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### Axis Calculations

The central axis length of the corkscrew is similar to the shift angle of the loop or the vertical angle of a curve. It is the direction the corkscrew is linearly stretched'' along to create the three-dimensional element. The distance along the central axis varies linearly with the arclength along the corkscrew.

Let represent the projected arclength in the - plane of the corkscrew from to . Let represent the length along the axis over the same range of . Refer to figure 2.7. Since the axis length varies linearly as the arclength along the corkscrew, and therefore varies linearly as the projected arclength along the corkscrew,2.7 the following can be shown. The range of is entirely within the circular region of the corkscrew. Its projected arclength in the - plane can therefore be determined from the following. From the figure a relationship can be found for in terms of . Making substitutions from above determines the total axis length.  The shift angle of a corkscrew, , is analogous to that of a loop. Figure 2.8 depicts the arclength of the corkscrew as the hypotenuse of the triangle, while the lower leg represents the projected length in the - plane. The length of the axis is the length of the right leg. The arclength of the corkscrew is given by the Pythagorean Theorem. 2.7 Refer to figure 2.8. Since the angle is constant, as discussed in section 2.1, this is a true statement.    Next: Back to the Corkscrew... Up: Corkscrew Elements Previous: Corkscrew Elements   Contents
Darla Weiss 2000-02-13