Flexible tensegrity wing design and insights in principles of swimming kinematics of batoid rays.

A novel tensegrity wing design is first proposed which can emulate the kinematic waves of the pectoral fin of batoid rays and has a simple structure for manufacture. The attitude control and the regulation of wing natural frequency are realized by wing morphing. Then analytical insights in batoid ray swimming are gained by analyzing the analytical wing (cable)-fluid interaction model, whose parameters are determined based on the biological data. The stride length (traveled distance per cycle normalized by the body length (BL)) is shown to be almost invariant among different-sized rays if the phase and amplitude of wing flexion angles remain unchanged. This result is supported by biological data, 1.5 and 1.47 respectively for the manta ray and cownose ray, though their flapping frequencies (0.15-0.45 Hz and 0.64-1.25 Hz respectively) and body sizes (1.25 m and 0.15 m respectively) are very different, and similar to the expression for the carangiform fish swimming. In other words, the swimming kinematics of two different swimming forms are described by a similar analytical equation when the body resonance is exploited. The fluid force and cable tension are both found to be proportional to the fourth power of the body size and the square of the wing flapping frequency, which may tell that the flapping frequency of the manta ray (BL = 1.25 m) is much smaller than that of the cownose ray (BL = 0.15 m) is to avoid both the large actuation tension and fluid force density due to the size increase.