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In this work, the possibilities of systematically constructing large structural mechanisms using existing spatial overconstrained linkages with only revolute joints as basic elements has been explored. A general approach has been proposed, which can be divided into three steps: selection of suitable tilings, construction of overconstrained units and validation of compatibility. This approach has been successfully applied to the construction of the structural mechanisms based on Bennett linkages and hybrid Bricard linkages. Several possible configurations are discussed. All of the novel structural mechanisms presented here contain only revolute joints, have a single degree of mobility and are geometrically overconstrained. Research work could lead to substantial advancement in building large spatial deployable structures.