Design, analysis, and simulation of a planar serial-parallel mechanism for a compliant robotic fish with variable stiffness

Biological evidence suggests that fish use muscles to stiffen their bodies and improve their swimming performance. Inspired by this phenomenon, we propose a planar serial-parallel mechanism with variable stiffness to mimic a swimming fish. Based on Lighthill's elongated-body theory, we present a general method to design the body stiffness, which is related to morphological parameters and the swimming frequency. The results show that the stiffness profile is directly proportional to the square of the driving frequency. Furthermore, a SimMechanics model of a robotic fish is innovatively built. Numerical results show that the fish with the designed stiffness has the maximum speed when the driving frequency is close to the resonance frequency of fish body, and that the maximum speed is linearly proportional to the resonance frequency. The range of the Strouhal number given by simulations is also consistent with the range 0.25 < St < 0.35 required by the optimal efficiency. All these results agree well with biological observations, indicating that the swimming performance of fish is significantly affected by the body stiffness and the driving frequency.