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3.13. slug

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The worm [ 6 ] is represented by the following equations. To keep the formulas a little clearer, we use the constant h.

 

h = e u/(6pi)

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x = a (1 - h) cos(u) cos(0.5 v) cos(0.5 v)

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y = 1 - e u/(b pi) - sin(v) + h sin(v)

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z = a (-1 + h) sin(u) cos(0.5 v) cos(0.5 v)

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To represent the area, the two parameters u and v must have the following values ​​(definition range).

 

u is an element from the set of numbers [0, 6 pi]

 
 

v is an element of the number set [0, 2 pi]

 

The value u Max determines the number of windings of the worm, with u Max = 6 pi there are 3 windings.

The domain of definition of v is required to get a complete circle as a cross-section, it cannot be changed with the plugin.


Fig. 17


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