Abstract
Many of tensegrity frames have infinitesimal mechanisms that are usually stabilized by the prestress. However there are some special tensegrity frames having mechanisms that can not be stabilized by the prestress. They exhibit large displacements, without affecting the initial prestress states, associated with finite mechanisms. In the paper three classes of the tensegrity prisms, diamond-type, star-type and complex-type, are investigated by using group representation theory. It is then shown that only complex-type tensegrities have finite mechanisms. Infinitesimal mechanisms of three types of tensegrities are classified and finite mechanisms of complex-type tensegrities are listed by using group representation theory. Relationships to the force density method are also discussed.
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