Tensegrity Systems (eBook)

Mauricio C. de Oliveira, Robert E. Skelton (Autoren)

eBook Download: PDF

2009 | 1. Auflage
XIV, 216 Seiten
Springer US (Verlag)
978-0-387-74242-7 (ISBN)

Infos

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.

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Tensegrity Systems discusses analytical tools to design energy efficient and lightweight structures employing the concept of "e;tensegrity."e; This word is Buckminister Fuller's contraction of the words "e;Tensile"e; and "e;Integrity,"e; which suggests that integrity or, as we would say, stability of the structure comes from tension. In a tensegrity structure the rigid bodies (the bars) might not have any contact, thus providing extraordinary freedom to control shape, by controlling only tendons. This book will provide both static and dynamic analysis of special tensegrity structural concepts, which are motivated by biological material architecture. This will be the first book written to attempt to integrate structure and control design. All other books on structure design and books on control design assume these are independent topics, but performance can be greatly improved if the dynamics of the structure and the dynamics of the controls are coordinated to reduce the control efforts required to accomplish the system performance requirements.

Inhalt

Contents 6
Preface 10
Introduction and Motivation 14
Tensegrity in Nature 20
Tensegrity in Art 24
Tensegrity in Architecture 27
Tensegrity in Engineering and Science 30
Fundamentals of Tensegrity Structures 32
Temporary Shelters and Tents 39
Deployable Tensegrity Columns 40
Deployable Plates and Antennas 42
Deployable Wings 45
Beds and Broomsticks 46
Station-Keeping Buoy 47
Dynamics of Tensegrity Systems 50
Control of Tensegrity Systems 50
Chapter Summary 56
Analysis of Static Tensegrity Structures 58
Nodes, Members, and Connectivity 58
Potential and Force 60
Linear Springs and Strings 62
Equilibrium 63
Affine Transformations 67
Dual Structures 68
Class 1 Tensegrity Structures 69
Stiffness Matrix 70
Modes and Modal Vectors 72
Eliminating Rigid Body Modes 75
Stability 76
Eliminating Internal Nodes 77
External Forces 79
Optimal Volume of Loaded Structures 79
Chapter Summary 81
Advanced Material 82
Affine Transformations 82
Class 1 Tensegrity Structures 82
Stiffness Matrix 83
Modes and Modal Vectors 83
Design of Compressive Structures 86
Self-Similar Structures in Compression 88
Failure by Material Yielding 90
Buckling Constraints 91
T-Bar Systems 93
The T-Bar Unit 93
The T-Bar Self-Similar Rule 97
Optimal Column with Constant Width 100
Yielding in T-Bar Self-Similar Systems 104
Three-Dimensional T-Bar System 104
D-Bar Systems 107
The D-Bar Unit 107
The D-Bar Self-Similar Rule 110
Yielding in D-Bar Self-Similar Systems 113
Three-Dimensional D-Bar System 114
Unit-Self-Similar Designs 116
Using Box Units 116
Using D-Bar Units and T-Bar Units 117
Tensegrity Prisms 119
Minimal Regular Prisms 119
Equilibrium 120
Design Under Compressive Load 121
Tensegrity Columns 123
Unit-Self-Similar Design 123
Tensegrity Plates 126
Topology A 127
Topology B 128
Design Under Compressive Load 130
Hexagonal Three-Bar Flat Plates 132
Non-minimal Regular Prisms 135
Equilibrium 136
Chapter Summary 137
Advanced Material 138
Equilibrium of Regular p-Bar Tensegrity Prism 138
Tensegrity Plates 140
Design of Bending Structures 142
Michell Topology 142
Michell Spirals 142
Michell Topology 143
Michell Topology in Static Equilibrium 146
Force Equilibrium at a Generic Node 146
Linear Propagation of Forces 148
Michell Topologies Under a Single Bending Load 150
Material Volume of Michell Topologies 151
Material Volume for a General Set of ExternalForces 152
Michell Topologies Under a Single Bending Load 152
Michell Topologies with Minimum Material Volume Under a Single Bending Load 154
The Limit as Complexity Grows 156
Penalizing Joint Mass Leads to Finite OptimalComplexity 159
Chapter Summary 160
Advanced Material 162
Force Equilibrium at a Generic Node 162
Proof of Theorem 4.2 163
Michell Topologies Under a Single Bending Load 164
Michell Topologies with Minimum MaterialVolume Under a Single Bending Load 165
The Limit as q Goes to 167
Analysis of Tensegrity Dynamics 169
Vectors and Notation 169
Dynamics of a Single Rigid Rod 171
Nodes as Functions of the Configuration 175
String Forces 176
Generalized Forces and Torques 176
Equations of Motion 177
Class 1 Tensegrity Structures 178
Constrained Class 1 Tensegrity Structures 182
Single Constrained Rigid Rod 183
General Class 1 Tensegrity Structures 185
Chapter Summary 186
Advanced Material 187
Dynamics of a Single Rigid Rod 187
Constrained Class 1 Tensegrity Structures 189
Closed-Loop Control of Tensegrity Structures 191
Control of Tensegrity Systems 192
A Single Rigid Rod 192
Control Inputs 193
General Class 1 Tensegrity Structures 194
Lyapunov-Based Control Design 195
A Single Rigid Rod 195
A Control Design Problem 197
Admissible Control Inputs 199
Some Simple Examples 201
Chapter Summary 206
Advanced Material 207
Proof of Theorem 6.1 207
Proof of Lemma 6.2 209
Bibliography 211
Index 225

Produkt-Details

• Erscheint lt. Verlag: 4.6.2009
• Zusatzinfo: XIV, 216 p. 60 illus.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: analytical tools • Control design • Dynamic Analysis • energy efficient • linear controllers • Stab • stability • Static Analysis • structural concepts • Structure • structure design • system performance • Tensegrity • tensegrity structure
• ISBN-10: 0-387-74242-5 / 0387742425
• ISBN-13: 978-0-387-74242-7 / 9780387742427