Posted by Me. on 16/02/2021 12:22:05:
So – if I'm reading this correctly – a plank of wood and a sharp nail will do If I draw a straight line between 3 points and divided the 1st number i thought of by the square route of Pi….. or would a rotary dividing plate table be the answer to my original question….
Thanks for all the input – I'm sure my question got answered.
KTF
It did! In the absence of a specific reason for needing a Dividing Head, you probably want a Rotary Table plus Index Plate accessories.
But on the way, your question raised some interesting issues and I can't help picking up on Tony Pratt's comment "it's just maths", and Martin (Oily Rag's ) remarks about analogue vs digital and computer accuracy!
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.
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How accurate is a stepper motor compared with manually turning the handle of a Rotary Table? In practice, the error is no worse than that experienced by humans, and could be better because computers don't get tired or bored. Angular accuracy is fundamentally limited by how well made the table is and the worm, gear, bearings, and alignment will all be somewhat amiss even in a first class tool. There is always error.
My HV6-style rotary table has a 90:1 worm, so each turn of the handle moves the table 4°. How accurately I can set it manually depends on the scale, how well I read the crude vernier, how consistent the worm and gear are end-to-end, plus a multitude of other small mechanical quirks.
Most stepper motors have a basic 200 steps per rotation, which is 0.02° per step when applied directly to a 4° handle. But that's not how it's done because stepper motors can be micro-stepped . A motor applying 1600 micro-steps to a 4° per turn handle is turning in increments of 0.0025°, or 0° 0' 9". Are the holes in an analogue Index plate spaced that accurately, and does the pin engage all of them without wobble? Probably not. It's not the number system or digital stepping that limits accuracy, it's the hardware.
Martin also criticises computers because decimal arithmetic isn't always spot on, quoting 10/3 * 3 = 9.999 recurring compared with 3⅓ x 3 equals exactly 3. Fair enough except fractions are equally bad! The square root of 2, e, pi and an infinity of other numbers can't be represented accurately by fractions. So decimal numbers fail the Oily Rag test, and rational fractions fail mine. It's a score draw! Both systems require the user to understand error.
One of several advantages decimal numbers have is the error level can be reduced to a suitably convenient value simply by calculating more digits. And although both systems are erroneous it's less clumsy to calculate with pi = 3.1415926539214210447087 than pi = 104348/33215, especially when a calculator or computer does the work.
Finally, surely unfair for Martin to criticise computers for tiny binary rounding errors in comparison with the arithmetic performance of the average human. People make lots of silly mistakes due to boredom, distractions, and faulty memory. Some of us much worse than others…

Dave