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January 3 - Febuary 28, 2021

Meeting Abstract

73-13  Sat Jan 2  Legged locomotion at low Reynolds numbers: limitations on insects and microrobots St. Pierre, R*; Bergbreiter, S; University at Buffalo; Carnegie Mellon University

Forces imposed on legged locomotors from the physical environment sets inherent constraints on the locomotive behavior of the system. Insects are some of the fastest terrestrial legged locomotors relative to their sizes, reaching relative locomotion speeds in excess of 100 body lengths per second. At these small sizes, the low body inertia is accelerated and decelerated quickly as legs push against the ground. At the same time, surface forces, such as friction and viscosity, emerge with similar magnitudes as inertial forces. Therefore, small scale, legged insects are affected by both inertial forces and surface forces during locomotion, imposing a set of physical constraints that legged locomotors must navigate. Here, we use the Reynolds number, a non-dimensional number that quantifies the ratio of the inertial forces to environmental viscous forces to identify legged locomotive systems that are limited by surface forces. A fit to the log-transformed body mass and Reynolds number for biological legged locomotors from 3.7 g to 30 μg shows a higher exponential relationship of Reynolds number to the body mass (mb0.70) compared to inertial scaling (mb0.50), indicating an effect from surface forces on locomotive performance. We utilized a physical microrobot model (1 mg) running at biologically relevant speeds (up to 45 body lengths per second) and quantified inertial and viscous forces in the system, and found limitations in stride frequency and locomotion speed from joint viscosity. Scaling simple locomotion models also reveals transition points where viscous forces ultimately limit locomotion. While surface forces are dissipative and would seemingly impede locomotion, they also increase the stability of a system, and have implications for control in rapid locomotion of insects and microrobots.