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unfold sheet
May 29, 2009, 05:51:25 PM
I have a 3D drawing that I created using lofting. It is a basic square to round. I would like to be able to unfold the face of this shape but TC cannot accomplish this. Any sugestions would be helpful.

Thanks
Mike Batty

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May 29, 2009, 07:55:16 PM
I've been playing with that particular problem for a year or more, off and on, and have never found a really good solution. Best approach I've found is this: Start the object as a truncated cone, with the base diameter equal to the desired base dimension multiplied by the square root of 2. Place a 2D square of the correct base dimensions in the plane of the base of the cone. With the 3D Slice tool, make four cuts in the cone, using Slice By Plane -- for each cut designating the slicing plane by two adjacent corners of the square and the nearest quadrant point of the circular top of the cone. (Draw a circle there so you can snap to its quadrant points.)

Attached screenshot shows the cone sliced that way, with the four pieces of scrap moved aside. Base square is blue; circle on top of the cone is green.) The "Unfold Face" tool will work on the four curved faces of the central object, and the other four faces are of course flat. I went so far as actually to fabricate one of these with aluminum flashing, and it turned out reasonably well.

Henry H

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May 29, 2009, 10:54:48 PM
Nice solution, Henry.  There's another way.  A tapered fillet on a prism will also unfold, and in a production scenario has only one neck curve to cut.

*edit*  I thought about this a couple minutes after I posted and realised that the way I'd described it, the blend profile would be normal to the slope of the shoulder, and that the profile at the top of the shape would be four elliptical arcs, rather than a circle.  So, back to first principles.  Why won't TC unwrap the loft?  For perfect sheet development, you need a ruled surface comprised of triangular faces only.  An exploded TC loft of this shape gives quadrilaterals.  Moreover, they overlap.  Exploding a loft with line guides down the shoulders left quads that span both profiles, which should be more likely to unwrap, but still no result.  A bit more thought later, I realised that the answer is with the offset cone tool.
Check the 2D profile box, and the offset cone box.  Use a 90 degree arc segment for the base instead of the circular profile.  Resultant open offset cone surface will unwrap, and is one curved cut and uninterrupted creases.

« Last Edit: May 30, 2009, 07:18:09 PM by murray dickinson »

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May 30, 2009, 08:38:30 PM
That's very neat, Murray. FWIW, if you slice away just a little of the lower part (getting rid of the sharp corners), the object can be Shelled to give it a nonzero thickness.

Henry H

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June 02, 2009, 04:39:05 PM
Thanks for the suggestions. I was just looking for an easy way to layout a transition without having to purchase unfolding software. This info will definitely  make it easier to do a layout than the old manual method.

Mike

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June 07, 2009, 10:03:44 PM
Attached screenshot illustrates a basic design that can be flattened in one step using "Unbend Sheet." Briefly stated, here's how to draw it:

Working exclusively in the World Workplane, draw a 16-sided regular polygon to approximate the round top. Draw a square for the bottom, then modify the corners just a tad so the square becomes another 16-sided polygon. Draw a 4-sided 3D Polyline to outline each face. (Take advantage of symmetry and use Mirror Copy as much as possible to ease the workload.)

Simple-Extrude each of these 3D Polylines. (If they were all drawn while working in the World WP, they'll extrude along the World Z axis.) For each extrusion, select with the Facet Editor the face that corresponds to a face of the finished object and apply Format|Create Surface|From Face(s). (There's a toolbutton for this, which is a bit easier to use than the Format menu.)

Boolean-Add these sixteen "surfaces." Fillet the sixteen edges where the faces intersect, using a radius equal to the thickness of the sheet metal plus the inside bend radius. (I used .024" sheet and .03" bend radius.) Shell the object to the sheet metal thickness. (You want to shell inward; zoom in and note whether shelling proceeds inward or outward and be prepared to Undo and change the sign of the Thickness if it goes the wrong way.)

You'll have to make a slit in one of the sides in order to flatten this object. I Simple-Extruded a straight line, shelled the extrusion to a thickness of .0005", and subtracted this from the object. With that accomplished, Unbend Sheet worked just fine.

Henry H

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June 08, 2009, 04:46:36 AM
Henry, excellent.  Can I suggest using the offset cone tool as a construction aid?  Four offset cones from the polygon circle approximations added to four from the rectangular base as per the picture. As you noted in your earlier post, the sharp points need to be sliced off to enable the shelling you've described.  Then format surface|from solid, remove the cap and base and follow your other processes.

*edit* You mention working exclusively in world plane because TC's fussy about unbending if things are created on other planes.  I get around that by completing the construction, then saving it as .sat.  When you reinsert the .sat file, it'll ignore planes and unbend whereas the native TC object won't.  Go figure.

« Last Edit: June 08, 2009, 07:49:38 AM by murray dickinson »

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June 08, 2009, 09:51:24 AM
Can I suggest using the offset cone tool as a construction aid?  Four offset cones from the polygon circle approximations added to four from the rectangular base as per the picture.

Great idea, Murray; it follows naturally from your earlier suggestions.

You mention working exclusively in world plane because TC's fussy about unbending if things are created on other planes.

Actually, my reason for working in the World WP is that when a 3D Polyline is Simple-Extruded, it extrudes parallel to the Z axis of the WP that was current when it was created. Was hoping to minimize the number of potential sources of confusion ;-)

Henry H

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June 08, 2009, 02:26:45 PM
Are you not experiencing the fussiness that I am, Henry?  Until I reinsert the model, unbend isn't happening, the faces won't highlight.
I've also saved a couple of clicks by subtracting the slit in the shape with a very skinny box.  My contribution to the war against RSI...
« Last Edit: June 08, 2009, 03:16:42 PM by murray dickinson »

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June 08, 2009, 06:31:49 PM
I experienced a different kind of fussiness with your method, Murray, although in the end it worked well. After making the four corner cones, I created the four large flats, one at a time, by lofting between one side of the (exploded) base rectangle and one side of the (exploded) polygon. (Shoulda thought of that sooner.)  Added all the faces but couldn't convert them into a Solid because of the "Is this an open shell?" objection -- so I sliced a little off the bottom, filleted the joints, and shelled the object to give it a thickness. Cut the slit and then applied Unfold Face with no problem.

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June 08, 2009, 07:25:37 PM
It gets easier and easier...

Replace each corner of the rectangular base with three small line segments parallel to the corresponding sides of the polygonal top, then Loft. (The result is shown in the attached screenshots.) Fillet the intersections of the side faces; shell, omitting the top and bottom; slit one face; apply Unbend Face.

Henry H

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June 08, 2009, 08:02:37 PM
While Henry's method is undeniably elegant, using the offset cone methodology is geometrically exact and  doesn't require any further calculation.  But it does leave the face layouts scattered about.  Subtracting some objects from the edges can help with instant identification so use of the 3 point assembly tool is direct.  The pictures show a number of spheres along the straight edges of the layout, placement entirely random using the "nearest" snap to the edges.  The layouts have matching cutouts along the straight edges, giving direct visual reference for assembly.  The steps I've described also have the 3 point assembly tool automatically correcting the alignment when the unfold is flipped from the workplane placement, which is sometimes hard to pick if the edges are numbered instead.