# Biomimetic Origami: Planar Single-Vertex Multi-Crease Mechanism Design and Optimization
## 1 Introduction  
Deployable structures have seen growing applications in aerospace, robotics, and related engineering fields, with their lightweight and efficient designs significantly improving space utilization [1, 2, 3]. In aerospace, [PERSON]'s team [4] developed scissor-like foldable trusses for flat storage, while [PERSON]'s group [5, 6, 7] enhanced satellite antenna systems through hexagonal prism mechanisms and rectangular pyramid units, demonstrating reliable kinematic control in dynamic environments. Origami-inspired approaches have opened new design possibilities, as shown in Figure 1. Carefully engineered crease patterns enable flat sheets to fold into compact forms and deploy into complex 3D shapes [8]. Fundamental folding mechanisms were established through studies on multi-vertex configurations [9, 10, 11], while subsequent engineering applications explored programmable curved surfaces [12, 13]. Building on these principles, [PERSON] et al. [9] integrated origami with vaulted structures, and [PERSON]'s team [10] created rotating space-deployable devices using spiral crease patterns. Communication technology applications include [PERSON]'s reconfigurable antennas [11], supported by [PERSON]'s mechanical framework [12]. These innovations extend to modular units [14, 15, 16, 17] and multi-scale control systems coordinating microscopic folding with macroscopic deployment [16, 17, 18]. The design methods of origami mechanisms come from various sources [19]. They include mathematical derivations [20, 21] and inspirations from nature, which artists andscientists have observed and summarized. Many biological structures in nature offer valuable insights for origami design [22; 23; 24]. For example, the wings of beetles provide unique inspiration [24]. Their fan-shaped wings, with radially arranged venation patterns, show a natural single-vertex multi-crease origami (SVMCO) design (Figure 1d). In this structure, several folds converge at a central point to enable compact folding and rapid deployment. By mimicking these efficient folding and unfolding mechanisms from nature, origami designs can achieve compact storage and, when unfolded, a larger functional form. This form of origami creates multiple creases emanating from a single point, allowing for the construction of highly intricate and complex geometric forms [27; 28]. In contrast to traditional origami, which distributes creases across several vertices, SVMCO focuses on concentrating creases at a single vertex [29]. This approach offers new possibilities for creating more compact and efficient designs, especially in applications that require precise control over shape transformation. SVMCO is particularly useful in deployable structures and mechanical metamaterials [30; 31; 32; 33], where manipulating multiple creases from a single vertex enhances control over movement and transformation. Single-vertex multi-crease origami (SVMCO) structures use circular folding patterns that work like mechanical linkages. Researchers have found that their folding behaviours depend heavily on three key factors: the angles between creases, the length of folds, and how thick the panels are [34; 35; 36]. For example, studies show that changing the central angle of folds--like switching from \(60^{\circ}\) to \(90^{\circ}\) designs--can drastically affect how these structures move and hold weight [37; 38]. To ensure smooth deployment, engineers carefully plan the crease patterns. They create alternate mountain and valley folds in radiating patterns to reduce stress and use computer models to balance movement and material strain [39; 40; 41]. Recent improvements focus on making these structures lighter yet strong. One method thins out non-essential panels without losing stiffness [42; 43], while another uses algorithms to design folds that absorb energy better [44]. Although progress has been made in SVMCO-based designs, research is still ongoing, with several challenges and gaps remaining.