Array around an ellipse

Looking for some options (lots of guide lines is a pain) as to how best to make a bunch of cut outs around the perimeter of an ellipse. I am not seeing a fast way in SketchUp.
I would like 16 cutouts about 1 3/4" apart center to center. Not sure how best to solve for the length of an ellipse that has 6" as its minor dimension.
Chisel Holder.skp|attachment
(29.1 KB)

How about drawing circles with 1-3/4 in. radii. Start at the center and work toward the end. Draw a new circle where the previous on crosses the edge of the ellipse.

With that spacing, you only have room for about 12 openings.

I just drew a series of circles 1 3/4" radius to space the centres round the ellipse as one way of finding the centres for your cutouts. (further side of image). Or use the Rotated Rectangle tool (later versions of SU) or plugin, to draw a series of squares registered on one ‘endpoint’ in the ellipse, in the context of your semi-elliptical component, then pushpull them for the openings. I just drew the rectangles, outside the component. You’ll still only get about 12 altogether.

PS. As usual, @DaveR is incredibly quick on the draw

PPS. Why not make it straight, and your life easier? I have a straight rack, with apertures looking like this:

The round recess at the top of the slot stops the chisels falling out when I open or close the door of the tool cupboard. and the closer spacing isn’t an issue when reaching for one, or putting it back.

Quick and easy to make with either a spade bit or a Forstner bit, one size for the larger opening, drilled before making the smaller opening, then using either a handsaw or a bandsaw to cut the slots.

You could also use the Arc tool (not the 2-point Arc) and draw in arcs that meet the edge of the ellipse.

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What about spacing it out in a straight line first, and then using shape bender, or flowify or something similar?

Great solution! Old guy brain fog did not see that.

I am going to try that, Thanks!

Nice solution but I have a gazillion chisels and I see an ellipse will hold more chisels per length than a straight line

Yes, I can see that. Try a closer spacing anyway, to get in as many as you can, and the hole shape I suggest.

I encountered this problem once and wrote a script to solve it. It creates an ellipse where all segments have the exact same length. The script is attched. Open the script in a text editor and edit the parameters on line 145 - 147:

    ###### USER INTERFACE ####
    major =
    minor =
    q_bits = 16 #number of segments in a quarter ellipse (-> full ellipse has q_bits * 4 segments)

Copy the whole script (ctrl+a) from the texteditor and paste it into the ruby console and press enter.
regular_ellipse.rb (4.7 KB)



Brilliant, @DaveR. How did you get the spacing looking so equal? The Arc tool method you suggested earlier?

Thanks. I just continued on from the illustration with the arcs.

Lets take this a step further. If I know the number of cut outs around the perimeter and know the minor dimension how should I solve for the length?

You could probably do it mathematically, but I can’t remember the formula for the length of an ellipse’s perimeter given its axis lengths.

But if you are happy enough with an approximate answer, let SU do the maths.

Draw a circle 12" R, and perhaps with more than the default 24 sides - say 48 or 96. Align the vertices with the red axis [EDIT] Or perhaps better, the midpoint of an edge of the arc with the red axis.

Use the Scale too to expand the major axis to something bigger - say 16", as you know you need it bigger than the 14" you started with.

Draw the major axis, and delete the ‘back’ half of the resulting ellipse.

Highlight the edge of the half-ellipse.

Let Entity Info tell you the arc length. Divide that by the number of openings you want. See if the spacing is reasonable. If not, adjust again using the scale tool until you get a workable compromise.

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There is no formula for the length of the perimeter, it has to approximated. Quite surprising actually…

The script I posted above does solve the problem, it produces an ellipse where the segments have the same length, so for example, if you make a cut at every fourth joint (or any number) you will get equal spacing.

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entity info, did not think to look there. Thanks so much guys. I will make some saw dust later.
Stay safe everyone

Indeed. It can be expressed as a power series and there are various pretty accurate approximations but there is no exact finite expression. A thorough discussion of alternatives is given here.

Just for laughs, I tried the exercise with PowerCADD+WildTools. The GIF I made doesn’t seem to want to play here, but here’s a couple screen shots. The results seem good to at least 3 significant digits, maybe more.

Decided on an 8" long ellipse. The first one works great and need to make a bunch more. Thanks for all the help.

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