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Analysing a Workshop Oddity? (4 into 6 won't go?)
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* April 13, 2018, 09:58:23 AM
Not really a tip or trick but suggests possible peripheral uses...

I did this as a break from battling to learn basic stuff like viewports and workplanes...

Self-centring Lathe Chucks:
We know or can envisage a-

   3-Jaw chuck holds round, hexagonal and polygons of even multiples of 3.

   4-jaw chuck holds round, square and multiples of 4.
BUT
   4-jaw self-centring chuck also holds concentrically, hexagons.  Eh??? 4 jaws moving along the diagonals of an accurate square, gripping a 6-sided bar concentrically?

I did not know this until reading of it in a recent edition of Model Engineer magazine, with a remark on its counter-intuitive nature.

SO I analysed it by drawing:
Hexagon, 6inch dia, centred neatly on the grid.
Inner circle, tangential to the sides.
Outer circle, circumscribing.
Square, snapped to grid, enclosing the lot.
   - All these concentric.
Diagonals to the square, vertex-snapped.

Colour each component differently to make the cobweb readable.

Dimension the hexagon and circumscribing circle.
Select the inner circle and tweak its diameter, gently, by X & Y in Inspector bar until it passed through the diagonals' crossings of the hexagon's sloping sides.

Sure enough the intersections all lay in a symmetrical, square pattern.

Dimension that new circle.
The mathematician would use the drawing only to guide a lot of trigonometry a bit too tough for me, but allowing for the slight inaccuracy in eye-balling lines on screen, the ratio of about 6.0 : 5.40 probably holds for any size of hexagon. In the workshop, the intersections are the contacts of the chuck's jaws with the sloping flanks of the hexagonal stock, with the top and bottom faces horizontal and the chuck jaws at 45º to that. Having said that, the contact will be edge-to-surface, not surface-to-surface.

Yes, the fact revealed in the magazine surprised me, but while I could simply have played with the real chuck and a bit of bar, or a large nut, to prove it to myself,  I was intrigued by the geometry and if nowt else, it was a useful TurboCAD exercise in simply manipulating basic geometrical shapes on a single plane!


 

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Nigel.

On TC Deluxe 19: hobby use.


May 13, 2018, 03:58:14 AM
#1
Maybe I'm not following, but I tried duplicating your design from your instructions and came up with the attached image.

The ratio is 6.00 : 5.20.

Also, I did not have to modify the inner circle to intersect the sloping lines of the hexagon because I used the Circle / Double Point function and Mid Point-Snapped (aka M-snap) to the middle of the hexagon's opposing line segments.

Am I close?


Jeff

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TC Pro Platinum 2018, 2017, 2016 & 2015 (all with LightWorks & RedSDK) & V21
System: i7-5820K @ 3.30GHz, ASRock X99 Extreme4, 16GB DDR4-2133 RAM, Gigabyte GTX 970, Samsung NVMe SSD 950 (256GB), Windows 7 Pro (64-bit) SP1


* May 19, 2018, 03:43:39 PM
#2
Thank-you Jeffin!

Close?

Closer, because you used TurboCAD tools I've not yet grasped to that depth.

I was nudging things by eye but I realise those functions would give numerically-accurate contacts.

In similar vein, another possible analytical task that's occurred to me, though I've not tried it, is the problem of cutting screw-threads on a lathe whose change-wheels give only close, but not correct, ratios. This is particularly the case if the intended thread is metric and the lathe all-Imperial. As mine are. The cut thread's resulting, cumulative pitch error may not matter on less than perhaps 10 turns and finished to profile with a die, but accurate drawing would reveal the practical limits for any particular thread and gear-ratio. (Work out the nearest available ratio first, by. e.g., spread-sheet.)

The actual inspiration was tapping whopping great 1-1/8" BSF threads through existing, plain holes slightly too small for the poor tap, in the 5/8" thick steel plate of  a lathe's cabinet-base. I worked out which ISO-M series metric tap was sufficiently somewhere-handy to rough the threads out enough to start the BSF tap, but had to ascertain the limit before the interference between the two dissimilar profiles and pitches became significant. It was actually about half-way through.

I performed the test manually, drawing one thread on the other at an enlarged scale - but it ought yield easily to TC's copying functions from each thread's basic triangle plotted once, on a common grid line and origin. 

The physical part of the task, lying on the floor, semi-jammed between wall and cabinet, would have yielded to no computer......

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Nigel.

On TC Deluxe 19: hobby use.


May 20, 2018, 01:42:39 AM
#3
TurboCAD Pro has a Thread function for simple screws (first image), but you would probably be better off using the Helix function (even though it is more complex), which is available in Expert and Deluxe as well as Pro.

Once you have the Helix applied to the Cylinder that provides the basic information for your thread, you would have to define the cross-section of the thread and Rail Sweep it onto the Helix (second image).  From there, you can 3D Subtract it from the Cylinder to create the thread (not shown).

As I said, it is more complex.  You will have to determine the length of the thread and the pitch to calculate number of turns (and multiply that by 360°/revolution, because the function needs the information in degrees).

You can calculate and create in one System (Imperial or Metric) and convert to the other under the dropdown menu Options / Space Units (third image).  Make sure to have the Convert units after alteration to keep the correct size and increase the Precision to 10.

Oh, yeah... if you haven't already done it, change Options / ACIS / Faceter Quality to 100 (which should provide enough detail; if not, you could activate Expert Faceter Parameters and experiment with those settings)


Jeff

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TC Pro Platinum 2018, 2017, 2016 & 2015 (all with LightWorks & RedSDK) & V21
System: i7-5820K @ 3.30GHz, ASRock X99 Extreme4, 16GB DDR4-2133 RAM, Gigabyte GTX 970, Samsung NVMe SSD 950 (256GB), Windows 7 Pro (64-bit) SP1


* May 20, 2018, 09:39:50 AM
#4
Be aware that Rail-Sweeping a profile along a Helix introduces twist, but this can usually be corrected by fiddling with the Twist parameter in the Properties dialog.

Henry H

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* May 21, 2018, 02:10:26 PM
#5
EEEEK!!!  :)

Thank-you Jeffin & Henry, but I am far from that level of expertise. I have seen the title "Threads" in the Manual but I am still trying to learn quite basic 2D drawing, in which I stick to the simple, standard parallel-line convention for indicating a thread, with a text label to state size and type.

I didn't need to draw the full threads, nor even profile them fully, as my aim was simply to determine pitch-error accumulation. In fact a full drawing of two threads dissimilar in pitches, flank angles and heights, superimposed would be difficult to read and look more Escher than engineering. Might be quite pretty though!

My approach was simply to draw the threads'  basic outlines as two rows of triangles in different line colours, at large scale, and see by eye where one really starts to eat into the other.  As the true crest and root arcs are not important here, it's possible to solve this similarly by spread-sheet, and I am fairly conversant with doing sums and plotting graphs in Excel, though I am not certain if the latest versions of that programme have anything like the graphs capability it once had.

As for the famous artist... I looked at a long-section drawing of a square-threaded nut, in an engineering-drawing text-book dating from 1947. The cut surface is cross-hatched as standard but the exposed thread is "rendered" by shadows to make flank and root easier to differentiate. It still creates quite an optical illusion! 
« Last Edit: May 21, 2018, 02:12:24 PM by NigelG »

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Nigel.

On TC Deluxe 19: hobby use.