Co-ordinate positioning for circle of holes (not all equally spaced)

[bernard towersParticipant @bernardtowers37738]

Just what I thought Martin but didn’t dare say so after all the previous posts!

[JasonBModerator @jasonb]

Yes that is what I also said, end of this post

The OP’s holes are equally spaced all be it one is missing,

Could even use a web PCD function and simply do the co-ords for 127 holes at 3 different diameters, get your highlighter out and mark 63 on the first set in one colour, 63 on the next set another colour and the remaining one in another. This would work if you only have  abasic DRO with no functions or even just handwheels

Dave’s fancy patterns are thread drift.

[Martin ConnellyParticipant @martinconnelly55370]

My picture seems to have disappeared so here it is again in case it does not return.

Martin C

[JasonB]

On JasonB Said:…

Dave’s fancy patterns are thread drift.

Really?  The title of the thread is ‘Co-ordinate positioning for circle of holes (not all equally spaced)’  And zebethyal’s opening sentence is ‘Does anyone have a method for calculating co-ordinate positioning for a ring of holes that are not all equally spaced.’  I have not drifted from that remit.

Why fixate on zebethyal’s example?  Is it because it happens to be trivially easy compared with my more challenging cases?  Take the subject a step further and CAD doesn’t answer the wider question or the calculation aspect or the many examples where holes are ‘not all equally spaced’.  (In either angle and radius.)

Zebethyal’s hole problem is closely related to how curves for gears, cams and CNC tool paths are calculated.  I don’t believe it’s hard to see the connection between these and the value of programmatic solutions. Ever wondered how G-code is translated into the job and cutter movements needed to make an object by subtracting metal from a block of stock?  My posts about manipulating coordinates in this Topic should help, but seems computers, programming and maths are all too difficult.

Dave

[SillyOldDuffer]

On SillyOldDuffer Said:

Really?  […]

My posts about manipulating coordinates in this Topic should help, but seems computers, programming and maths are all too difficult.

It was ever thus, Dave

The ‘practical man’ will take the easy /expedient option,  whether or not he understands what is going-on

The theorist will revel in having understood.

Different strokes for different folks !

MichaelG.

[JasonBModerator @jasonb]

The title is decieving as the holes are actually equally spaced, it is just a case of picking which ones you want to drill. Not realising this and giving a misleading title may have lead people astray and the theorist should have worked out that they are equally spaced. They are equally spaced in a 127 hole pattern that is spread over three diameters due to the fact they would overlap if all placed on one.

The OPs opening post said “There are a number of PCD calculators out there, however these all assume that the number of holes are all equally spaced.” However as mine and Martins examples show if you use an equal spacing of 127 and just pick the ones that don’t overlap then all these PCD calculators and a DRO and CAD will give what is needed based on equal spacing.

The practical man looks and sees that they are equal and uses the simplest methods to draw the part  and use the simplest way to arrive at the coordinates CAM. Or if you don’t need a drawing then the online PCD calculators are ideal

Computers are not difficult it is assessing the problem and then making best use of a computer to give the required results in this case the co-ordinates for the plate shown with it’s EQUALLY SPACED holes.

As for the maths, taking the outer ring you could say the 63 holes have 62 EQUAL spaces and a remainder. The middle row also has 62 EQUAL spaces and a remainder. The inner ring is the remainder. That is primary school maths.

This is done with the first PCD calculation that google threw up. results are not really any different to the spreadsheet produced on the first page. Just the first two of the three diameters to give the idea

Also works for the prime number example, does your easygraph image also produce the co-ordinates?

[JasonBModerator @jasonb]

And if you need proof that the practical method works take my recently completed Jekyll engine. Due to the valve block overlapping the cylinder end flange you can’t get a full ring of holes in around the bottom.

Designed with CAD and holes placed using the circular pattern feature of the orange hole with 7 EQUALLY spaced holes and the two that fell within the block were then deleted.

The holes were drilled in a similar fashion using the mill’s DRO and a 7 hole PCD just pressing the next hole button a couple of times to skip over the ones where the valve block was.

So the practical man gets the job done while the theroist makes the classic exam mistake of not reading the question and assesing the problem, not helped by the trick question. Although their answer may look impressive it won’t score the points or get the job done before the exam time runs out 😉

maybe I should have studdied applied maths🤔

 

[SillyOldDuffer]

On SillyOldDuffer Said:

Ever wondered how G-code is translated into the job and cutter movements needed to make an object by subtracting metal from a block of stock?

Dave

If you take a look at my early answer where I showed the G-code that can be used as a source for the co-ordinates you will see that the code is the result. In the case of the hole pattern it is actually the post processor within the CAM that has done the calculations to transfer the holes in the 3D model into the G-code. Gets a bit different when the G-code tells the cutter to move in an arc or at an angle between two points.

The Post processor is just like the online PCD calculators, the CAD programs circular feature, the DRO’s PCD function they all do it for you so no need to start working out formula for a spread sheet or go downloading multiple other programs.

[Martin ConnellyParticipant @martinconnelly55370]

engineer verb [T] (PLAN SKILLFULLY)
 
to plan or do something in a skillful way

Definition of engineer from the Cambridge Academic Content Dictionary

I also suggest a few minutes reading: The Origin of the Word ‘Engineering’

https://interestingengineering.com/culture/the-origin-of-the-word-engineering

Sometimes going down theoretical paths is interesting but other times there is a definite need that just requires the simplest available solution. Offering a number of solutions allows the choice to be made that best suit the person making the choice. Both the theoretical and the practical options may interest the originator so we should not get in a tizzy over what is best of the two or knock people who would like to offer different solutions. It is also easy ,with the sometimes imprecise sentence structures that English uses, to mis-understand something that someone is trying to put into words, it is clear in their own mind what they are saying but for the reader maybe not so clear.

Martin C

[JasonB]

On JasonB Said:

On SillyOldDuffer Said:

Ever wondered how G-code is translated into the job and cutter movements needed to make an object by subtracting metal from a block of stock?

Dave

If you take a look at my early answer where I showed the G-code that can be used as a source for the co-ordinates you will see that the code is the result. In the case of the hole pattern it is actually the post processor within the CAM that has done the calculations to transfer the holes in the 3D model into the G-code. Gets a bit different when the G-code tells the cutter to move in an arc or at an angle between two points.

The Post processor is just like the online PCD calculators, the CAD programs circular feature, the DRO’s PCD function they all do it for you so no need to start working out formula for a spread sheet or go downloading multiple other programs.

We’re still not on the same page Jason!  Your hole examples only cover the simple case, where most of the holes are equally spaced around a common radius.   As this is trivially easy to solve with eyeball methods, practical man shouldn’t be too pleased with himself!  I’m addressing the wider issue raised by the thread title, which is how to solve coordinate problems where the hole angles and radii are not equally spaced by angle around a common radius.  For that, it’s time to engage theory.

Jason says “The Post processor is just like the online PCD calculators, the CAD programs circular feature, the DRO’s PCD function they all do it for you so no need to start working out formula for a spread sheet or go downloading multiple other programs.”   True, except that’s a conceptual step behind what I’m failing to explain.

Perfectly reasonable for a practical man to see the post-processor and other programs as black-boxes that magically do the needful without him having to understand the underlying theory.   But someone had to design the post processor, CAD/CAM weren’t delivered by a stork.  This is engineering at a higher level requiring applied mathematics, building on centuries of smart theory.

Practical workshop experience doesn’t help here because the tools and methods used by software engineers are different, and they’re obliged to solve seriously difficult logic problems.   For example, when calculating the tool-path needed to cut a part from solid stock, it’s not possible to simply direct the tool by the shortest route, which is easy to program.   What’s needed is an algorithm that ensures the tool won’t crash into the stock or remove metal in transit that’s going to be needed later.   It has to maintain the integrity of the finished shape.  Much more difficult.

Most of what I do in the workshop stands on the shoulders of giants whose genius is taken for granted.  I used HV6 index wheels as an example of something a program can do very simply, and the same code can be tweaked to do index wheels for other rotary tables.  Except I cheated by not tackling the maths!  I dodged the maths by copying the number of holes required from the manual.

The HV6 has a 90:1 worm and is indexed by 3 wheels each with 6 rings of equally spaced holes.  Wheels needed:

AWheel = [15, 16, 17, 18, 19, 20]
BWheel = [21, 23, 27, 29, 31, 33]
CWheel = [37, 39, 41, 43, 47, 49]

The number of holes in each ring is calculated to provide all the common angles from a 90:1 table.   As it’s not obvious how angles are wound out, the HV6 comes with a table showing which wheel, ring and clock setting are needed to do the necessary division.  A problem with this system is the indexer can only do integer arithmetic, so some angles are approximations, and many others not available.   OK for most practical purposes, but a stepper motor driven by a microcontroller does better and is easier to use.

An engineer who can do the maths, calculated the minimum number of wheels and holes needed to produce a useful range of angles.  HV6 wheels won’t work on a 60:1 or 48:1 rotary tables so the sums have to be done again for them.  Woe if an indexers table is wrong or lost, because Practical Man is unlikely to have the skills to work it out himself!

Specifying the gears needed to cut a given range of threads on a lathe is a similar problem.  Smallest number of wheels possible, they have to fit on the banjo, and the number of teeth have to generate the required ratios.  Again, practical man only has to follow a table, which is fine until the table is lost, or a second-hand machine is bought with missing or incorrect gears.

If Practical Man runs into an indexing or gear set-up problem, his best hope is a forum friend having the information.  Otherwise, he has to tackle the maths, which is intimidating.  Don’t care for it myself, but see the value, and am prepared to have a go.

I’m fascinated equally by practical and theoretical engineering.  Apologies if my excursions into theory offend those who enjoy hands-on more than thinking, but I’m not going to write ‘Up Jumped Baby Bunny” posts just to please them.   I’d rather understand than be ignorant, and believe most Model Engineers are like minded.  Also believe engineers should strive to do better, which might mean learning new tricks, and changing their minds.  Change is horrible I know, but anyone who finds that unacceptable has no obligation to read my posts.

Dave

[Martin ConnellyParticipant @martinconnelly55370]

My question regarding the uneven spacing of holes is “How are the hole positions defined to start with?” They can’t be random as that would be pointless. Once the process of defining the holes is known then a possible solution to locating them should be achievable. We know the original question was regarding 127 holes required to cut a 127 tooth gear and we are all probably assuming it is for cutting metric/imperial threads on a machine with a leadscrew not matching the desired thread. Based on this some solutions were proposed. Anything beyond that needs the problem to be defined further.

Martin C

[Martin Connelly]

On Martin Connelly Said:

My question regarding the uneven spacing of holes is “How are the hole positions defined to start with?” They can’t be random as that would be pointless. Once the process of defining the holes is known then a possible solution to locating them should be achievable. We know the original question was regarding 127 holes required to cut a 127 tooth gear […]

Sorry, I don’t have time to join the debate … but may I just mention that the second part of the original question was probably much more challenging than the first
[ the linked discussion is worth reading ]

MichaelG.

[Martin ConnellyParticipant @martinconnelly55370]

I assumed (I know) that the holes were spaced every fifth position apart from the one that is spaced 2 positions along from the previous hole. That way with a 5 position vernier pin location on the body of the spin indexer the full selection of 127 was possible. That means that the method of drawing them in CAD, CAM or using a spreadsheet are still valid processes to get the coordinates or just drill then on a RT with a “printed paper” dividing plate.

Martin C

[Michael GilliganParticipant @michaelgilligan61133]

Q.E.D.

and everyone is [or, should be] happy.

The cat is skinned.

MichaelG.

[Author]

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