Comprehensive analysis of efficient swimming using articulated legs fringed with flexible appendages inspired by a water beetle.

Drag-based swimming is usually accompanied with the shape change of rowing appendages to generate asymmetric force during the power stroke and recovery stroke. To implement this in an aquatic robot, one may actively control the surface area of its legs during the swimming. However, a small sized robot with a limited number of actuators should adjust the surface area of legs in passive manner. For this reason, we proposed a novel articulated leg with flexible appendages inspired by a water beetle. These leg structures were designed to implement an efficient recovery stroke with less resistive force during the recovery stroke, while its surface area was increased again if suitable relaxation time was applied to perform improved power stroke. To identify an optimal leg design, 36 different types were fabricated by changing the passive joint thickness, appendage materials, length, and morphology. Several correlations and dominant parameters were identified, and it was shown that the swimming leg with fixed joint and appendage stiffness cannot always generate the largest torque in all the swimming frequency. Also, a two-dimensional dynamic model was proposed based on an underactuated manipulator, and the model validation was proceeded by comparing with two selected leg designs. In addition, a 5.5 cm long robot with one pair of legs was built to further investigate their locomotory performance. By varying the beating frequency and relaxation time, thorough analysis was addressed in terms of the position, velocity, non-dimensional traveled distance, Strouhal number, and quasi-propulsive efficiency. Here, some important relationships between dimensionless numbers were established. Furthermore, it was found that introducing a relaxation phase between the power stroke and recovery stroke can increase the traveled distance per stroke with slight expense of propulsive efficiency.