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Could you help me with the creation of an helicoid like thisand after flatten. I know the helicoid is a developpable surface. How may I define it? And after unbend?
That appears to be a helical ribbon which, while it is a
ruled surface, is not developable (e.g. Gaussian curvature
is not equal zero). You can use Flatten Quilt to get a fair
approximation or, if you think it is developable (I'd be
interested in seeing it), post a neutral (preferably
including the 'foundation' before thickening surface) or
link to your reference material.
Dunno. I've never had a class.
It appears Pro/E has a more stringent criteria, though.
Ref PTC KB "Suggested Technique for Determining if a Sheetmetal Surface is Developable"
"the method used to determine if sheetmetal surfaces are
developable be setting the config.pro option mesh_spline_surfs"
To get a Flat Pattern or Regular Unbend both* driving and offset surfaces
must be both developable and, internally, ruled surfaces. By definition
developable surfaces are a subset of ruled surfaces.
* Not a consideration in Rhino. Solid B-Reps are not flattened.
An equivalent in Pro/E would be to flatten an offset, to neutral
axis, offset of a Solid B-Rep face.
Ruled surfaces can be precisely represented by "spline surfaces"
with U & V degrees higher than one and still be quite developable
(though cannot be Flat Patterned in Pro/E).
A simpler, maybe more graphic, demonstration:
Set the config option mesh_spline_surf yes. Extrude an arc. VSS an arc
section along a normal to section vector without modifying the section.
Note that VSS creates a "spline surface". Both surfaces are obviously
cylindrical sections, the only difference being internal (query a *.neu)
representations. I guess that the VSS isn't checked and 'simplified' as
might be done. Just for fun Edit Def the VSS and change the Option:
Variable section to Constant section. Take it one step further; repeat
the exercise extruding and sweeping tangent solid sections, convert to
sheetmetal and flatten. Don't make the arcs equal radius or Pro/E will
merge (truly merge vs. 'join') the surfaces when the VSS is Constant
section.
Thinking back a bit, all this answers a question I posted a few years ago [url]http://www.mcadcentral.com/proe/forum/forum_posts.asp?TID=30 143[/url]
and I suspect that checking will verify a guess that 'washing' thru a
translation runs the imported surfaces thru a simplifying function with the
result being conversion of eligible spline surfaces to ruled surfaces.
But, anyway, back to the question: I don't believe PTC ever says anything
about Gaussian curvature with reference to sheetmetal parts or creating
flat patterns. Two possible reasons I can think of for that; Pro/E's more
restrictive criteria and the relationship between compound curvature, of
which Gaussian curvature is a measure, and developability is common
knowledge. (Possibly less well known(?); Gaussian curvature is an
indicator of developability because it is the product of principle
curvatures. A zero multiplicand yields a zero product.)
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