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

[ZebethyalParticipant @zebethyal]

Hi There,

Does anyone have a method for calculating co-ordinate positioning for a ring of holes that are not all equally spaced.

There are a number of PCD calculators out there, however these all assume that the number of holes are all equally spaced.

My requirement is for the 99% of the holes to be equally spaced, but the gap between the first and last may not be the same as for the rest.

A couple of examples:

Both are variations on plates that can be used on a Spin Indexer to generate a 127 tooth gear, the first has 127 holes on 3 different pitch circles (OxTools variant), the second uses a 5 hole vernier to achieve the same result with 26 holes (RJSakowski on the Hobby-Machinist forum).

The OxTool one actually does fit a PCD if it is large enough, but the reduced version has every second hole moved to a second pitch circle and the last one to a third.

The gap between the first and last hole, on a given pitch circle, is different for both of these compared to all the other holes.

The 5 hole vernier for the second variant may have the same issue as again a full circle of holes may not have the first and last equally spaced.

I guess I could calculate them all in a spreadsheet using trigonometry, I just need to get my head around the associated maths.

[JasonBModerator @jasonb]

If you have the 3D CAD, just produce a 2D drawing from that and dimension the holes as needed. I would suggest X and Y from the middle.

[ZebethyalParticipant @zebethyal]

Many thanks Jason, that is of course a viable option and one I had only vaguely considered.

I created the above in SketchUp, but could probably create in Fusion360 just as easily, which would be more suited to creating the 2D ‘dimensionable’ version.

[DC31kParticipant @dc31k]

As Fusion is the offspring of AutoCAD, ACAD has a ‘list’ command, that you could select entities and it would write their properties into the text window.

Put a point entity at the centre of each hole, select all of them and ‘list’ to the console.

A variation on this is to save just the point entities into an ASCII dxf file and open that in a text editor to extract the information.

The utility of the textual information might be dependent on the order in which you create the points. they would list in creation order, so create them systematically and they will list systematically.

If you tell us PCD, first hole bearing from due north and angular increment, we could do the maths independently as a check on your own work.

The easiest way to obtain these in a spreadsheet is to use polar coordinates. x = r cos(theta) and y = r sin(theta). The angle is measured anticlockwise from the horizontal positive x-axis (mathematical and navigational angles are measured in different directions). For the Ox one, with two hole circles, the outer thetas would be 0, 2/127 * 360, 4/127 *360, 6/127 * 360 etc. The first hole on that outer circle would be at three o’clock. For the first hole on the inner circle, start at 1/127 * 360 and then 3/127 * 360, 5/127 * 360 etc.

[ZebethyalParticipant @zebethyal]

Many thanks DC31k,

That has allowed me to build a spreadsheet that can calculate the holes for both discs based on the centre being 0,0 and position 0 at 3 o’clock, as you mention.

For the OxTools one, PCDs are 45, 40 and 35mm, pick even numbers for outer, odd numbers for middle and #126 for inner ring.

For the other one, PCD is 2.4″ (60.96mm) I need to pick every 5th hole for the ring

Just had to remember to convert the angle to radians before the trig function for it to work correctly in Excel.

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