This study presents a topology optimization framework for synthesizing planar link mechanisms involving overlapping links. Although topology optimization has been widely applied to compliant mechanisms, its application to link mechanisms remains limited. To address this gap, we introduce a multilayer elasticity model in which two layers are connected by springs, enabling the simultaneous optimization of link and joint placements and link structures. The optimization problem is formulated to generate the target path on the end effector, while accounting for the degrees of freedom required for proper mechanical function. Numerical examples demonstrate that the proposed method successfully generates functional link mechanisms by integrating both layout and structural design. This study contributes to the advancement of topology optimization methods for mechanism design by establishing a framework capable of synthesizing planar link mechanisms with overlapping configurations.

Depression remains a global mental health challenge, with current treatments often limited by therapeutic instability, side effects, and patient adherence. This study investigated Exocarpium Citri Grandis essential oil (ECG oil) as a natural antidepressant. Extraction was optimized using Plackett-Burman Design-Response Surface Methodology (PBD-RSM), achieving a 15.224% yield. GC-MS analysis identified D-limonene, α/β-pinene, and γ-terpinene as major active components. In vivo, both oral and nebulized ECG oil significantly alleviated depressive-like behaviors in a zebrafish larval model and chronic unpredictable mild stress (CUMS) mice (evidenced by tail suspension, open field, forced swim, and sucrose preference tests). Biochemically, ECG oil enhanced neurotransmitter activity and reduced monoamine oxidase A (MAOA) levels. Furthermore, network pharmacology coupled with molecular docking and experimental validation (qRT-PCR and Western blot) revealed that ECG oil exerts its efficacy by modulating key targets, including OXT, ESR1, PTGS2, and LEP. Conclusively, ECG oil represents a promising natural therapeutic for depression by regulating neurotransmitter and neuroinflammatory pathways.