You could try this bolt circle calculator from Little Machine Shop

John

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… 

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

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.

John

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

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

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

.

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.

MichaelG.

.

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

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

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, 30/60&ordm.. but I have to look them up if I ever need them!

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.

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.

Dave

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

Just a general observation on the cussedness of things, I have three books with Chord Tables and none of them mentions PCD or Circle Spacing in the index. You have to know to look for 'chords', which isn't exactly user-friendly!

Tubal Cain's excellent 'Model Engineer's Handbook', 3rd Edn is guilty of this, but the book covers the maths behind chords rather well and provides a Circle Spacing Table on pages 2.34 / 2.35. It's another reason to buy a copy!

Dave

Hi, yes this looks like it is good to use with my mini mill, which I have those readout bars with the remote display that Arc Euro sells.

Regards Nick.