SUMMARY As a result of years of research on the comparative biomechanics and physiology of moving through water, biologists and engineers have made considerable progress in understanding how animals moving underwater use their muscles to power movement, in describing body and appendage motion during propulsion, and in conducting experimental and computational analyses of fluid movement and attendant forces. But it is clear that substantial future progress in understanding aquatic propulsion will require new lines of attack. Recent years have seen the advent of one such new avenue that promises to greatly broaden the scope of intellectual opportunity available to researchers: the use of biorobotic models. In this paper we discuss, using aquatic propulsion in fishes as our focal example, how using robotic models can lead to new insights in the study of aquatic propulsion. We use two examples: (1) pectoral fin function, and (2) hydrodynamic interactions between dorsal and caudal fins. Pectoral fin function is characterized by considerable deformation of individual fin rays, as well as spanwise (along the length) and chordwise (across the fin) deformation and area change. The pectoral fin can generate thrust on both the outstroke and instroke. A robotic model of the pectoral fin replicates this result, and demonstrates the effect of altering stroke kinematics on the pattern of force production. The soft dorsal fin of fishes sheds a distinct vortex wake that dramatically alters incoming flow to the tail: the dorsal fin and caudal fin act as dual flapping foils in series. This design can be replicated with a dual-foil flapping robotic device that demonstrates this phenomenon and allows examination of regions of the flapping performance space not available to fishes. We show how the robotic flapping foil device can also be used to better understand the significance of flexible propulsive surfaces for locomotor performance. Finally we emphasize the utility of self-propelled robotic devices as a means of understanding how locomotor forces are generated, and review different conceptual designs for robotic models of aquatic propulsion.

SUMMARYWe designed a robotic fish caudal fin with six individually moveable fin rays based on the tail of the bluegill sunfish, Lepomis macrochirus. Previous fish robotic tail designs have loosely resembled the caudal fin of fishes, but have not incorporated key biomechanical components such as fin rays that can be controlled to generate complex tail conformations and motion programs similar to those seen in the locomotor repertoire of live fishes. We used this robotic caudal fin to test for the effects of fin ray stiffness, frequency and motion program on the generation of thrust and lift forces. Five different sets of fin rays were constructed to be from 150 to 2000 times the stiffness of biological fin rays, appropriately scaled for the robotic caudal fin, which had linear dimensions approximately four times larger than those of adult bluegill sunfish. Five caudal fin motion programs were identified as kinematic features of swimming behaviors in live bluegill sunfish, and were used to program the kinematic repertoire: flat movement of the entire fin, cupping of the fin, W-shaped fin motion, fin undulation and rolling movements. The robotic fin was flapped at frequencies ranging from 0.5 to 2.4Hz. All fin motions produced force in the thrust direction, and the cupping motion produced the most thrust in almost all cases. Only the undulatory motion produced lift force of similar magnitude to the thrust force. More compliant fin rays produced lower peak magnitude forces than the stiffer fin rays at the same frequency. Thrust and lift forces increased with increasing flapping frequency; thrust was maximized by the 500ϫ stiffness fin rays and lift was maximized by the 1000ϫ stiffness fin rays. Supplementary material available online at

Fish are a potentially rich source of inspiration for the design of smart materials. Fish exemplify the use of flexible materials to generate forces during locomotion, and a hallmark of fish functional design is the use of body and fin deformation to power propulsion and maneuvering. As a result of nearly 500 million years of evolutionary experimentation, fish design has a number of interesting features of note to materials engineers. In this paper we first provide a brief general overview of some key features of the mechanical design of fish, and then focus on two key properties of fish: the bilaminar mechanical design of bony fish fin rays that allows active muscular control of curvature, and the role of body flexibility in propulsion. After describing the anatomy of bony fish fin rays, we provide new data on their mechanical properties. Three-point bending tests and measurement of force inputs to and outputs from the fin rays show that these fin rays are effective displacement transducers. Fin rays in different regions of the fin differ considerably in their material properties, and in the curvature produced by displacement of one of the two fin ray halves. The mean modulus for the proximal (basal) region of the fin rays was 1.34 GPa, but this varied from 0.24 to 3.7 GPa for different fin rays. The distal fin region was less stiff, and moduli for the different fin rays measured varied from 0.11 to 0.67 GPa. These data are similar to those for human tendons (modulus around 0.5 GPa). Analysis of propulsion using flexible foils controlled using a robotic flapping device allows investigation of the effect of altering flexural stiffness on swimming speed. Flexible foils with the leading edge moved in a heave show a distinct peak in propulsive performance, while the addition of pitch input produces a broad plateau where the swimming speed is relatively unaffected by the flexural stiffness. Our understanding of the material design of fish and the control of tissue stiffness is still in its infancy, and the development of smart materials to assist in investigating the active control of stiffness and in the construction of robotic fish-like devices is a key challenge for the near future.

A B S T R A C TMany fish swim using body undulations to generate thrust and maneuver in three dimensions. The pattern of body bending during steady rectilinear locomotion has similar general characteristics in many fishes and involves a wave of increasing amplitude passing from the head region toward the tail. While great progress has been made in understanding the mechanics of undulatory propulsion in fishes, the inability to control and precisely alter individual parameters such as oscillation frequency, body shape, and body stiffness, and the difficulty of measuring forces on freely swimming fishes have greatly hampered our ability to understand the fundamental mechanics of the undulatory mode of locomotion in aquatic systems. In this paper, we present the use of a robotic flapping foil apparatus that allows these parameters to be individually altered and forces measured on self-propelling flapping flexible foils that produce a wave-like motion very similar to that of freely swimming fishes. We use this robotic device to explore the effects of changing swimming speed, foil length, and foil-trailing edge shape on locomotor hydrodynamics, the cost of transport, and the shape of the undulating foil during locomotion. We also examine the passive swimming capabilities of a freshly dead fish body. Finally, we model fin-fin interactions in fishes using dual-flapping foils and show that thrust can be enhanced under correct conditions of foil phasing and spacing as a result of the downstream foil making use of vortical energy released by the upstream foil.

SUMMARYA biorobotic pectoral fin was developed and used to study how the flexural rigidities of fin rays within a highly deformable fish fin affect the fin's propulsive forces. The design of the biorobotic fin was based on a detailed analysis of the pectoral fin of the bluegill sunfish (Lepomis macrochirus). The biorobotic fin was made to execute the kinematics used by the biological fin during steady swimming, and to have structural properties that modeled those of the biological fin. This resulted in an engineered fin that had a similar interaction with the water as the biological fin and that created close approximations of the three-dimensional motions, flows, and forces produced by the sunfish during low speed, steady swimming. Experimental trials were conducted during which biorobotic fins of seven different stiffness configurations were flapped at frequencies from 0.5 to 2.0Hz in flows with velocities that ranged from 0 to 270mms -1 . During these trials, thrust and lift forces were measured, kinematics were recorded in three dimensions, and digital particle image velocimetry was used to evaluate flow hydrodynamics. The results of the trials revealed that slight changes to the fin's mechanical properties or to the operating conditions can have significant impact on the direction, magnitude and time course of the propulsive forces. In general, the magnitude of the 2-D (thrust and lift) propulsive force scaled with fin ray stiffness, and increased as the fin's flapping speed increased or as the velocity of the flow decreased.