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TECHNICAL PAPERS

Design of Machines With Compliant Bodies for Biomimetic Locomotion in Liquid Environments

[+] Author and Article Information
Pablo Valdivia y Alvarado

Mechanical Engineering Department, Massachusetts Institute of Technology, Cambridge, MA 02139pablov@mit.edu

Kamal Youcef-Toumi

Mechanical Engineering Department, Massachusetts Institute of Technology, Cambridge, MA 02139youcef@mit.edu

J. Dyn. Sys., Meas., Control 128(1), 3-13 (Sep 19, 2005) (11 pages) doi:10.1115/1.2168476 History: Received March 15, 2005; Revised September 19, 2005

The aim of this work is to investigate alternative designs for machines intended for biomimetic locomotion in liquid environments. For this, structural compliance instead of discrete assemblies is used to achieve desired mechanism kinematics. We propose two models that describe the dynamics of special compliant mechanisms that can be used to achieve biomimetic locomotion in liquid environments. In addition, we describe the use of analytical solutions for mechanism design. Prototypes that implement the proposed compliant mechanisms are presented and their performance is measured by comparing their kinematic behavior and ultimate locomotion performance with the ones of real fish. This study shows that simpler, more robust mechanisms, as the ones described in this paper, can display comparable performance to existing designs.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Top and side views of a fish with a flexible beam model approximation of its tail in dotted lines (left). Isometric views of a beam-like tail static and excited (right).

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Figure 2

Tail model top view. The lateral deflection of the tail axis at a given point x and time t is denoted by h(x,t). The tail of length ℓ has a density ρ, a modulus of elasticity E, a cross-sectional area A, and a second moment I. A time varying moment M(t) is applied at a distance a from the tail base (left). Diagram portraying beam design procedure: Analytical model results are compared with target deformations in order to determine appropriate model inputs (right).

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Figure 3

Prototype designs: Each tail is made of a combination of stiff parts and flexible material. The stiff parts are used for actuation support. A servo powers each tail by pulling from two inextensible cables attached to a stiff plate embedded inside it. A receiver and batteries are embedded in the frontal part of the body to allow for radio control.

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Figure 4

Tail fabrication, from left to right: Rigid plate with cables that connect to servo. Rigid tail elements are positioned inside the tail mold. Tail after compliant material has cured. Finished prototype.

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Figure 5

Top row: dorsal and side views of Tail 1, bottom row: dorsal and side views of Tail 2

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Figure 6

Comparison of desired and modeled kinematic behavior for Tail 1. Body wave frequency ω=3.5Hz, driving frequency Ω=3.5Hz, (-) Desired, (-∙) Model.

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Figure 7

Comparison of desired and modeled kinematic behavior for Tail 2. Body wave frequency of ω=3.5Hz, driving frequency Ω=3.5Hz, (-) Desired, (-∙) Model.

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Figure 8

Experimental setup: Kinematics, Velocities, and Thrusts developed by prototypes can be tested in a 2.4m×0.6m×0.6m acrylic tank. Prototypes can be mounted to a carriage that runs along the center of the tank supported by vacuum pre-loaded air bearings. The carriage is equipped with a linear encoder so as to measure the prototype’s locomotion speed by simply measuring the velocity of the carriage. Forces acting on the prototypes along the axis of motion can be measured using a flexure transmission connected to a load cell. Sensor data and power supplied to the prototypes can be monitored by a Dspace data acquisition system.

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Figure 9

Experimental deformation compared with desired and predicted values for Tail 1, (-) Desired, (-∙) Predicted

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Figure 10

Experimental deformation compared with desired and predicted values for Tail 2, (-) Desired, (-∙) predicted

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Figure 11

Comparison of average thrusts (top) and average velocities (bottom) achieved by both designs. Published performance data of swimming velocities of current robotic fish designs and real fish is included for comparison.

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