]> A Practical Guide to Tensegrity Design: 6.2.4 Dome Step 4: Add guys

6.2.4 Dome Step 4: Add guys

With the truncation methodology discussed here, adding guys, and points on the ground to attach them to, is usually advisable. A valid tensegrity could be obtained without these guys, but it would be a very rickety one. Minor lateral forces applied to the structure would move it substantially. With the guys in place, the structure will resist lateral forces more robustly.

The guys are where the outer layer of tendons meets the ground. Their attachment points should be chosen so they mimic the effect of the outer-layer tendons which would have appeared in this vicinity but were discarded due to the truncation. The guy attachment points are in the same plane as the base points and will fall on a circle which is a dilatation of the base-point circle. More precisely, the attachment-point circle is chosen to be the intersection of a sphere approximating the outer layer of tendons with the ground. Call the radius of this circle r' avg. Figure 6.10 shows a cross-section of the dome and sphere with the measurements of r' avg, and ravg and havg from Section 6.2.3, shown.

two-dimensional diagram with dome/sphere layers, base, and lengths
Figure 6.10: Double-Layer Dome: Base-Point and Guy-Attachment-Point Radii

r' avg is calculated using the formula

r' avg= Σ i=1 nhs2 Pi' nhs2 2- havg2

where nhs is the number of basic points in the sphere, and Pi ' is an outer-layer basic point of the sphere. For the 6ν sphere, the value of nhs is 18, and the value of r' avg is 5.150852 --2.1761042 =4.66860.

Another question is how much to rotate the guy-attachment points relative to the base points. A sensible place to start would seem to be half the angle between the base points, π9 in this case. These can be adjusted later if that can help ease distortions of the realization of the sphere's configurations in the dome.

With this in mind, it seems reasonable to put the guy lengths in the objective function to let the computations themselves give feedback on the necessary rotation factor. The guy weights should be chosen also so as to aid the realization of the sphere's configurations in the dome as closely as possible.

Table 6.22 lists the coordinates which resulted from applying the above procedures to deriving the guy-attachment points. Table 6.23 gives the data for the one guy-attachment point which is generated using a symmetry transformation. Table 6.24 enumerates the data for the six guys which are added to the model in this step.

 Point  Coordinates
x y z
P30'
P31'
P32'
 -4.795937   -0.711963   1.738777 
 -3.058334   -3.264453   2.553663 
 -0.477574   -4.877340   1.585790 
 
Table 6.22: 6ν T-Octahedron Dome: Guy Attachment Point Coordinates


 Point 
Coordinates
x y z
 Basic 
Point
 Transform 
Number
P33 '
z30 ' x30 ' y30 '
P30 ' 3
 
Table 6.23: 6ν T-Octahedron Dome: Guy-Attachment-Point Symmetry Correspondence


 Member 
#
 End Points   Weight   Constrained 
Length
Sphere
 Member 
175
176
177
178
179
180
P30' P23'
P23' P31'
P31' P24'
P24' P32'
P32' P28'
P28' P33'
 0.4000 
 0.4000 
 0.4000 
 0.4000 
 0.4000 
 0.4000 
 N/A 
 N/A 
 N/A 
 N/A 
 N/A 
 N/A 
 N/A 
 N/A 
 N/A 
 N/A 
 N/A 
 N/A 
 
Table 6.24: 6ν T-Octahedron Dome: Guys