Confused ....Advice needed rotary table vs dividing head

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.

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What was Jason’s answer ?

MichaelG.

42 everyone knows that

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

Very noble of you, Dave

... I will wear the with pride

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

MichaelG.

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

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

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

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

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.

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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.

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.

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.