A study of undulatory and rotational wave motion in the beam for the locomotion of underwater robots

A computational approach to study the undulatory and rotational motion in the beam for underwater locomotion is reported in this work. It is focused to understand different thrust producing mechanisms for robotic application and also to identify the critical parameters affecting the locomotion. The present work is to consider the forces exerted on the beam as it moves relative to the surrounding medium and to relate the propulsive speed of the beam to the form and speed of propagation of the bending waves generated by the beam, where the thrust is predicted using force and velocity relationship. The results show that the propulsive velocity is higher in the higher modes which are due to the higher natural frequency of the beam and results in increases of thrust, due to the increase of wave velocity and decrease of wavelength. It is observed that the thrust is 3.141 N for the propulsive velocity of 2 m/s, and thrust is found to be higher in the higher modes and lower in the lower modes due to smaller wavelength and high amplitude. Fish bends back and forth from head to tail, creating a forward thrust during locomotion and the tail beat amplitude, propulsive velocity and frequency are the parameters influence the thrust propulsion, irrespective of whether they coincide with the resonant frequency of the fish or not. For larger amplitudes and high propulsive velocity, it is observed that the thrust is increasing with amplitude. In the lower modes of undulatory propulsion, the negative thrust is caused by the recovery stroke during bending of the beam and negative pressure developed along the concave portions of the beam bends. A mathematical explanation is provided to solve the rotational locomotion of beam rolling about its longitudinal axis with passing bending waves along its tail. The undulatory movement is more feasible than rotational motion, because the resistance and inertia of the beam moving in a viscous medium are less compared to the rotational movement.