Geometric construction and analysis of deployable mechanisms based on Sarrus and Bricard linkages with double-layer extensions

Deployable mechanisms are essential for large-scale space structures and reconfigurable engineering systems, where compact stowage and reliable deployment are critical. This paper proposes a geometric construction framework for the systematic synthesis of deployable mechanisms based on Sarrus and Bricard linkages and further extends it to the innovative development of double-layer deployable mechanisms (DLDMs). Taking Sarrus and Bricard linkages as basic units, four novel deployable units are constructed via co-platform connections. By coupling identical deployable units through co-structural integration, four corresponding classes of deployable mechanisms are obtained. The framework is further generalized to generate large-area and regular polygonal deployable mechanisms through the networking of deployable units. The generated mechanisms are systematically analyzed by deriving rod-length parameter constraints, establishing rotational angle relationships, and evaluating kinematic characteristics. Finally, a double-layer connection strategy is incorporated into the deployable units to form double-layer deployable units, from which DLDMs are constructed via co-structural integration. The generated DLDMs retain the degree of freedom (DOF) and rotational-angle relationships of their single-layer counterparts while exhibiting improved structural organization. The proposed approach provides a rigorous geometric foundation for modular deployable design and offers design rules for scalable, reconfigurable structures in space and terrestrial applications.