## Tensegrity Systems (Google eBook)Tensegrity Systems discusses analytical tools to design energy efficient and lightweight structures employing the concept of “tensegrity.” This word is Buckminister Fuller's contraction of the words “Tensile” and “Integrity,” 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. |

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### Contents

1 | |

III | 7 |

IV | 11 |

V | 14 |

VI | 17 |

VII | 19 |

VIII | 27 |

IX | 29 |

LIX | 117 |

LX | 119 |

LXI | 122 |

LXII | 123 |

LXIII | 124 |

LXIV | 125 |

LXV | 127 |

LXVI | 129 |

X | 32 |

XI | 33 |

XII | 34 |

XIII | 37 |

XV | 43 |

XVI | 45 |

XVII | 47 |

XVIII | 49 |

XIX | 50 |

XX | 54 |

XXI | 55 |

XXII | 56 |

XXIII | 57 |

XXIV | 59 |

XXV | 62 |

XXVI | 63 |

XXVII | 64 |

XXVIII | 66 |

XXX | 68 |

XXXI | 69 |

XXXII | 70 |

XXXIV | 73 |

XXXV | 75 |

XXXVI | 77 |

XXXVII | 78 |

XXXVIII | 80 |

XXXIX | 84 |

XL | 87 |

XLI | 91 |

XLIII | 94 |

XLIV | 97 |

XLV | 100 |

XLVI | 101 |

XLVII | 103 |

XLIX | 104 |

L | 106 |

LII | 107 |

LIII | 108 |

LIV | 110 |

LVI | 113 |

LVII | 114 |

LVIII | 115 |

LXVII | 130 |

LXVIII | 133 |

LXIX | 135 |

LXX | 137 |

LXXI | 138 |

LXXII | 139 |

LXXIV | 141 |

LXXV | 143 |

LXXVI | 146 |

LXXVII | 147 |

LXXVIII | 149 |

LXXIX | 150 |

LXXX | 151 |

LXXXI | 152 |

LXXXII | 154 |

LXXXIII | 157 |

LXXXIV | 159 |

LXXXV | 163 |

LXXXVI | 164 |

LXXXVIII | 165 |

LXXXIX | 166 |

XC | 170 |

XCI | 171 |

XCII | 173 |

XCIII | 174 |

XCIV | 175 |

XCV | 177 |

XCVI | 179 |

XCVII | 180 |

XCIX | 181 |

C | 182 |

CI | 183 |

CIII | 185 |

CIV | 187 |

CV | 189 |

CVI | 194 |

CVII | 195 |

CVIII | 197 |

199 | |

213 | |

### Common terms and phrases

actuator angle bar of length bars and strings buckling center of mass chapter class 1 tensegrity compressive load compressive members computed conﬁguration vector constraints control design control inputs coordinates D-Bar unit deﬁned deﬁnition denote diﬀerent dual dynamics eﬃcient eigenvalues equations of motion equilibrium Example external forces ﬁgure ﬁll ﬁnal ﬁnite ﬁrst ﬁxed force densities fractals geometry given Hence inﬁnity Kenneth Snelson Lagrange multiplier Lemma linear Lyapunov function Michell Spiral Michell Topology minimal mass minimal regular minimal tensegrity prism modal vectors node non-minimal Note obtained optimal complexity pi+k plate prestress radius regular minimal tensegrity rigid bodies self-similar iterations self-similar rule shown in Figure solution speciﬁed Springer Science+Business Media stability stiﬀness string connectivity T-Bar T-Bar self-similar tensegrity conﬁguration tensegrity structures tensegrity system tensile members tension Theorem three-bar three-dimensional top and bottom truss Unit-self-similar vector WPSB yielding zero