A Practical Guide to Tensegrity Design
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6.2.5 Dome Step 5: Compute the dome

6.2.6 Dome Step 6: Make adjustments to fix problems

The same clearance goals that are used for the 4ν t-octahedron spherical truss in Section 8.2.3 seem appropriate for this structure. With these thresholds, eight member pairs are singled out as having poor clearances. The poor clearances are mostly between pairs of struts. Table 6.25 enumerates the member pairs involved and the corresponding clearances. In addition, the solution exhibits a substantial range in member forces in the tendons, from a minimum of 0.7076 (#143) to a maximum of 5.5859 (#99).

The interference problem is the most fundamental one. A range of tendon forces can be dealt with at construction time by using different materials depending on the relative force for the tendons, though in some situations it might be worthwhile to see what can be done to moderate the range of forces at design time. The forces are greatest in the convergence and interlayer tendons and smallest in the binding tendons and guys.

The interference problem can mostly be attributed to the low frequency of the model. At lower frequencies, the inward-pointing tripods whose peaks are the inner convergence tendon triangles tend to be shallow. This means the non-adjacent component members approach each other too closely in the vicinity of the convergence triangle.

The interference problem can be fixed by decreasing the lengths of the outer binding tendons which constrain the extent of the base of the tripod. Since the binding tendons are all weighted members of the objective function in this model, this means increasing the weight corresponding to the outer binding tendon in question. The outer binding tendon to select is the one which most parallels the strut with the clearance problem. Increasing the weight on this tendon gives the strut a steeper trajectory on its path from the outer to the inner layer and thus keeps it from approaching nearby tendons and struts at the convergence too closely. Table 6.26 lists the outer-binding tendon corresponding to each strut with an interference problem and the new value selected for the tendon's weight.

The revised model is brought to convergence using three iterations with the exact method in conjunction with Fletcher-Reeves. The derivatives of the objective function with respect to the independent coordinate values are all less than and all clearances are above their respective thresholds.

Tables 6.27 to 6.31 show the values for the final lengths and relative forces. As before, excluded members are marked with ‡. Tables 6.32 and 6.33 show the final values for the coordinates of the basic points. Figures 6.11 and 6.12 show how the final structure appears as viewed from the side and base of the structure respectively. For clarity, interlayer tendons have been excluded⁸ and members in the background have been eliminated by truncation. For reference, selected points are labeled.

Figure 6.11: 6ν T-Octahedron Dome: Side View

Figure 6.12: 6ν T-Octahedron Dome: Base View

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7 Tensegrity Member Force Analysis