Show messages: All
1-14
15-16
From: bemfarmer
After much study, the ASWT was re-modeled.
The blade Surface, formed in Moi, is "developable", and so can be Unrolled, (in Rhino 8), to a flat pattern with little or no distortion.
The blade Surface 3dm file was opened in Rhino 8, and the Unroll command was used to create a flat pattern.
The Flattened area was 2.3% greater than the blade surface area. Increase in "u" isocurve density in Rhino 8 made no visible difference.
No way to increase the "v" isocurve density was found.
The Rhino 9 Unroll command is very slow, perhaps 5 to 10 minutes. First it calculates the before and after Area, to give an idea of "distortion".
It was difficult for this novice Rhino 8 user to find the desired commands and settings, but some progress was finally achieved.
The blade is formed using an Archimedean spiral as a tapered Helix rail. The Helix is formed with the MoI Helix command, and tapers from maxRadius to zero.
The core cylinder region, "~shaft", is deleted from the blade.
The blade Surface is NOT an Archimedean tapered screw, nor a portion of a Toroid, due to the "open radius of theta = 60 degrees region", and how the two rails are swept.
(The rail spiral is NOT "logarithmic", nor "fibonacci".)
I may do a script or node, including updated "optimum" parameters, values and definitions.
And also check out how the actual degrees of the 3 blades, measured at a plane intersection, compare to the 60 degree, 45 degree, 30 degree (better) style.
- Brian
From: bemfarmer
There are said to be 5 types of helicoids.
The pictures in the links are hard to tell apart.
Scripting their parametric equations may help to discern the differences.
There are also many links to other, older, papers.
The ASWT may be a conical version of the Oblique helicoid, or of the Developable helicoid. (???)
V. J. Paul, “A review of geometry investigations of helicoids,”
https://www.researchgate.net/publication/325860850_A_Review_of_Geometry_Investigations_of_Helicoids/fulltext/5b29e65faca27209f374d62b/A-Review-of-Geometry-Investigations-of-Helicoids.pdf
Five Types of Ruled Helical Surfaces for Helical Conveyers, Support Anchors and Screws
https://www.matec-conferences.org/articles/matecconf/abs/2017/09/matecconf_icmme2017_06002/matecconf_icmme2017_06002.html
- Brian
Found some nice links to knitting as well.
Show messages: All
1-14
15-16
