Abstract

Recently, the truss antennas with deployable tetrahedron unit mechanisms have been successfully applied in orbit, owing to the advantages of large calibers, high accuracy and large folding ratios. As multi-loop coupled mechanisms, deployable tetrahedral mechanisms have multiple different output links, whose supporting limbs connecting output links and the base are mutually coupled. These mechanisms are also called the passive-input overconstrained mechanisms because their passive torsion springs are used as drivers, and because the number of the drivers contained is more than the degrees of freedom (DOFs). In this work, a method based on equivalent concept of first link-removing and then restoring is proposed for DOF analysis of the multi-loop coupled deployable tetrahedral mechanisms. With one coupled chain removed, the equivalent serial chains between the coupled components and the base are established in the remainder of the mechanisms. Then the coupled chain removed is restored and the equivalent of the multi-loop coupled mechanisms is obtained. The Lagrange method is used to establish the dynamic equation of the passive-input overconstrained mechanisms; the influence of the stiffness and number of torsion springs on the unfolding motion is examined.

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