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Research Papers

Modeling of Flexible Robots With Varying Cross Section and Large Link Deformations

[+] Author and Article Information
Laura Celentano

Dipartimento di Ingegneria Elettrica
e delle Tecnologie dell'Informazione,
Università degli Studi di Napoli Federico II,
Via Claudio 21,
Napoli 80125, Italy
e-mail: laura.celentano@unina.it

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 3, 2015; final manuscript received November 26, 2015; published online December 28, 2015. Assoc. Editor: Dejan Milutinovic.

J. Dyn. Sys., Meas., Control 138(2), 021010 (Dec 28, 2015) (12 pages) Paper No: DS-15-1084; doi: 10.1115/1.4032133 History: Received March 03, 2015; Revised November 26, 2015

In this paper, a very easy, numerically stable and computationally efficient method is presented, which allows the modeling and simulation of a flexible robot with high precision. The proposed method is developed under the hypotheses of flexible links having varying cross sections, of large link deformations and of time-varying geometrical and/or physical parameters of both the robot and the end-effector. This methodology uses the same approach of the modeling of rigid robots, after suitably and fictitiously subdividing each link of the robot into sublinks, rigid to the aim of the calculus of the inertia matrix and flexible to the aim of the calculus of the elastic matrix. The static and dynamic precision of the method is proved with interesting theorems, examples and some experimental tests. Finally, the method is used to model, control, and simulate a crane, composed of three flexible links and a cable with varying length, carrying a body with a variable mass.

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Figures

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Fig. 1

Schematic representation of the generic flexible link

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Fig. 2

Forces and torques acting on an element ΔL of the link

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Fig. 3

Elastic lines of a clamped link

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Fig. 4

Clamped link and hinged link

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Fig. 5

Property of the static deformation

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Fig. 8

Deviations between d(z) and s(z)

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Fig. 7

Optimal approximation of a flexible link with rigid and flexible sublinks

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Fig. 10

Illustration of Theorem 4 in the case where ν=3

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Fig. 13

Elastic lines determined with the linear method, with the proposed one (ν=4, 10) and with the exact method

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Fig. 9

Illustration of Theorem 3 in the case where ν=3

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Fig. 18

Scheme of the considered robot crane

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Fig. 11

Deflections computed with linear and nonlinear theory for F = 1 N and integral interval [0 Ld]

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Fig. 12

Deflections computed with linear and nonlinear theory for F = 5 N and integral interval [0 Ld]

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Fig. 26

Oscillations in absence and presence of gravity

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Fig. 27

Oscillations of a clamped link in presence of gravity

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Fig. 17

Optimum broken line with the condition of ν+1=4

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Fig. 19

Behaviors of: (a) β1d(t),β2d(t),β3d(t), (b) Lf(t) and Mc(t), and (c) Fx(t) and Fy(t)

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Fig. 20

Behaviors of: (a) e1(t), e2(t), e3(t) and (b) qf1(t), qf2(t),..., qf9(t)

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Fig. 21

Configurations of the robot crane during the grip and transport of a heavy load disturbed by a bump

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Fig. 22

Aluminum clamped link

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Fig. 23

Simulink scheme of a single link robot

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Fig. 24

Deflection of a clamped link in absence of gravity

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Fig. 25

Deflection of a clamped link in presence of gravity

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Fig. 14

Behaviors of the vertical tip displacement determined with the linear method and the proposed one (ν=10)

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Fig. 15

Link with varying cross section

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Fig. 16

Optimum broken line with the condition of ν+1=3

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