Confused ….Advice needed rotary table vs dividing head

[EmgeeParticipant @emgee]

If an arc is needed rather than a full circle it is only too easy to go a gnats whatsit past the desired point. It might only leave a shallow witness mark, but it is surprisingly difficult to remove it. Lots of filing and an end that no longer looks semi-circular. I prefer filing buttons for rounding the ends of rods and clevises.

Andrew

I agree it is a pain if you overtravel, I usually add 0.20mm to the radius to be cut to avoid the tool mark you describe.

Using the dividing head as set-up on your mill looks like a bit of a pain with the controls at the back of the head, especially if you are using the sector arms.

Emgee

[SillyOldDufferModerator @sillyoldduffer]

Posted by Tony Pratt 1 on 16/02/2021 14:54:21:

Posted by SillyOldDuffer on 16/02/2021 13:59:06:

Q1. Using this plate, what indexing ratio is needed to rotate the rotary table by 5.29°? (There are two candidates.)

Q2. What's the error, in degrees, of both indexing ratios?

Show working! If you happen to have a lookup table for a 40:1 ratio, please don't cheat by using it. The test is doing the maths.

Dave, is your 5.29 — 5 point 29 degrees or 5 degrees 29 minutes?

Tony

Hi Tony, 5 point 29 degrees – I'm not malicious!

Dave

[SillyOldDufferModerator @sillyoldduffer]

Posted by JasonB on 16/02/2021 18:40:31:

Posted by SillyOldDuffer on 16/02/2021 13:59:06:

Q1. Using this plate, what indexing ratio is needed to rotate the rotary table by 5.29°? (There are two candidates.)

Q2. What's the error, in degrees, of both indexing ratios?

Dave,

1. You mention that using published tables is cheating. Do we assume you have rounded the 5.29deg as tables only tend to give No of divisions in which case 68 would be closest as 360deg is not divisible you 5.29deg at least not to a whole number

2. I had better get in before Andrew and ask if you will be doing the indexing as that may increase the likelyhood of an error Sorry could not resist.

1. Not rounded, and not a whole number. The point is to explore the maths behind a non-trivial example.

Fortunately for me it's rarely necessary to dig into the maths, though it's hard to avoid in design work. Most jobs on my rotary table involve straightforward obvious angles, and the HV6 table covers a lot of common cases. The maths behind index plates is interesting because it also covers approximating gear ratios for unusual threads, working with index plates that don't have an exactly suitable circle, milling spirals, and producing feed-rates. Also answering questions like, 'On a given lathe what's the smallest set of change gears that can provide close approximations of both imperial and metric threads?'

2. Who me make a mistake? Never happened…

Dave

[Me.Participant @me1]

……

Edited By Me. on 17/02/2021 10:36:02

[Me.Participant @me1]

I was sure it was 42 – now I'm not…..

[Anonymous]

Posted by SillyOldDuffer on 17/02/2021 09:57:42:

…….'On a given lathe what's the smallest set of change gears that can provide close approximations of both imperial and metric threads?'

None, because with an imperial or metric leadscrew one or other set of threads will be exact and the other an approximation, not both approximations.

Andrew

[Michael GilliganParticipant @michaelgilligan61133]

Posted by SillyOldDuffer on 16/02/2021 13:59:06:

[…]

Not everyone is good at maths, which I think can be demonstrated by this relevant question: Assuming a Rotary Table has a 40:1 worm and an indexing plate with hole circles from 30 to 60, each circle in steps of one, thus:

Q1. Using this plate, what indexing ratio is needed to rotate the rotary table by 5.29°? (There are two candidates.)

Q2. What's the error, in degrees, of both indexing ratios?

Show working! If you happen to have a lookup table for a 40:1 ratio, please don't cheat by using it. The test is doing the maths.

—————————–

.

Please, Sir … will this do ?

[ sorry, I didn’t bother completing Q2 ]

The gist of the working is to first multiply by 100, so that we’re working with an integer target.

Then find how many hundredths of a degree each hole represents on each circle.

Then find how many holes are required for 529 hundredths.

Quick & Dirty spreadsheet looks like this:

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.

Row 10 looks pretty good to me …

and I’ve sanity-checked the formulae by substituting some easier angles in B2

MichaelG.

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Edited to correct a typo, and to mention that if anyone needs more detail, just ask.

Edited By Michael Gilligan on 17/02/2021 22:24:35

[Me.Participant @me1]

Phew – thanks for that.

I'm never going to be sure I will ever have to rotate my table/Head….(when i get one) by 5.29 degrees, but when I do I will know how to work out which plate hole combo I will need to use.

[Me.Participant @me1]

Is it just me (as in Me) – why when you look at this picture the line a 12 o'clock is straight up and down but when you turn the picture through 45 degrees the new 12 o'clock line is not…..

Have I discovered a floor in the dividing disc design or is it just an Illusion……. Spooky….

And also – why the line at the 6 o'clock position has half the amount of holes when you look at the picture as posted – Anyone have Pythagoras's phone number I think hes missed a trick with this.

[Me.Participant @me1]

PS – I do know why but when someone that doesn't know what the picture is of, then it does confuse very quickly.

[SillyOldDufferModerator @sillyoldduffer]

Posted by Me. on 18/02/2021 08:33:24:

… why when you look at this picture the line a 12 o'clock is straight up and down but when you turn the picture through 45 degrees the new 12 o'clock line is not…

Have I discovered a floor in the dividing disc design or is it just an Illusion…

And also – why the line at the 6 o'clock position has half the amount of holes when you look at the picture as posted…

Illusion, or at least the brain detecting patterns other than the one intended. Here's a real Index-plate showing similar effects:

It's because the number of holes in each circle increases by one, so they stagger around the plate, aligning in various ways. This plate gives index holes stepping at:

Holes Degrees
15 24
16 22.5
17 21.18
18 20
19 18.95
20 18

Index plates are used with a plunger and clock-hand indicator and are set up from a table like this:

PDF Version Here.

Indexers provide a relatively easy way of keeping count when a dividing head or rotary table is turned repeatedly through an angle. The HV6's Basic Indexing Table covers the common case, which is when a circle is divided into an equal number of angles, say to drill holes on a PCD, putting flats on a work piece, or making gears.

For example, to drill 7 holes in a PCD, angle approx 51.43°, fit Index Plate 'B', select hole ring 21, do 12 full turns of the handle, ie 48°, then move 18 holes along the 21 hole ring to add 3.43°, total 51.43°. The clock-hands are set to indicate 18 hole movements so the operator doesn't have to keep count of them, and can be moved indicate the next target. The operator has to count 12, and woe if he miscounts 11 or 13, or selects the wrong index hole. A microcontroller is much easier to drive.

Another point, the 'Basic Index Table for HV6' is just that, basic! It doesn't help when the angle needed isn't one of the listed divisions, as is the case with my 5.29° question. The table's shortcoming may not be a problem if you can do the maths and identify a reasonable approximation.

Microcontrollers are popular because they don't rely on an integer only index plate to keep track and can get close to pretty much any angle required. Best of all, the operator just enters what he wants and presses 'go': he doesn't have to concentrate or understand how it works.

Haven't looked at Jason's answer yet, but I bet he's right!.

Dave

Edited By SillyOldDuffer on 18/02/2021 13:50:47

[old martParticipant @oldmart]

I have a set of three plates for the Soba 6" rotary table and consulted the charts only to find that the plate holes available left out quite a lot of indexing positions. I wanted 118 which was not available, so a table of positions to the nearest minute of arc was printed out and we had to do the job the slow way.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by SillyOldDuffer on 18/02/2021 13:48:31:

[…]

Haven't looked at Jason's answer yet, but I bet he's right!.

Dave

.

What was Jason’s answer ?

MichaelG.

[Dave HalfordParticipant @davehalford22513]

Posted by Michael Gilligan on 18/02/2021 17:23:55:

Posted by SillyOldDuffer on 18/02/2021 13:48:31:

[…]

Haven't looked at Jason's answer yet, but I bet he's right!.

Dave

.

What was Jason’s answer ?

MichaelG.

42 everyone knows that

[SillyOldDufferModerator @sillyoldduffer]

Posted by Michael Gilligan on 18/02/2021 17:23:55:

Posted by SillyOldDuffer on 18/02/2021 13:48:31:

[…]

Haven't looked at Jason's answer yet, but I bet he's right!.

Dave

.

What was Jason’s answer ?

MichaelG.

Oh no, I've done it again! My brain must have skipped a groove or three. Your answer is the only one received! That naughty boy Jason hasn't handed his homework in yet.

Sorry. Take a Gold Star in apology…

Dave

[Michael GilliganParticipant @michaelgilligan61133]

Very noble of you, Dave

… I will wear the with pride

Now, please don’t find any gross errors in my logic !

MichaelG.

[JasonBModerator @jasonb]

Dave, Jason has been too busy painting his Heinrici engine and drawing up a Stuart Victoria to give in his homework but Michael seems to have half answered.

The 34 hole ring looks the best bet with 20 holes giving 5.2941168deg so the error is 0.0041168deg

next best would be 58 ring using 34 holes to give 5.2758612deg so error is 0.0141387

Having said that Dave's original question said using a Rotary table with 40:1 worm. Now this may have been a typo as it's usually Dividing heads that have 40:1 so I'd opt for sticking his plate onto my 90:1 rotary table and using the 41 31 hole plate with 1 full turn and 10 holes get 5.2903deg which is good enough for me. 

 

Edited By JasonB on 18/02/2021 19:49:32

[JasonBModerator @jasonb]

Just to add that my logic was a bit different to Michael's.

First work out how many degrees 1 full turn gives, in Dave's case 360/40 = 9deg per turn.

Divide 9 by desired angle of 5.29 = 0.58777777

Then quick spread sheet to multiply each number of holes in the ring by 0.587777 and pick the nearest to a whole number

[Howard LewisParticipant @howardlewis46836]

The spreadsheet to produce a corrected chart for the HV6 allows extra rows to be inserted for any number of divisions that are required.

Hopefully when the worksheets for the three Division Plates are examined, there will a combination that gives an integer hole number.

Unfortunately, it does not look as if any of the three plates will provide 118 divisions .

On one occasion I did use a non integer, (1 turn and 10.004 holes on a 49 hole plate ) but I thought that by the time that the error of 0.004 of a hole would not matter too much after being reduced by the 90:1 ratio. It seemed mto work satisfactorily!

Howard

Edited By Howard Lewis on 19/02/2021 04:42:37

[SillyOldDufferModerator @sillyoldduffer]

Time for the answer!

Only two entries from the entire forum, and both disqualified for using technology not available when Dividing Heads, Rotary Tables, and Index Plates were first invented.

Honourable discharges though because I approve of their method because it's practical and less hard work than doing it manually. However, before computers brute force techniques like this were too much work. Michael calculates sixty floating point numbers each with 18 digit precision, no joke with paper and pencil. Even today, with the answers neatly printed, the requirement to search a longish list for the closest match to an integer is irksome, but hey ho, not a showstopper and it could be fixed. I like it.

Here's a traditional method, in which brains are substituted for brawn. The method involves defining a fraction in such a way that an ever more accurate approximation of the target is found at each step. It's the technique used to identify 22/7, 355/113 and other ratios as approximations of pi.

Extracting the partial quotients: sorry, rotating the photo chopped off the first step which is:

900/529 = 1 remainder 371

Then, with 1,1,2,2,1,6,1,6

We find the closest approximation is 10/17, which is 20 on the 34 hole ring or 30 on the 51 hole ring, for an error of about 0.004 degrees.

Might be possible to do better. The method can be extended using Combined Fractions to generate additional approximations between those calculated as shown above. More accurate than the lower bound, but not as close as the upper.

Apologies for the poor photos and fingers crossed I've got the sums right. (Maths isn't my strong point.)

Dave

[Me.Participant @me1]

as the upper.

Apologies for the poor photos and fingers crossed I've got the sums right. (Maths isn't my strong point.)

Dave

Well I think that just about puts that to bed – and as for the above comment – you could have fooled me…. LOL

I thank everyone for their contribution to this thread – I'm sure somewhere along the way I sort of got an answer to my question. I think the answer was – sell the Mill and buy a puppy much less to worry about.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by SillyOldDuffer on 19/02/2021 15:20:18:

Time for the answer!

Only two entries from the entire forum, and both disqualified for using technology not available when Dividing Heads, Rotary Tables, and Index Plates were first invented.

Honourable discharges though because I approve of their method because it's practical and less hard work than doing it manually. However, before computers brute force techniques like this were too much work. Michael calculates sixty floating point numbers each with 18 digit precision, no joke with paper and pencil. Even today, with the answers neatly printed, the requirement to search a longish list for the closest match to an integer is irksome, but hey ho, not a showstopper and it could be fixed. I like it.

[…]

.

I remember a chap at KODAK who was still designing lens systems ‘longhand’ … and his ‘Road to Damascus’ moment, when he saw how quickly brute force optimisation could do the job.

Just for interest : I don’t know exactly how fast my little spreadsheet works, but those sixty numbers are produced ‘in the blink of an eye’ when the target angle is changed … and that’s using the ‘Numbers’ App on the iPad, not some super-computer.

Nice to see it done on paper though … useful skill for the post Apocalyptic re-birth of mankind.

MichaelG.

[Nicholas FarrParticipant @nicholasfarr14254]

Hi, well I worked it out a different way, but was not sure if it was correct, the first thing I did was to divide 360 by 5.29 and I ignored everything after the point as I wasn't interested in knowing the error, but the figures suggested it was small. I calculated both 40-1 and 90-1 R/T's. My calculations were very short, but I did use a electronic calculator, well two actually.

Regards Nick.

[Michael GilliganParticipant @michaelgilligan61133]

Following Dave’s critique, I have improved my spreadsheet a little:

The reduction ratio can now be input, and the close approximations are identified

… the method used for this is a little clunky, but it works.

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It’s still set-up for up to two decimal places on the required angle,

still displays the calculations to an unnecessary 16 decimal places,

and uses Dave’s series of holes …but obviously this could be revised to match an existing set of plates.

MichaelG.

[Author]

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