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Bird-inspired tendon coupling improves paddling efficiency by shortening phase transition times

Jianfeng Lin, Zhao Guo, Alexander Badri-Spröwitz

Abstract

Drag-based swimming with rowing appendages, fins, and webbed feet is a widely adapted locomotion form in aquatic animals. To develop effective underwater and swimming vehicles, a wide range of bioinspired drag-based paddles have been proposed, often faced with a trade-off between propulsive efficiency and versatility. Webbed feet provide an effective propulsive force in the power phase, are light weight and robust, and can even be partially folded away in the recovery phase. However, during the transition between recovery and power phase, much time is lost folding and unfolding, leading to drag and reducing efficiency. In this work, we took inspiration from the coupling tendons of aquatic birds and utilized tendon coupling mechanisms to shorten the transition time between recovery and power phase. Results from our hardware experiments show that the proposed mechanisms improve propulsive efficiency by 2.0 and 2.4 times compared to a design without extensor tendons or based on passive paddle, respectively. We further report that distal leg joint clutching, which has been shown to improve efficiency in terrestrial walking, did not play an major role in swimming locomotion. In sum, we describe a new principle for an efficient, drag-based leg and paddle design, with potential relevance for the swimming mechanics in aquatic birds.

Bird-inspired tendon coupling improves paddling efficiency by shortening phase transition times

Abstract

Drag-based swimming with rowing appendages, fins, and webbed feet is a widely adapted locomotion form in aquatic animals. To develop effective underwater and swimming vehicles, a wide range of bioinspired drag-based paddles have been proposed, often faced with a trade-off between propulsive efficiency and versatility. Webbed feet provide an effective propulsive force in the power phase, are light weight and robust, and can even be partially folded away in the recovery phase. However, during the transition between recovery and power phase, much time is lost folding and unfolding, leading to drag and reducing efficiency. In this work, we took inspiration from the coupling tendons of aquatic birds and utilized tendon coupling mechanisms to shorten the transition time between recovery and power phase. Results from our hardware experiments show that the proposed mechanisms improve propulsive efficiency by 2.0 and 2.4 times compared to a design without extensor tendons or based on passive paddle, respectively. We further report that distal leg joint clutching, which has been shown to improve efficiency in terrestrial walking, did not play an major role in swimming locomotion. In sum, we describe a new principle for an efficient, drag-based leg and paddle design, with potential relevance for the swimming mechanics in aquatic birds.
Paper Structure (4 sections, 5 equations, 7 figures, 1 table)

This paper contains 4 sections, 5 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Results
  4. Conclusion

Figures (7)

  • Figure 1: Picture of the robotic Duck Leg. Overlaid is an extensor tendon acting on the foot once the leg extends. Two brushless motors drive the leg through belts, in leg angle and leg length direction. The foot is self-folding during the recovery phase, and the extensor tendon supports its rapid extension into the power phase.
  • Figure 2: Overview of the two hypotheses tested. (a) The torque applied through a coupling extensor tendon helps resetting the foot orientation after the recovery stroke. This decreases the phase transition time. In comparison: long transition time in green leaves little time for the power phase. A short transition time increases the time the paddle can spend in the power phase (blue). (b) We hypothesize that the global spring tendon stores energy throughout the power phase and supports flexing the leg at the end of the phase through its coupling, leading to an improved overall power phase.
  • Figure 3: Design and tendon configurations of Duck Leg. (a) Duck Leg's design details. Hip and knee joints are actuated by brushless motors, connecting to the joints by belts. The global spring tendon and several extensor tendons mechanically couple the remaining joints. (b) Schematics of tested tendon configurations, in sum three sets: the full global spring tendon (global tendon, GT), the half global spring tendon (half tendon, HT), and a set without a global spring tendon (no tendon, NT). Extensor-tendon configurations include either all extensors (AE), two extensors (2E), no extensors (NE), or a local spring (LS).
  • Figure 4: The experimental platform of Duck Leg.
  • Figure 5: Snapshots of back and side view of paddling gaits of GT-AE, GT-NE, and HT-AE. Compared to GT-NE, which does not have connected extensor tendons, GT-AE opens the foot faster (at 0.50s, the foot is almost fully open). HT-AE has the similar foot opening time due to the similar extensor configurations, but the ankle displacement is relatively small compared to GT-AE.
  • ...and 2 more figures