Bio-inspired bush bearing design principles: allometric analysis of synovial joints in quadrupedal mammals

In bio-inspired design, it is essential to have tendency equations to characterize the sizing implemented by nature. This article focuses on the geometrical dimensions of synovial joints, such as the elbow. These joints are essential for facilitating movement and supporting the mechanical loads passing through the endoskeleton in mammals. These joints operate under various lubrication regimes to minimize friction and wear. Understanding the biological mechanisms of lubrication in synovial joints can provide valuable insights for the fields of biomechanics and mechanical engineering. This study focuses on the relationship between the lubrication regime of the elbow joint and the mass of quadrupedal mammals. An allometric approach was used to analyze the dimensions of the distal humerus, average contact pressure, and average sliding speed in 110 species of quadrupedal mammals. The results highlight the importance of fluid film lubrication in synovial joints, achieved through morphological adaptations. The ratio between the diameter and width of the distal humerus appears to adapt to balance contact pressure, similar to the design procedure used in mechanical engineering. We noted that the contact pressure is almost identical across the sample of the 110 species of quadrupedal mammals studied. This study provides a foundation for the design of bio-inspired joints.