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Bolt circle without DRO

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William Ayerst20/03/2021 13:47:49
259 forum posts

Good afternoon gents,

I've been musing about an idea to drill out bolt holes in a circle without a DRO. I'm sure there is a solution out there, what is it? I understand that we can scribe three or six bolt hole patterns by deriving the position from the radius, but what about others? And/or using edge finders from a datum position?

My thought was that I can calculate the X/Y coordinates of each bolt hole using a CAD solution from a given datum, and then using an edge finder from that datum, drill each hole in sequence - but I've realised that it probably won't work!

I can't edge both X and Y simultaneously, and I can't edge find the second axis without moving my first (found) axis back and forth at least as much as the diameter of the edge finder - which introduces backlash into the equation again.

I guess I could potentially find X and move to the correct X position, and then edge find Y from where I've ended up but, it's not always guaranteed that the Y axis at the point I'm aligned in X for my hole is going to be related to the datum.

Anyway, this is somewhat academic but was just wondering if it can be done, or whether it really is just better to use a PCD formula to calculate the measurement of a divider and scribe, then use a wiggler to position the holes and then transfer punch your way through the process?

Journeyman20/03/2021 14:05:44
1146 forum posts
230 photos

You could try this bolt circle calculator from Little Machine Shop


Nicholas Wheeler 120/03/2021 14:08:35
906 forum posts
86 photos

Laying out PCDs has long been a common requirement, so the formulas used are available in all sorts of places. For example page 14 of Zeus gives them for 3 through 12 hole PCDs.

Mick B120/03/2021 14:22:48
2153 forum posts
117 photos

Zeus booklets carry trig solutions to a variety of the most usual PCD, with standard factors to multiply with the PCD value to arrive at co-ordinates.

Ah, I got distracted to remove some lugs from a bucket for me missus, and Nicholas beat me to it... cryinglaugh


Edited By Mick B1 on 20/03/2021 14:24:38

William Ayerst20/03/2021 14:24:50
259 forum posts

Right sorry, so I wasn't asking about how to generate a PCD - I was asking about how one would go about physically drilling a bolt circle of a given PCD on a slide or milling table without a DRO. If it's the case of using a wiggler and eyeballing that's fine but it seems as though there should ? be a way to do it from the dials!


i.e. now I have the information for (example) from the little machine shop output I have a series of X/Y coordinates - but without a DRO I am reliant on using edge finders and mental arithmetic, and I don't know how one would edge find in both axis from a single datum point

Edited By William Ayerst on 20/03/2021 14:26:23

Journeyman20/03/2021 14:39:20
1146 forum posts
230 photos

Yes, the Little Machine Shop calculator gives you the X and Y offsets from a datum. You would need to set the mill X and Y using an edge finder then zero the dials. Use the generated table and wind the handles for each hole the listed X and Y offset. You need to know the X,Y centre position in relation to right hand edge and the bottom edge, this is the offset fed into the calculator. Then its just a matter of turning the handles and keeping tabs on where you are (easier said than done). Good idea to mark out the hole positions first and centre pop, then you have a visual indication to confirm that you have wound the handles the right amount. Don't forget to allow for the diameter of the edge finder when you set the dials to zero.


Edited By Journeyman on 20/03/2021 14:43:36

JasonB20/03/2021 15:42:51
22555 forum posts
2634 photos
1 articles

You just use the handwheel dials to move the part to your co-ordinates and compensate for any backlash. In the case of doing it with a vertical slide you would use that and the cross slide handwheel.

There is a chapter in my book which shows how to do it with just the handwheels on the mill, same method applies to on the lathe

Edited By JasonB on 20/03/2021 15:48:34

noel shelley20/03/2021 16:05:44
1275 forum posts
21 photos

I think this info is in the ZEUS book ? Noel.

Nicholas Wheeler 120/03/2021 16:27:50
906 forum posts
86 photos

The DRO doesn't tell you where to drill, just that you're at the points you calculated. It makes the job easier, that's all.

JasonB20/03/2021 16:42:00
22555 forum posts
2634 photos
1 articles
Posted by Nicholas Wheeler 1 on 20/03/2021 16:27:50:

The DRO doesn't tell you where to drill, just that you're at the points you calculated. It makes the job easier, that's all.

It does if you use the DRO function as that saves you having to do any calculations.

Alan Wilkinson 120/03/2021 17:01:50
49 forum posts

Use a round table, Just find the center then move out the radius drill hole move round the required degrees and drill again, simples

Michael Gilligan20/03/2021 17:31:37
20052 forum posts
1040 photos
Posted by William Ayerst on 20/03/2021 13:47:49:


My thought was that I can calculate the X/Y coordinates of each bolt hole using a CAD solution from a given datum, and then using an edge finder from that datum, drill each hole in sequence - but I've realised that it probably won't work!



It will work if you have:

  • a clearly defined, trustworthy, datum;
  • Accurately aligned X and Y axes
  • Good feedscrews

... This is the very essence of ‘jig boring’ machines.

A very useful [but generally costly] gadget is the Ickey Ball ; which offers a spherical datum

... With a little thought, you can replicate its function [well enough for most ‘model engineering’ purposes] easily and cheaply.



Edit: __ Alternatively, of course, it is often possible to do such jobs in the lathe ... for which you need a drilling attachment, such as those featured in a recent thread.

Edited By Michael Gilligan on 20/03/2021 17:37:48

John Olsen20/03/2021 20:39:30
1240 forum posts
94 photos
1 articles

You can get a very reasonable accuracy by drawing it full size in CAD, printing the diagram, and then using that as a pattern to centre pop the location of the holes. I've also done quite a few with a simple direct dividing attachment. With that you just have to get the first hole at the correct radius, then step around.


old mart20/03/2021 20:49:15
3717 forum posts
233 photos

I use the rotary table where possible for holes on a pcd. _igp2653.jpg

not done it yet20/03/2021 21:28:03
6716 forum posts
20 photos

Depends on the job.

My first job like this (I think) was holes for bolting a lathe chuck to a backplate and the backplate to the lathe, or a face plate to a lathe. Simple enough - I scribed a circle with the lathe at the required diameter, one small dot with a centre punch, set dividers to about the right distance and ‘walked’ round the circular scribed line. I adjusted dividers until the dividers finished in the original dot. Close enough, so scribed lines, dot punched and drilled holes. The only difficult part, at the time as I recall, was scribing that first circle at the desired radius.

Obviously I would not do it that way these days!

Nigel Graham 220/03/2021 22:05:38
2009 forum posts
27 photos

If I understand this correctly, William is asking 2 questions:

1) Can I calculate PCD co-ordinates?

Yes- there are various ways and as a couple of people have said, the Zeus book of tables gives the X and Y factors for setting-off the holes from the centre-lines. You could also use trig. Both sets of calvculations don't need anything more elaborate than a calculator or a spread-sheet - but if you use the latter with a ngles, be sure it's using degrees and not radians.


2) How do I then form the two datum-points from which to move the work-piece to the right places?

The obvious way is to use a rotary-table and work from its centre and the location of the first hole, but one way without that (and it does entail further sums):

If the work-piece lacks a feature allowing direct centring, such as a turned boss or bored hole, I would set up two straight-edges on the table at accurate right-angles to the table and each other, and nest the work such that the perimeter of the surface to be drilled is against them.

Use the edge-finder to locate off the straight-edges, find the centre and set that first as (0,0).

Now consider if the hole pattern has to co-incide with some feature on the work-piece. One example would be the crank-end cylinder cover on a steam-locomotive, where the studs may have to be arranged with respect to the mountings for the slide-bars. If so, make the most critical hole (and if appropriate its opposite one) lie on the X or Y axis.

It's now possible to move the work by the appropriate off-sets corrected for the radius, but always approach from the same direction and work in cross-travel pairs. Counting X upwards from left to right, Y up towards the column.

So for example, 8 holes with H1 and H5 being at North and South, on the reference Y axis, numbered clockwise.

Move the table inwards to (0, Ymin) where Ymin is the pitch-circle radius.

Drill or bore H1.

Move the table in by the appropriate Y distance, lock the cross-slide. Set H8 and H2, according to their X offsets, drill them.

Repeat for H7, H3, then H6, H4.

Then H5 (0,Ymax)

The headache with this approach is that without a DRO you need calculate what the dials will actually read for, but this method minimises the amount of error-risking winding back and forth.

It would be wise to mark out the hole locations beforehand, to act as a guide.

The most likely error would be miss-counting handwheel turns.

E.g. A 45º location's offset is 1.1414 R in X and Y (pitch-circle radius X sq.rt of 2), which in inches on my mill means five and half full turns plus 14 little divisions. So markings would show a missed or over-wound turn glaringly! *

NB: always wind Y in one direction only, preferably up-counting even if to correct a small over-wind. Return the long-travel (X) well past the work and approach from the same direction each time.


* Like pi, that root-2 rule is useful to remember even if you need look up or calculate the number itself. It is the diagonal of a square of 1 unit sides, for. e.g. 45º divisions, setting-off a 45º angle or finding the maximum size of a square that can be cut on a round bar.

There is an equivalent for any regular polygon, such as the hexagon ( 6 vertices, 30/60º.. but I have to look them up if I ever need them!

Martin Kyte20/03/2021 22:30:43
2721 forum posts
48 photos

There is always the button method. Make a set of buttons equal to the separation of the holes in the Pitch Circle.

Make another equal to the diameter of the Pitch Circle less the diameter of the other buttons. Fix the single button on the PCD centre and arrange all the rest so they touch the centre button and the adjacent pair of outer buttons. This will accurately locate the centres for the PCD holes. If the buttons are provided with loose fit through holes they can be held in position with screws into tapped holes roughly set out. With judicious choice of length for alterating buttons the job can be clocked true on the faceplate to one of the longer buttons, the button removed and the hole drilled and bored. Do alternate holes (the longer buttons) and then the intermediate shorter ones once clearance has been acheived around them.

Long winded I know but it can be achieved on the lathe just using a clock and a mic.

I'm sure a rough and ready similar version could be thought of using super glue and buttons made as drill guides of if the job is very big clamps.

regards Martin

Nicholas Farr21/03/2021 11:15:48
3310 forum posts
1524 photos

Hi William, you can calculate up to 100 holes with this chart assuming your holes are equispaced, but you need to do a bit of trig.



The one illustrated on the chart is fairly easy, as shown in the sketch above and you could start from any hole, but if you start with hole 0 and then move right 30mm and 51.961mm up to hole 1 and then move right a further 60mm to hole 2, then move back down 51.961 and a further 30mm right to hole 3, then just repeat going down and moving left to get holes 4 and 5. As has been said though, you will need to take into account the backlash in your screws and bearing in mined that the 51.961 is only correct to three places in this example.

Regards Nick.

Hopper21/03/2021 11:39:17
6180 forum posts
319 photos

Posted by William Ayerst on 20/03/2021 13:47:49:

- but I've realised that it probably won't work!

I can't edge both X and Y simultaneously, and I can't edge find the second axis without moving my first (found) axis back and forth at least as much as the diameter of the edge finder - which introduces backlash into the equation again.

I guess I could potentially find X and move to the correct X position, and then edge find Y from where I've ended up but, it's not always guaranteed that the Y axis at the point I'm aligned in X for my hole is going to be related to the datum.

Sure you can. As Jason says, you use the handwheel graduations and allow for backlash. Allow for backlash? Yes. By using the same direction of approach each time. So you set your X axis with the edge finder by winding carefully the handle in one direction only, the direction in which you will commence machining. Set the X dial to zero once the edge is found. Then do the same for the Y axis. Then bring your X axis back to Zero, winding from the same direction as before.

It's the way things were done for 200 years before DROs arrived. Easier done than said actually.

Another way of doing it, to a couple of thou accuracy is to carefully lay out the hole positions with scribed lines in a thick layer of layout blue. Then use a "wiggler" (eg Starrett etc) which is a pointer about 3" long welded to a ball bearing that is held in the chuck. The chuck is spun fast and piece of wood used to set the tip of the pointer to run true. Then you can align the pointer with the crossed layout lines for each hole in turn , using a great deal of care and a magnifying glass. You can usually get it right within the width of the scribed line, which is about two thou.

SillyOldDuffer21/03/2021 18:36:15
8461 forum posts
1882 photos

Further to Nick's answer, a little maths goes a long way.

Imagine you have six holes to drill on a 100mm radius. With a rotary table this is easy. Centre the mill on the centre of the table, then move X or Y by 100mm, and drill the first hole. As there are six holes, turn the rotary table by 360/6 holes = 60°, and drill the next hole, repeat turns of 60° until all six holes are drilled job done.

The rotary table makes it easy, but note the coordinates of each hole are determined only by the radius and an angle. This is called a polar coordinate.

What if you don't have a rotary table? One way is to blue the job up, ding the centre point, scribe a 100mm radiis circle, centre pop the position of the first hole 0°, and then use a protractor to identify and centre-pop the position of the other holes, at 60°, 120°, 180°, 240° and 300°. Then centre the mill spindle over each centre-pop with a wiggler needle, clamp, and drill. Same method works with a pillar drill.

Another is to calculate Cartesian coordinates from the Polar Coordinates, as described by Nick. Cartesian coordinates are expressed as a pair of X and Y measurements from 0,0, which in this case will be made the centre of the Pitch Circle Diameter. Mill tables work in X,Y, so the answer is to convert polar into cartesian coordinates which is easy with a computer, scientific calculator or 4-figure tables.

Given a polar coordinate consisting of a radius and angle θ,

X = radius x cos( θ ), and
Y = radius x sin( θ )

In the example below, Hole B is Polar 100<30°, which is Cartesian 50, 86.60


Drilling the holes it's good practice to take advantage of any symmetry in their placement to minimise changing X or Y. For example, as B is aligned horizontally with F and vertically with C, it's less dial twirling to drill those next rather than A, D, or E. Less likely to make mistakes and accumulating error is avoided if the holes aren't drilled A,B,C,D,E, F in order.

Although the method works with dials, a basic DRO that doesn't calculate PCDs makes the job easier because you don't have to keep count of dial revolutions.

Cartesian can be converted into polar coordinates if needed, but I've never had to do it in my workshop.





Edited By SillyOldDuffer on 21/03/2021 18:36:54

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