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Table of Contents

Cover
Dedication
List of Figures
List of Tables
Foreword
Preface
Acknowledgements
1 An Introduction to Tensegrity
1.1  Basic Tensegrity Principles
1.2  Applications of Tensegrity
1.3  Early Tensegrity Research
1.4  Recent Tensegrity Research
1.5  Other Space Frame Technologies
1.6  Book Scope and Outline
2 Basic Tensegrity Structures
2.1  Basic Tensegrity Structures: Introduction
2.2  T-Prism: The Simplest Tensegrity
 2.2.1  T-Prism Intuition
 2.2.2  T-Prism Mathematics: Cylindrical Coordinates
 2.2.3  T-Prism Mathematics: Cartesian Coordinates
 2.2.4  T-Prism Mathematics: Further Generalizations
2.3  T-Icosahedron: A Diamond Tensegrity
2.4  T-Tetrahedron: A Zig-Zag Tensegrity
2.5  Basic Tensegrity Structures: Conclusions
3 General Tensegrity Structures
3.1  General Programming Problem
 3.1.1  General Programming Problem: Introduction
 3.1.2  General Programming Problem: Objective Function
 3.1.3  General Programming Problem: Member Constraints
 3.1.4  General Programming Problem: Symmetry Constraints
 3.1.5  General Programming Problem: Point Constraints
 3.1.6  General Programming Problem: Vector Constraints
3.2  Solving the Problem
4 Higher-Frequency Spheres
4.1  Higher-Frequency Spheres: Introduction
4.2  Diamond Structures
 4.2.1  Diamond Structures: Descriptive Geometry
 4.2.2  Diamond Structures: Mathematical Model
 4.2.3  Diamond Structures: Solution
4.3  Zig-Zag Structures
 4.3.1  Zig-Zag Structures: Descriptive Geometry
 4.3.2  Zig-Zag Structures: Mathematical Model
 4.3.3  Zig-Zag Structures: Solution
5 Double-Layer Tensegrities
5.1  Double-Layer Tensegrities: Introduction
5.2  Double-Layer Tensegrities: Trusses
5.3  Double-Layer Tensegrities: Geodesic Networks
5.4  Double-Layer Tensegrities: Hexagon/Triangle Networks
6 Double-Layer Tensegrity Domes
6.1  Double-Layer Tensegrity Domes: Introduction
6.2  A Procedure for Designing Double-Layer Tensegrity Domes
6.2.1  Dome Step 1: Compute the sphere
6.2.2  Dome Step 2: Implement the truncation
6.2.3  Dome Step 3: Adjust the base points
6.2.4  Dome Step 4: Add guys
6.2.5  Dome Step 5: Compute the dome
6.2.6  Dome Step 6: Make adjustments to fix problems
7 Tensegrity Member Force Analysis
7.1  Force Analysis: Introduction
7.2  Endogenous Member Forces
7.2.1  Endogenous Force Analysis: Method
7.2.2  Endogenous Force Analysis: A Justification for the Method
7.2.3  Endogenous Force Analysis: Another Justification for the Method
7.2.4  Endogenous Force Analysis: A Sample Calculation for the Exact Formulation
7.2.5  Endogenous Force Analysis: Calculations for the Penalty Formulation
7.2.6  Generality of Weighted Models
7.3  Exogenous Member Forces
7.3.1  Exogenous Force Analysis: Method
7.3.2  Exogenous Force Analysis: Mathematical Framework
7.3.3  Exogenous Force Analysis: Initialization
7.3.4  Exogenous Force Analysis: A Sample Calculation
7.3.5  Exogenous Force Analysis: Complex Hubs
7.3.6  Exogenous Force Analysis: Another Sample Calculation
8 Analyzing Clearances in Tensegrities
8.1  Clearance Analysis: Introduction
8.2  Clearance Analysis: Formulas
8.2.1  Clearance Formulas: Distance Between Two Line Segments
8.2.2  Clearance Formulas: Angle Between Two Line Segments
8.2.3  Clearance Formulas: A Sample Application
8.2.4  Clearance Formulas: Another Sample Application
A Other Double-Layer Technologies
B Proof that the Constraint Region is Non-convex
C References