Wave propagation in a basally-actuated robotic filament

Breaking of time-reversal symmetry is necessary for drag-based propulsion at low Reynolds number. Many eukaryotes self-propel using active filaments (particularly cilia), which propagate asymmetric beat patterns though the fluid due to the coordinated action of dynein motors. For a flexible passive filament however, purely basal actuation is generally thought to be insufficient to achieve the large-amplitude bending waves observed in biological cilia. However, in the context of engineering applications, the actuation of filaments via an applied oscillating torque at the proximal end is an effective and parsimonious design. Here we present a simple realisation of enhanced wave propagation in a macroscale robophysical model of a cilium. The artificial cilium, about 5cm in length, beats in a high viscosity fluid to recover low Reynolds number fluid mechanics. Building on previous designs (Diaz et al, 2021), our robotic cilium consists of multiple passive rigid segments connected by hinges and is symmetrically driven by a basal motor. By introducing mechanically asymmetrical hinges, we produce an asymmetrical beat pattern from purely symmetric basal driving. We investigate the effect of link-number on the beat pattern, and compare the resulting waveforms with predictions from a theoretical and computational model of a proximally-driven filament with differential bending stiffness. Finally, we investigate the hydrodynamic pairwise interaction of two cilia.