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Helical math
Message
From
30/03/2011 16:13:41
Mike Yearwood
Toronto, Ontario, Canada
 
 
To
30/03/2011 15:38:17
General information
Forum:
Visual FoxPro
Category:
Other
Title:
Environment versions
Visual FoxPro:
VFP 9 SP2
OS:
Vista
Network:
Windows 2008 Server
Database:
MS SQL Server
Application:
Desktop
Miscellaneous
Thread ID:
01505547
Message ID:
01505587
Views:
69
>>Hi all
>>
>>I'm having a mathematic difficulty. I've read all I can find on the subject. I need a formula. I have a circle with a hole in it, cut along a radius and pulled into a helix. I want a formula to return the intersections of this circle with an inner cylinder at 0, 90, 180 and 270 degrees and with an outer cylinder at 0, 60, 120, 180, 240 and 300 degrees. The radius of the inner and outer cylinders is known. The height the helix climbs along the inner and outer cylinders after one full turn is also known.
>>
>>So, I want x, y and z at each angle and radius, but I do not know the height (z) of the intersection points as they spiral through 3d space. I can obtain x and y on a 2D unit circle using sin, cos and tan (and probably an array), but can't determine z.
>>
>>Hope I explained that well.
>
>If you know the height the helix climbs on the inside and outside cylinders, is there any reason the climb rate is not constant as you rotate i.e. linear rate of climb? In other words, if you rotate 180deg from the bottom, are you not exactly half way up both the inside and outside climbs?

I'm looking at a physical model wherein that does not seem to be the case, because it is buckling out of shape. Your insight might remove the buckling.

Thanks. I'll give it a try.
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