Skelton / de Oliveira Tensegrity Systems

1. Auflage 2009
ISBN: 978-0-387-74242-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 216 Seiten

This book discusses analytical tools for designing energy efficient and lightweight structures that embody the concept of tensegrity. The book provides both static and dynamic analysis of special tensegrity structural concepts, which are motivated by biological material architecture. This is the first book written to attempt to integrate structure and control design.

Autoren/Hrsg.

Skelton, Robert E.

de Oliveira, Mauricio C.

Inhaltsverzeichnis

1;Contents;6
2;Preface;10
3;Introduction and Motivation;14
3.1;Tensegrity in Nature;20
3.2;Tensegrity in Art;24
3.3;Tensegrity in Architecture;27
3.4;Tensegrity in Engineering and Science;30
3.4.1;Fundamentals of Tensegrity Structures;32
3.4.2;Temporary Shelters and Tents;39
3.4.3;Deployable Tensegrity Columns;40
3.4.4;Deployable Plates and Antennas;42
3.4.5;Deployable Wings;45
3.4.6;Beds and Broomsticks;46
3.4.7;Station-Keeping Buoy;47
3.4.8;Dynamics of Tensegrity Systems;50
3.4.9;Control of Tensegrity Systems;50
3.5;Chapter Summary;56
4;Analysis of Static Tensegrity Structures;58
4.1;Nodes, Members, and Connectivity;58
4.2;Potential and Force;60
4.3;Linear Springs and Strings;62
4.4;Equilibrium;63
4.4.1;Affine Transformations;67
4.4.2;Dual Structures;68
4.4.3;Class 1 Tensegrity Structures;69
4.5;Stiffness Matrix;70
4.5.1;Modes and Modal Vectors;72
4.5.2;Eliminating Rigid Body Modes;75
4.5.3;Stability;76
4.5.4;Eliminating Internal Nodes;77
4.6;External Forces;79
4.6.1;Optimal Volume of Loaded Structures;79
4.7;Chapter Summary;81
4.8;Advanced Material;82
4.8.1;Affine Transformations;82
4.8.2;Class 1 Tensegrity Structures;82
4.8.3;Stiffness Matrix;83
4.8.4;Modes and Modal Vectors;83
5;Design of Compressive Structures;86
5.1;Self-Similar Structures in Compression;88
5.1.1;Failure by Material Yielding;90
5.1.2;Buckling Constraints;91
5.2;T-Bar Systems;93
5.2.1;The T-Bar Unit;93
5.2.2;The T-Bar Self-Similar Rule;97
5.2.3;Optimal Column with Constant Width;100
5.2.4;Yielding in T-Bar Self-Similar Systems;104
5.2.5;Three-Dimensional T-Bar System;104
5.3;D-Bar Systems;107
5.3.1;The D-Bar Unit;107
5.3.2;The D-Bar Self-Similar Rule;110
5.3.3;Yielding in D-Bar Self-Similar Systems;113
5.3.4;Three-Dimensional D-Bar System;114
5.4;Unit-Self-Similar Designs;116
5.4.1;Using Box Units;116
5.4.2;Using D-Bar Units and T-Bar Units;117
5.5;Tensegrity Prisms;119
5.6;Minimal Regular Prisms;119
5.6.1;Equilibrium;120
5.6.2;Design Under Compressive Load;121
5.7;Tensegrity Columns;123
5.7.1;Unit-Self-Similar Design;123
5.8;Tensegrity Plates;126
5.8.1;Topology A;127
5.8.2;Topology B;128
5.8.3;Design Under Compressive Load;130
5.8.4;Hexagonal Three-Bar Flat Plates;132
5.9;Non-minimal Regular Prisms;135
5.9.1;Equilibrium;136
5.10;Chapter Summary;137
5.11;Advanced Material;138
5.11.1;Equilibrium of Regular p-Bar Tensegrity Prism;138
5.11.2;Tensegrity Plates;140
6;Design of Bending Structures;142
6.1;Michell Topology;142
6.1.1;Michell Spirals;142
6.1.2;Michell Topology;143
6.2;Michell Topology in Static Equilibrium;146
6.2.1;Force Equilibrium at a Generic Node;146
6.2.2;Linear Propagation of Forces;148
6.3;Michell Topologies Under a Single Bending Load;150
6.4;Material Volume of Michell Topologies;151
6.4.1;Material Volume for a General Set of ExternalForces;152
6.4.2;Michell Topologies Under a Single Bending Load;152
6.5;Michell Topologies with Minimum Material Volume Under a Single Bending Load;154
6.5.1;The Limit as Complexity Grows;156
6.5.2;Penalizing Joint Mass Leads to Finite OptimalComplexity;159
6.6;Chapter Summary;160
6.7;Advanced Material;162
6.7.1;Force Equilibrium at a Generic Node;162
6.7.2;Proof of Theorem 4.2;163
6.7.3;Michell Topologies Under a Single Bending Load;164
6.7.4;Michell Topologies with Minimum MaterialVolume Under a Single Bending Load;165
6.7.5;The Limit as q Goes to ;167
7;Analysis of Tensegrity Dynamics;169
7.1;Vectors and Notation;169
7.2;Dynamics of a Single Rigid Rod;171
7.2.1;Nodes as Functions of the Configuration;175
7.2.2;String Forces;176
7.2.3;Generalized Forces and Torques;176
7.2.4;Equations of Motion;177
7.3;Class 1 Tensegrity Structures;178
7.4;Constrained Class 1 Tensegrity Structures;182
7.4.1;Single Constrained Rigid Rod;183
7.4.2;General Class 1 Tensegrity Structures;185
7.5;Chapter Summary;186
7.6;Advanced Material;187
7.6.1;Dynamics of a Single Rigid Rod;187
7.6.2;Constrained Class 1 Tensegrity Structures;189
8;Closed-Loop Control of Tensegrity Structures;191
8.1;Control of Tensegrity Systems;192
8.1.1;A Single Rigid Rod;192
8.1.2;Control Inputs;193
8.1.3;General Class 1 Tensegrity Structures;194
8.2;Lyapunov-Based Control Design;195
8.2.1;A Single Rigid Rod;195
8.2.2;A Control Design Problem;197
8.2.3;Admissible Control Inputs;199
8.3;Some Simple Examples;201
8.4;Chapter Summary;206
8.5;Advanced Material;207
8.5.1;Proof of Theorem 6.1;207
8.5.2;Proof of Lemma 6.2;209
9;Bibliography;211
10;Index;225