Design of tensegrities : control vs. structural requirements

Tensegrity systems are the systems of choicefor structures that need to be able to change shapein an arbitrary way.Shape changes are realized by varying the lengthof structural elements in a controlled manner.The required accuracy of shape control defines thenecessary resolution, \ie the spacing of the nodal pointscovering the envelope of the tensegrity structure.This poses a lower limit on the number of basic unitscomposing the tensegrity.The number of units also influences structural properties,like stiffness-to-mass ratio or vibrational frequencies and modes.This paper studies the trade-off betweenaccuracy requirements in shape control versusstructural requirements.The analysis given is based on symbolic relationsbetween structural parameters,like those describing geometry and topology,including the number of structural units,and structural properties, like stiffness-to-mass ratio.These relations stem from symbolic finite elementcomputations and are exact, no approximations being requiredin the train of computations leading to them.They enable a straightforward analysisof the trade-off between the two, often conflicting,classes of requirements.Tools are demonstrated,using the results of the analysis,that facilitate the design of structureswhere a balance between structural propertiesand shape representation accuracy is important