# Biomimetic Origami: Planar Single-Vertex Multi-Crease Mechanism Design and Optimization
## 3 Mathematical Modelling and Structural Support for Thick-Panel Origami Mechanisms
### Design of Rib Support Structure  
In order to support the deployment of the SVMCO structure, this section designed a single-degree-of-freedom rib support mechanism.  
The rib support mechanism design draws inspiration from the rib structure drilled lizards and proposes a single-degree-of-freedom support system as shown in Figure 15. The rib support mechanism consists of a central support platform, a support frame, and six identical branch link systems. The central support platform includes the central reflective surface (1), lead screw beam (2), and slider (4). The branch link systems are made up of a connecting beam (3), panel connecting hinge (5), and T-shaped beam (6). The fixed support frame (7) provides overall stability to the structure. The structure enables the overall deployment and folding of the system through the upward and downward movement  
Figure 14: Hinge setup configurations, the red area represents the antenna reflector, while the blue area indicates the back of the panel; (**a**) symmetric translation with linear hinge alignment (circles); (**b**) directional stretching with redistributed hinges (circles).  
of the slider (4) along the lead screw beam (2). Each branch link system functions as a parallel mechanism, including a PRR (Prismatic-Revolute-Revolute) branch connected to the central support platform and an R (Revolute) branch connected to the support frame (7). A T-shaped beam (6) connects to the back of the SVMCO panel via a revolute joint.  
In practical applications, the slider (4) along the lead screw beam (2) connected to the central reflective surface (1) of the panel drives the rib support structure. In the folded position, the support structure shown in Figures 15(a) and 16(a). Moving up the slider (4) moves the T-shaped beam (6) and its connection points horizontally outward, deploying the panel. When the panel is fully deployed, the lead screw reaches its maximum travel point and the central platform aligns with the inner circle of the annular panel, as shown in Figures 15(b) and 16(b).  
Figure 16: Kinematic sketch of rib support mechanism: (**a**) folded configuration, (**b**) deployable configuration.  
Figure 15: Rib support structure model inspired by the skeletal distribution and connection method of the frilled lizard: (**a**) skeletal structure [46], (**b**) description of the design concept [45], and (**c**) resulting support structure.  
This biomimetic design, inspired by the rib mechanism of drilled lizards, improves the deployability and efficiency of the structure, ensuring smooth operation and reducing mechanical interference. The design effectively prevents interference between facets in thick-sheet origami models. Moreover, the design of the back frame ensures control over the degree of freedom of the panel. The folding and deploying of the panel in multiple directions are limited by the single degree of freedom of the back frame, providing stability for the entire mechanism. The motion of the branch links is synchronized, ensuring the uniform deployment of the panel and preventing interference or inconsistent motion, thus ensuring smoothness and precision during the unfolding process.