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From: bemfarmer
Here is the GloboidHelixBeta002 script.
For a spiral around a torus, rather than a worm, Gear teeth may be set equal to Worm turns.
- Brian
Attachments:
_GloboidHelixBeta002.zip
From: bemfarmer
Here is the _GloboidLadder script, which can be used with Network command to create one globoid surface.
Due to the changing curvature, Sweep does not form the proper surface. Lineweb does not create the proper rungs either.
The script can be run again for the other surfaces of the trapezoid.
A curved ladder analogy is used for the net. Another analogy would be a roller coaster train track, where the cross ties, which correspond to the ladder rungs, connect the two rails. The net consists of 2 (or possibly more) rail spirals, and numerous rungs which are line segments. Each rung line represents a cutting edge of the trapezoid tool, at a different rotation angle. More documentation is in the .js file. The previous trapezoid .3dm file is included in the zip.
The user selects two points in the Right View, such as adjoining points of a trapezoid, or another pair of points for decorative spirals.
After the script creates the ladder net, Network command can be run, to create the surface.
Works with MoI3, and MoI4beta. MoI3 is a little bit slower, but shows the progressive rung line segment building.
Network works in a few seconds, unless the configuration or number of points is excessive.
The script is .beta. Perhaps the script could be modified to use other curves, instead of line rungs, by using Orient command.
This would require a third, non-collinear point, so as to have a frame for the orientation of the curve...(?)
- Brian
Attachments:
_GloboidLadderBeta002.zip
From: bemfarmer
To reduce some confusion on teeth and trapezoids:
Re-reading the multiple papers by Polowniak/Sobolak, there are different versions of trapezoids. In their mathematical model of a worm gear, there is a small circumferential clearance between two trapezoids, one for the wheel, and one for the worm. Only one trapezoid is shown in the attached .3dm file, which could be for the tooth notch in the wheel, or for the worm, or for a cutting hob, which resembles a worm, for cutting the wheel. So the 2 dimensional trapezoid shown in the attached .3dm file is in the plane x=0, and could represent the 2 dimensional worm wheel notch between 2 teeth of the wheel, or a tooth of a hob cutting tool which could machine the wheel. Or the trapezoid could be a worm tooth profile. In machining a worm, a trapezoidal cutting blade can be used.
Worm wheel teeth are 3 dimensional. The upper and lower edge of the worm tooth cause the wheel teeth to be tapered...
The papers have more matrix math for them...
- Brian
From: bemfarmer
Bug: If the globoid net is closed, ( gear teeth = worm turns, ) there is a duplicate line rung at the end, which needs to be deleted before network will work.
From: bemfarmer
Beta3 does not add the last line segment, if the two globoid curves are closed. (gearTeeth = wormTurns = 1)
- Brian
Attachments:
GloboidRingTwist.3dm
GloboidStartTriangle03.7z
_GloboidLadderBeta003.zip
Image Attachments:
GloboidRingTwist.png
GloboidTriangle.png
From: bemfarmer
Free gear book pdf.
https://www.academia.edu/36781112/Gear_Geometry_and_Applied_Theory_pdf?email_work_card=view-paper
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