Design into 3D: Modeling a Bow-tie/Dutchman

This is a difficult shape to draw in Carbide Create since one needs outside rounding (easy) and internal rounding (difficult). Having a program do the math reduces this to just specifying a couple of parameters:

With the variables specified, we add support for units and the attendant calculations and begin placing things:

As a check on this, drawing things up in parallel in Carbide Create will help us to see what is involved:

Note that the circle and rectangle need to be rotated as a unit, and a copy of the circle rotated in place as well so as to allow for snapping:

A bit of duplication and flipping (and rotating the circles) allows us to arrive at:

which when unioned yields:

and when zoomed in on, shows a very slight rounding is necessary:

Duplicating this geometry and subtracting the circle from the nascent bow-tie gives us a node we can snap against for measurement purposes:

Since Carbide Create only affords an option to draw from the center out this must necessarily be reduced in size by a scaling factor of 0.5 and repositioned.

Switching gears to Freehand we find that the dimensions in question are:

But we are asking the wrong question — what needs to happen here is we need to inscribe a circle inside a figure which has angles of:

180 - 15 * 2

so, 150 degrees, so a 12-sided figure, so a dodecagon

Carbide Create makes it simple to draw a circle with an inscribed dodecagon (since it draws polygons using the radius to a point):

So the math should be:

  • determine the length of the base of a right triangle which has a hypotenuse of radius and an apex angle of 15 degrees
  • use that base distance of calculate the height of a right triangle which has opposing angle of 15 degrees

to determine the distance which the circle should be lowered from the point of the interior angle of the bow-tie.

This dimension of course gets re-used in a number of places, so we’ll start at the lower left corner we are using as an origin:

With those numbers worked out, it’s a simple matter to make a module to make half:

and then to mirror it and place the copy appropriately.

Then it’s simply a matter of subtracting the cylinder to radius the middle:


Next is exporting OpenSCAD, wiring up the customizer and adding the projection() command so as to be able to export a DXF or SVG.


Design into 3D_ Bow-tie.dxf (8.8 KB)

Design into 3D_ (711 Bytes)

Will you have encyclopedic knowledge.

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Thanks, mostly I’m just stubborn and manage to look up the specifics I need.

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Very interesting and complete solution. Designing the object with tooling geometry in mind allows for direct machining of both the bow tie and pocket on the machine.

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