Free vibration analysis of a robotic fish based on a continuous and non-uniform flexible backbone with distributed masses

Abstract

Abstract. This paper presents a Differential Quadrature Element Method for free transverse vibration of a robotic-fish based on a continuous and non-uniform flexible backbone with distributed masses (represented by ribs) based in the theory of a Timoshenko cantilever beam. The effects of the masses (Number, Magnitud and position) on the value of natural frequencies are investigated. Governing equations, compatibility and boundary conditions are formulated according to the Differential Quadrature rules. The compatibility conditions at the position of each distributed mass are assumed as the continuity in the vertical displacement, rotation and bending moment and discontinuity in the transverse force due to acceleration of the distributed mass. The convergence, efficiency and accuracy are compared to other analytical solutions proposed in the literature. Moreover, the proposed method has been validate against the physical prototype of a flexible fish backbone. The main advantages of this method, compared to the exact solutions available in the literature are twofold: first, smaller time-cost and second, it allows analysing the free vibration in beams whose section is an arbitrary function, which is normally difficult or even impossible with analytical other methods.

Comparison of leg dynamic models for quadrupedal robots with compliant backbone

“…The authors showed that the articulated trunk allowed longer strides and significantly affects the dynamics of the robot as well as its power efficiency. Such effect has been observed also in 19 , 20 and 21 for hopping robots with compliant legs, and on flexible backbones for fish-like robots 22 . Also, a similar effect is also present in insects and birds, whose thoraxes contain compliant structures that accumulate and release energy during the flapping cycle at the benefit of consumption, and also flight stability, see, e.g.…”

“…also in 19,20 and 21 for hopping robots with compliant legs, and on flexible backbones for fish-like robots 22 . Also, a similar effect is also present in insects and birds, whose thoraxes contain compliant structures that accumulate and release energy during the flapping cycle at the benefit of consumption, and also flight stability, see, e.g.…”

Comparison of Leg Dynamic Models for Quadrupedal Robots with Compliant Backbone

“…[1] Such effect has been observed also in [21,22] and [23] for hopping robots with compliant legs, and on exible backbones for sh-like robots [24]. Also, a similar effect is also present in insects and birds, whose thoraxes contain compliant structures that accumulate and release energy during the apping cycle at the bene t of consumption, and also ight stability, see, e.g.…”

An Autonomous Charging System for a Robotic Fish

“…In [19,40], a single servo motor is used in conjunction with a passive tail; in [41], a single electric motor is utilized but in a crankshaft configuration; various active materials are incorporated in prototypes, such as piezoelectrics [17], ionic polymer composites [18,23], and shape memory alloys [42]; a hydraulic system is proposed in [43]; and multiple servomotor and multi-linked designs are put forward in [16,20,36,44].…”