Fernando Alonso-Cruz

The design of compliant mechanisms is a multidisciplinary field that integrates structural optimization, kinematics, and materials science to develop systems capable of generating motion through elastic deformation. Over the past six decades, research on compliant mechanisms has grown quickly, encompassing applications ranging from micro- and nano-manipulation to soft robotics and precision engineering. This study presents a comprehensive historical and thematic overview of compliant mechanism design methods through a bibliometric analysis conducted in accordance with the PRISMA methodology. A bias reduction method is proposed for bibliometric analysis, and its limitations are discussed. A total of 10,425 documents published between 1966 and 2025 were retrieved from the Scopus database, revealing an average annual growth rate of 10.35%. The analysis was performed using the Bibliometrix and VOSviewer software packages to conduct performance analysis and science mapping, enabling the identification of influential authors, key publications, and emerging research clusters. The performance analysis results allow, among other things, the identification of the most cited authors and works, which, in turn, facilitates faster identification of the original authors and ideas that gave rise to subsequent thematic branches. Science mapping identified dominant thematic fields underlying past, present, and future trends in compliant mechanisms and their applications. A reader beginning their exploration of the field of compliance mechanisms will find in this work a guide refined by statistical methods, free from the personal bias of its authors. On the other hand, those seeking to understand thematic trends in the field of compliant mechanisms, as well as niche research opportunities, can use the networks and tables generated to explore new possibilities.

Capillary imbibition is the process by which liquids are absorbed into porous materials as a result of capillary pressure differences at the pore scale. Accurate characterization of imbibition dynamics, particularly in the presence of gravitational potential, is essential for understanding fluid transport in diverse systems such as soil, fractured rocks, filtration media, and plant roots. This study presents systematic imbibition experiments using filter papers with pore sizes of 2.5 µm, 11 µm, and 20 µm, each inclined at 80° to quantify the influence of gravitational potential on imbibition behavior. For horizontally positioned samples, the imbibition front propagated radially and symmetrically, exhibiting a power law dependence on time. The measured temporal exponents ranged from 0.386 to 0.403, consistently lower than the theoretical value of 1/2 predicted by the Lucas–Washburn law. With increasing permeability, the temporal exponent approached the Washburn limit, indicating a marked dependence of imbibition dynamics on pore structure. For the inclined configuration at an 80° angle, the imbibition fronts remained nearly circular but exhibited a pronounced displacement of the front center toward gravity. This displacement increased with permeability, from approximately 0.497 cm for the 11 µm filter paper to 3545 cm for the 20 µm filter paper, highlighting the combined effects of permeability and gravitational potential on fluid movement. Furthermore, the advance of the imbibition front was significantly slower in the smallest pores (2.5 µm) compared to the larger ones. Experimental results were evaluated against a theoretical model proposed by Medina, demonstrating moderate quantitative agreement at early times, when gravitational potential effects are less significant. These findings confirm that both the temporal scaling exponent and the spatial evolution of the imbibition front are governed by the porous medium’s permeability and inclination angle, providing experimental evidence of deviations from ideal Washburn behavior in real porous systems.