Abstract This paper presents a series of deployable mechanisms based on n-UU (universal joint) Wren parallel mechanism (PM) units, which undergo one degree-of-freedom (DOF) Borel-Bricard motion. First, the PM unit is developed into ortho-planar mechanisms by adopting an R-R joint. The link parameters of the mechanism are optimized to maximize the folding ratio while avoiding interference. Then, the optimized PM units are piled up to construct a novel 1-DOF multi-layer mechanism which has the largest folding ratio among similar structures in the literature. Moreover, polyhedral deployable mechanisms are obtained by connecting the PM unit using U joint or U-U joint. Apart from saving space, the polyhedral mechanisms can transform among different shapes of polyhedrons. Finally, variations of the n-UU PM are investigated with different shapes of platforms, and each mechanism has its unique movement characteristics.