Design And Experimental Study On The Oscillating Propulsion Of A Compliant Robotic Fish

The oscillating propulsion mechanism has been a research focus of fish bionics,due to their super swimming performances. The biological researches uncoveredthat the biological structure of the fish was a complicated serial-parallel mechanismwith the muscle, skin and muscle tendon, etc., and that fish used muscles to stiffenits body to improve the swimming performance by matching the driven frequency.Inspired by the biological structure, this paper proposes a model of compliantfish with variable stiffness using planar serial-parallel structure. In the model, thecaudal vertebra is replaced by a rigid body in ’T’ shape, and the muscles are regardedas a parallel connection with a spring and a damper. Based on Lighthill’s elongatedbody theory and the amplitude envelope of the body lateral deflection, we provide ageneral method to design the body stiffness at any driven frequency, and present theproposition to adjust the body stiffness, namely, the ratio of the bodystiffness k₁/k₂equals to the square ratio of the driven frequency ω₁²/ω₂². Thisproposition provides an easy way to design the body stiffness, and a theoretical basisto design a robotic fish for a better swimming performance.Furthermore, a SimMechanics model of a compliant fish using the planarserial-parallel structure is built to describe a steady rectilinear locomotion. Driven ata certain position, the fish with different swimming frequencies has different speedsand Strouhal numbers. The simulation results show that wh en the driven frequencyis close to the design frequency, the fish with the design stiffness has a maximumspeed, and the maximum speed is linearly direct proportion to the design frequency.Further, the range of the Strouhal number is also consistent with the range0.25<St<0.35for the optimal efficiency. Both the swimming velocity and theStrouhal number are consistent with the biological observation data. It is verifiedthat the model of compliant fish with adjustable stiffness using the planarserial-parallel mechanism is innovative and effective. More important, thisrelationship between natural frequency and driven frequency is also proved by theexperimental results of a robotic fish made by viscous-elastic material.