A Practical Guide to Tensegrity Design

Table of Contents

Preface

This is the second edition of *A Practical Guide to
Tensegrity Design*. The first edition was released in spiral-bound
format generated from LaTeX source in 1994.
Section 1.3 on the early
history of tensegrity has been rewritten.
New material on realistically modeling the complex details
of hubs has been added throughout the book.
Illustrations have been clarified and augmented.
Two electronic editions have been prepared, one using XHTML
and MathML,
and the other in PDF format generated from the updated LaTeX source.

The book covers the basics of doing calculations for the design and analysis of floating-compression tensegrities. In this sort of tensegrity, the struts aren't connected to each other. They are the most difficult to do computations for since calculating member lengths is more than just computing distances between points: the points themselves have to be properly placed. Examples with complete data have been provided so you can calibrate your software accordingly. The book presumes you are well versed in linear algebra and differential calculus and are willing to explore their application in diverse ways. If you plan to implement the nonlinear programming algorithms, a knowledge of or interest in numerical techniques will be useful as well.

Chapter 1 gives some background information on floating-compression tensegrity and briefly describes other non-tensegrity space-frame technologies. Unfortunately it neglects other non-floating-compression tensegrity and tensegrity-related technologies. Chapter 2 exhibits some simple tensegrity structures and describes how they can be mathematically modeled. This is basically a history of my early explorations in tensegrity mathematics. As the chapter notes, I found the methods I used for these simple structures didn't scale very well to be useful for the design of more complex structures. The general philosophy of using optimization techniques carried through very well though.

Chapter 3 gets into the substance of the book. It describes the basic nonlinear-programming framework which can be applied to the design of any floating-compression tensegrity. Section 3.2 of this chapter, which suggests one methodology for solving the nonlinear programming problem posed in Section 3.1, can be ignored by those who wish to use another technique or who already have nonlinear-programming software or subroutines and don't need to implement them. The techniques described have served me well, but I don't know how they compare with others for solving constrained nonlinear programming problems.

Chapter 4 applies the method described in Chapter 3 to the design of some simple single-layer tensegrity spheres which are based on geodesic models. Chapter 5 extends the analysis to double-layer spheres, and Chapter 6 extends it again to domes.

The last two chapters describe the analysis of tensegrity structures. In Chapter 7, the interest is in the determinants of the forces in the members composing a tensegrity. Section 7.3 is probably in need of the competent attention of a structural engineer, but I hope it at least provides a good starting point. The description of vector constraints in the last parts of this section represents the best claim of this book to the word "practical" in its title. Analysis of practical structures generally requires the abandonment of the assumption of single-point hubs, and vector contraints are an effective way to deal with the complexity that results. Chapter 8 describes how distances and angles between members of a tensegrity can be computed.

I've found the tools described here useful for designing and analyzing tensegrities and hope they prove useful to you. I would be interested in hearing how they work out for you and receiving data you have generated from the design and analysis of tensegrity structures. I'd also appreciate suggestions for improvement and notification of mistakes of any sort including typographic errors.

Bob Burkhardt Shirley, Massachusetts September 16, 2008 |