talks about the use of a ball end mill, one could just as easily use an ordinary end mill. Many other tricky radiused cuts are possible via the judicious use of the program's output. Those who are mystified by anything mathematical can contact me for help on their particular application.





```
Let's say I have a 3" x 2" x 1/4" piece of metal and I want to round
off one of the 2" edges with a 1" radius. I can't do the job on the lathe for
obvious reasons. There can't be any holes in the finished product so I can't
conveniently pivot the workpiece against a cutter to form the radius.

	One approach is to rough out the radius on the milling machine using a
ball-ended mill.

	Assume:

		R = radius of desired profile (1" in the example)
		d = diameter of ball mill
		r = radius of ball mill = d/2
		theta = an angle (see below)

	Now assume the work is mounted in the vise with the 2" edge sticking up
and aligned with the x axis. Assume the end of the ball mill is just touching
the (center of) the 2" edge. Let theta be measured from the vertical about the
center of the radius to be cut. Thus theta = 0 corresponds to the starting
position just described. Now, it's easy to show that for some other value of
theta, the ball mill will just be tangent to the desired radius if its
position (i.e. the position of the center of the ball) is given by:

		x = (R+r) * sin(theta) [=0 when theta=0]
		z = (R+r) * (1 - cos(theta)) [=0 when theta=0]

where z is measured positive downward from the starting position and x is
measured +\- along the x axis from the starting position. So, if we step
theta by small amounts and make cuts with the tool positioned at the x,z
positions corresponding to each value of theta, we'll cut succesive "scallops"
into the workpiece, each of which is tangent to the required radius profile at
that angle. If the increments in theta are small enough, the resulting
scallops will often be small enough to ignore. If they're not, ten minutes
with a fine file will produce an acceptable finish.

	ROUNDER allows you to specify R, d, and the theta increment and
produces a file which contains a table of the values of:

		(R+r) * sin(theta) [x in the example]
		(R+r) * cos(theta)
		(R+r) * (1 - sin(theta))
		(R+r) * (1 - cos(theta)) [z in the example]

	The second and third values above may seem superfluous but not
everyone may want to set up the cut as in my example. As you try different
approaches, you'll find that being able to generate the other values is an
asset. If you don't need them, just cross out their columns on the printed
copy of the data file that you carry to the shop.

	A good suggestion is to rough out the profile of the radius with
hacksaw or whatever so the ball mill doesn't have to chew through a lot of
material. Just be sure to leave whatever starting reference point you're
going to use intact so you can accurately locate for the reference.
```


----------



## starbolin (Jan 23, 2010)

That's an interesting re-purposing of a bolt-circle calculator. Another method for radii cutting which allows you to directly cut a radii is to follow a template.

FYI approximating a curved surface by multiple square cuts is called kellering.


----------



## BobWarfield (Jan 23, 2010)

Rick, that's brilliant!

What a fine re-purposing of the bolt circle calculations. I love it.

In fact, I've got to add a little feature to my G-Wizard Calculator's bolt circle calculations to streamline it for just such occasions.

And, starbolin, thank you for reminding of a word I once knew, was on the tip of my tongue, but that I just have been unable to access for 3 or 4 months and too lazy to go look it up.

"Kellering"

Makes one wonder who this "Keller" might have been or where the name came from.

Cheers,

BW


----------



## rake60 (Jan 23, 2010)

The horizontal boring mills at work had DROs with bolt circle calculation software
built in to them. One night I was struggling with manually cutting a 3" radius in 
the top 48" bore of a brass bushing. 

I took my problem to a buddy who was running a horizontal mill and asked
him if he could work out a coordinate solution for me with his DROs bolt 
circle calculator. It worked out perfectly, and I never even tried to free 
hand a radius bigger than 1" after that. I'd just find an open DRO on a mill 
and run the bolt circle program. 

I no longer have access to those DROs but any bolt circle calculator works.

Rick


----------

