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Multi-body simulation of a flapping-wing robot using an efficient dynamical model

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Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

The aim of this article is to present an efficient dynamical model for simulating flapping robot performance employing the bond graph approach. For this purpose, the complete constitutive elements of the system under investigation, including the main body and accessories, flapping mechanism, flexible wings and propulsion system consisting of a battery, DC motors and gear boxes, are considered. A complete model of the system was developed appending bond graph models of the subsystems together utilizing appropriate junctions. The wings were also modeled using ANSYS only for an initial evaluation. Moreover, a computer model was developed employing the block-oriented structure of Simulink in MATLAB software for simulation studies. Further investigation was performed developing a finite element model of the flexible wing and multi-body simulation tool. SimMechanics toolbox of MATLAB software was used to investigate whether the equations obtained from the bond graph were extracted correctly and whether the relationships between all the subsystems are maintained so that they lead to a logical motion for the flapping wing. The very good agreement between the results achieved from various models illustrates the validity and accuracy of the proposed bond graph model in this study. As a result, the offered approach presents a comprehensive and efficient model to obtain a clear insight into the power flow between the subsystems included in a flapping robot and provides helpful information for the design of such systems.

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Abbreviations

A :

Cross-sectional area of the wing

C :

Capacitance

EI:

Flexural rigidity

e :

Effort

F :

Force

f :

Flow

f(t):

Time response function

G :

Module of gyrator

GY:

Gyrator

h :

Angular momentum

I :

Area moment of Inertia

i :

Current

J :

Mass moment of inertia

L :

Inductance

l :

Wing span

m :

Mass

m n :

Modal masses

MTF:

Modulated transformer

p :

Linear momentum

q :

Displacement

R :

Resistance

S e :

Source of effort

S f :

Source of flow

T :

Module of transformer

TF:

Transformer

T :

Time

v :

Voltage

V x :

Velocity in horizontal direction

V y :

Velocity in vertical direction

w(x, t):

Deflection of the wing

x 1 :

Force point of action

Y(x):

Mode shape function

τ :

Torque

ω :

Angular velocity

θ :

Flapping angle

α :

Rod’s angle with vertical direction

ρ :

Material density

β n :

Modal stiffnesses

ω n :

Mode frequencies

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Author information

Authors and Affiliations

  1. School of Science and Engineering, Sharif University of Technology, International Campus, Kish Island, Iran

    Zahra Jahanbin & Ali Selk Ghafari

  2. Department of Aerospace Engineering, Sharif University of Technology, Tehran, Iran

    Abbas Ebrahimi

  3. Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Ali Meghdari

Authors
  1. Zahra Jahanbin
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  2. Ali Selk Ghafari
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  3. Abbas Ebrahimi
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  4. Ali Meghdari
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Corresponding author

Correspondence to Zahra Jahanbin.

Additional information

Technical Editor: Glauco A. de P. Caurin.

Appendix: Bond graph models used to derive the dynamic equations of motion

Appendix: Bond graph models used to derive the dynamic equations of motion

Figure 14 shows the numbered bond graph model of a DC motor attached to a crank-rod mechanism and a rigid beam wing.

Fig. 14
figure 14

Flapping mechanism attached to the rigid beam wing

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Figure 15 shows the labeled bond graph model of a DC motor attached to a crank-rod mechanism and an elastic beam wing.

Fig. 15
figure 15

Flapping mechanism attached to the elastic beam wing

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Figure 16 illustrates the complete numbered bond graph model of the flapping bird equipped with the elastic wings and driven by a pair of DC motors and crank-rod mechanism and attached to the main body. All the bonds in the graphs were named in order to derive the dynamic equations of motion.

Fig. 16
figure 16

Complete numbered bond graph model of the flapping bird equipped with the DC motors, flexible beam wings, crank-rod mechanism and main body

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Jahanbin, Z., Selk Ghafari, A., Ebrahimi, A. et al. Multi-body simulation of a flapping-wing robot using an efficient dynamical model. J Braz. Soc. Mech. Sci. Eng. 38, 133–149 (2016). https://doi.org/10.1007/s40430-015-0350-4

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  • DOI: https://doi.org/10.1007/s40430-015-0350-4

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