This thesis addresses the type synthesis and static balancing of a class of deployable mechanisms, which can be applied in applications in many areas including aerospace and daily life.

Novel construction methods are proposed to obtain the deployable mechanisms. First, the type synthesis of the foldable 8-revolute joint (R) linkages with multiple modes is presented. Two types of linkages are constructed by connecting planar 4R linkages and spherical 4R linkages. The obtained linkages can be folded into two layers or four layers, and have multiple motion modes. A spatial triad is also adopted to build single-loop linkages, then the single-loop linkages are connected using spherical (S) joints or RRR chains to obtain deployable polyhedral mechanisms (DPMs). The DPMs have only 1- degree-of-freedom (DOF) when deployed, and several mechanisms with 8R linkages and 10R linkages have multiple motion modes and can switch modes through transition positions. In addition, when connecting single-loop linkages using half the number of the RRR chains, the prism mechanisms obtain an additional 1-DOF rotation mode.

Furthermore, the DPMs are developed into statically balanced mechanisms. The geometric static balancing approaches for the planar 4R parallelogram linkages, planar manipulators, spherical manipulators and spatial manipulators are developed so that the mechanisms can counter gravity while maintaining the positions of the mechanisms. Only springs are used to design the statically balanced system readily, with almost no calculation. A novel numerical optimization approach is also introduced which adopts the sum of squared differences of the potential energies as the objective function. Using the proposed static balancing approaches, the 8R linkages and the DPMs presented in this thesis can be statically balanced.